NONGENETIC SELECTION AND NONGENETIC INHERITANCE (Forthcoming in The British Journal for the Philosophy of Science)

Matteo Mameli London School of Economics Department of Philosophy, Logic and Scientific Method Houghton St. WC2A 2AE London UK g.mameli@lse.ac.uk

Abstract

According to the received view of evolution, only genes are inherited. From this view, it follows that only genetically-caused phenotypic variation is selectable and, thereby, that all selection is at bottom genetic selection. This paper argues that the received view is wrong. In many species, there are intergenerationally-stable phenotypic differences due to environmental differences. Natural selection can act on these nongenetically-caused phenotypic differences in the same way it acts on genetically-caused phenotypic differences. Some selection is at bottom nongenetic selection. The argument against the received view involves a reformulation of the concepts of inheritance and heritability. Inherited factors are all those developmental factors responsible for parent-offspring similarity; some inherited factors are genetic and some are not. Heritable variation is intergenerationally-stable phenotypic variation; some such variation is genetically-caused and some is not.

1 The Received View and Its Critics

2 The Possibility of Nongenetic Selection (The Lucky Butterfly)

3 The Reality of Nongenetic Selection

3.1 Imprinting Mechanisms

3.2 Other Learning Mechanisms

3.3 Other Nongenetic Mechanisms

4 Genetic and Nongenetic Inheritance Mechanisms

5 Genetic and Nongenetic Inherited Factors

6 Genetic and Nongenetic Heritability

7 Conclusions

1 The Received View and Its Critics

This paper is about the role of nongenetic inheritance in evolution and, more generally, it is about the correct way to conceive of the relation between inheritance and Darwinian selection. I am going to argue that some inherited developmental factors responsible for phenotypic variation are nongenetic and that Darwinian selection can act on such nongenetically-caused variation. Not all Darwinian selection is at bottom genetic selection.

Here is a map of the paper. In Section 2, I use a thought-experiment to show that Darwinian selection can act on phenotypic variation caused by intergenerationally-stable environmental variation. In Section 3, I provide evidence that this kind of selection is not just a logical possibility but something that happens quite often in the real world. In Section 4, I argue that inheritance mechanisms are best defined as those that cause offspring to resemble their parents and I provide examples of mechanisms of nongenetic inheritance. In Section 5, I argue that inherited factors are intergenerationally-stable developmental factors and I provide examples of nongenetic inherited factors. In Section 6, I argue that heritability is best defined as a property of phenotypic traits for which there is intergenerationally-stable variation, independently of whether such variation is

genetically-caused or not. In the rest of this section, I say briefly which ideas I am arguing against in this paper and which ideas I am not arguing against.

The received view is that nongenetic inheritance is either something that does not exist or something without evolutionary significance. From this view, it follows that only phenotypic differences caused by genetic differences can be heritable. Since Darwinian selection can act only on heritable phenotypic variation, this means that only genetically-caused phenotypic variation is selectable. And it means that whenever Darwinian selection produces a change in a population it also produces a change in the gene frequencies of the population. That is, according to this view, all Darwinian selection is at bottom genetic selection (cf. Williams [1966], [1992]; Maynard-Smith [1975/1993], [1988/1998]; Futuyma [1997]; Ridley [1996]; Dawkins [1976/1989], [1992/1999], [1996]; Griffiths et. al. [1999]). This paper argues that the received view and its consequences are false.

I am not the first to argue against the received view. Developmental systems theorists claim that the evolutionary significance of nongenetic inheritance follows from the developmental �parity� of genetic and nongenetic factors (cf. Oyama [1985/2000], [2000]; Griffiths and Gray [1994], [1997], [2001]; Gray [1992], [2001]; Griffiths [2001]; Oyama et al. [2001]). The problem with this idea is that developmental �parity� does not entail the existence of nongenetically-caused heritable and selectable phenotypic variation. And the existence of such variation is what needs to be established in order to show that the effects of nongenetic inheritance are comparable to the effects of genetic inheritance in natural selection processes.

According to developmental systems theorists, nongenetic factors are crucial for the intergenerational stability of ontogenetic form. They are right on this. Phenotypes are the joint product of genetic and nongenetic factors. This means that the phenotypic similarity between organisms and their offspring is due not only to genetic transmission but also to mechanisms of nongenetic inheritance. But this does not mean that there exists heritable and selectable nongenetically-caused phenotypic variation. For example, gravitational force plays a role in normal musculoskeletal development in terrestrial vertebrates. That is, the similarity in musculoskeletal features between parents and offspring is due in part to gravitational force. But since gravitational force is (more or less) uniform on Earth, this nongenetic factor is not responsible for heritable and selectable variation in musculoskeletal features (see Section 5). What we need then is a detailed account of the conditions required for nongenetic selection to occur.

Let me also say something about what this paper is not about. This paper is not about the �traditional� debate on gene-selectionism. The traditional debate is about whether it is better to describe natural selection processes by focusing on differences between genes or by focusing on (genetically-caused) differences between organisms and/or groups. Gene-selectionists are those who think it is better to focus on differences between genes (Williams [1966]; Dawkins [1976/1989], [1994], [1982/1999]; Maynard-Smith [1976]). Anti-gene-selectionists are those who think that it is better to focus on differences between organisms and, in some cases, on differences between groups (Gould [1977], [2001]; Sober [1984]; Sober and Wilson [1998]; Wilson and Sober [1994]). All the participants to this debate agree that the differences that are relevant to natural selection are either genetic differences or genetically-caused differences. It is this common assumption that I am arguing against.

Developmental systems theorists present a view that combines a rejection of traditional gene-selectionism with a rejection of a genocentric view of inheritance (Griffiths and Gray [1994], [1997], [2001]). It is perhaps because they want argue against two independent aspects of the received view of evolution at once that they do not address the problem of establishing the conditions that are necessary for nongenetic selection to occur. In contrast, I shall ignore the old debate about gene-selectionism. I shall only try to clarify the relation between nongenetic inheritance and nongenetic selection (cf. Bateson 2001).

2 The Possibility of Nongenetic Selection (The Lucky Butterfly)

Let us start with a thought-experiment. The main character in this thought-experiment is a butterfly that, for reasons that will become clear soon, I call the lucky butterfly. The lucky butterfly belongs to a species with three features that are important for the thought-experiment:

1. The individuals of this species are all genetically identical. There is no genetic variation and, for the way genetic transmission works in the species, no genetic variation can be produced by mutation, segregation, or recombination. In spite of this, genes play in these butterflies the same developmental role they play in all other organisms: they contribute to protein synthesis, and thereby to tissue formation, physiology, behaviour, and so on.

2. The butterflies exploit the plants of a particular species as food resource in the early stages of their life. They maintain the association with this plant by means of an imprinting mechanism that influences oviposition preferences. The butterflies lay their eggs on plants of the same species as the one on which they hatch. They manage to do this by eating the leaves of the plant on which they hatch, by imprinting on the taste of the leaves, and by laying their eggs on plants with the same taste.

3. In this species, like in many other species, bigger size is an advantageous trait. Bigger butterflies are stronger and thereby have more chances to survive and reproduce than smaller ones. That is, bigger butterflies have higher fitness than smaller ones.

What is special about the lucky butterfly? As a result of a developmental accident, the lucky butterfly�s imprinting mechanism malfunctions. So, this butterfly lays her eggs on a plant that is not the one on which she hatched and on which the other butterflies usually hatch. In general, a mistake like this one would produce negative effects on the fitness of the butterfly�s offspring. But the lucky butterfly lays her eggs on a plant that has been recently introduced in her environment and that, as it happens, is very good for the development of caterpillars of this species. As a result of eating the new plant, on average, the offspring of the lucky butterfly grow up bigger than the offspring of the other butterflies. This means that, on average, the offspring of the lucky butterfly have higher fitness than the offspring of the other butterflies. Hence, on average, the offspring of the lucky butterfly have more offspring than the other butterflies.

The offspring of the lucky butterfly have in general a properly functioning imprinting mechanism, since most of them do not suffer from developmental accidents like the one suffered by their mother. Therefore, having hatched on the new plant, most of them lay their eggs on plants of the new species. Their own offspring grow up bigger than the other butterflies, have higher fitness than the other butterflies, have more offspring than the other butterflies, lay their eggs on the new plant, and so on. The cycle repeats itself. Because of this process, the frequency of butterflies that lay eggs on the new plant starts to increase. And because of competition for reproductive resources, the more numerous the butterflies that hatch on the new plant become, the more difficult it is for the butterflies that hatch on the old plant to reproduce. After many generations, the butterflies that hatch on the old plant become extinct.1

At the end of the process, all the butterflies of this species hatch on the new plant and, on average, they are bigger than the original butterflies. What caused these changes in the species? The answer is natural selection. All that natural selection requires in order to change phenotype frequencies is heritable variation in the fitness of organisms, i.e. heritable variation in traits that affect the chances of survival and reproduction of organisms (Lewontin [1970], [1978]; Maynard-Smith [1975/1993], [1988/1998]; Sober [1993/1999]). Natural selection can increase the frequency of those traits that affect fitness positively and it can decrease the frequency of those traits that affect fitness negatively.2 In the butterflies, there is heritable variation in size caused by variation in plant of hatching. Since bigger size means higher fitness for the butterflies, selection can increase the frequency of bigger butterflies. And since heritable variation in size is caused by variation in plant of hatching, selection can increase the frequency of bigger butterflies only by increasing the frequency of butterflies that hatch on the new plant.3

An obvious objection to what I have just said is that it is wrong to say that there is heritable variation in size in the butterflies. According to the textbook definition, heritable variation requires genetic variation and, by assumption, there is no genetic variation in the butterflies. Heritability is a difficult technical concept. I discuss it in Section 6. In the rest of this section, I examine the evolutionary change in the butterfly species without using the concept of heritability.

Some terminology first. The development of every organism is produced by the interaction of genetic and environmental factors, the genetic and environmental traits of an organism. The genetic factors that affect the development of an organism are the genes and gene combinations present in its zygote.4 All the other factors that affect the development of the organism are said to be environmental.5 The interaction of the (genetic and environmental) developmental factors of an organism causes the development of the organism�s phenotypes, its phenotypic traits.6 If two organisms differ in some phenotypic trait, this must be due to some difference in genetic traits or to some difference in environmental traits, and possibly to both.

In the butterflies, there is selection for size. The reason for this is that bigger size means higher fitness for the butterflies. But from this it does not follow that selection for size is able to change phenotype frequencies in the butterflies. Selection for a phenotypic trait can change phenotype frequencies in a population only if there is intergenerationally-stable variation for that trait in that population. Let me explain.

Variation for a phenotype T is intergenerationally stable to the extent that the fact that two organisms differ with respect to T in a certain way (or by a certain amount) makes it likely that (on average) the descendants of the two organisms will differ with respect to T in the same way (or by the same amount). From the definition, it follows that variation for a trait T is intergenerationally stable in a population to the extent that, with respect to T, the organisms of the population (on average) resemble their parents more than they resemble other organisms.

Not only phenotypic variation but also developmental factors can be intergenerationally stable. A developmental factor D is intergenerationally stable to the extent that the fact that D affects the development of an organism makes it likely that D will affect the development of the descendants of the organism. The relation between the intergenerational stability of developmental factors and the intergenerational stability of phenotypic variation is that intergenerationally-stable phenotypic variation is due to variation in intergenerationally-stable developmental factors.7

So, why can selection for a trait T change the frequencies of the variants of T only if variation for T is intergenerationally stable? The reason is well known. If there is no correlation between the parental variants and the offspring variants, the fact that parents with better variants manage (on average) to have more offspring will have no effect on the statistical composition of the population in the next generation. Differences in fitness will cause no change in phenotype frequencies.

Is there any intergenerationally-stable variation for size in the butterflies? The butterflies are genetically identical. So, no difference in size can be caused by differences in genetic factors. In real species, where there is genetic variation, many (even though not all) genetic factors are intergenerationally stable. And this means that a portion of the genetically-caused phenotypic variation is intergenerationally stable. In particular, additive genetically-caused variation is intergenerationally stable (see Section 6). If there had been additive genetically-caused variation in size in the butterflies, that variation would have been intergenerationally stable. And since variation in size is fitness-relevant in the butterflies, that variation would have been selectable. In the absence of drift, phenotype frequencies would have changed and the mean size of the butterflies would have increased.

Does the lack of genetically-caused variation in size mean that selection for size cannot change phenotype frequencies in the butterflies? No. Even if the butterflies are genetic clones, they are not phenotypic clones. Different environmental factors affect the development of different butterflies. Some of these environmental factors affect butterfly size. That is, differences in size are environmentally caused in the butterflies. Are these differences intergenerationally stable? Some of

them are. Thanks to the existence of the imprinting mechanism, the species of plant on which a butterfly hatches is an intergenerationally-stable developmental factor. For this reason, variation in size due to variation in plant of hatching is intergenerationally stable and, thereby, selectable. Selection can increase the mean size of the butterflies despite the lack of genetically-caused variation for size.

We can call envirotypes those environmental factors that are intergenerationally stable. Plant of hatching is an envirotype for the butterflies. The process started by the lucky butterfly increases the frequency of bigger butterflies and it increases the frequency of butterflies that hatch on the new plant. That is, it increases the frequency of a phenotypic trait and it increases the frequency of an environmental (and envirotypic) trait. These changes are causally related since selectable variation in size is due to variation in plant of hatching. In the standard case studied by evolutionary biologists, selection changes phenotype frequencies by changing gene frequencies, i.e. it changes the frequency of phenotypic traits by changing the frequency of genetic traits. In the case of the butterflies, selection changes phenotype frequencies by changing envirotype frequencies, i.e. it changes the frequency of phenotypic traits by changing the frequency of envirotypic traits. Gene frequencies do not change in the butterflies. But envirotypic frequencies (the frequencies of intergenerationally-stable environmental traits) do. This means that not all selection is at bottom genetic selection. Some selection is nongenetic (or envirotypic) selection.

One thing to notice is that this particular process of nongenetic selection does not lead (at least not necessarily) to an increase in number of plants of the new species. In fact, it may well lead to a decrease in number of such plants�since the plants get exploited by more and more butterflies. Nonetheless, the process leads to an increase in the frequency of butterflies that have such plant as one of their developmental factors. It leads to an increase in frequency of the tokens of a certain butterfly-plant relation. In the same way, we can think of standard genetic selection as leading to an increase of the frequency in the tokens of certain organism-gene relations. A developmental factor (whether genetic or not) is always a developmental factor for a particular organism, i.e. it is a relational entity. It is for this reason that to each (genetic or environmental) developmental factor there corresponds a (genetic or environmental) trait of an organism.

In modern evolutionary biology, a Darwinian adaptation (for short, an adaptation) is defined as a phenotype that has increased in frequency because of selection for it (Williams [1966]; Futuyma [1997]; Sober [1993/1999]). At the end of the process that I have described, the butterflies have a phenotypic trait, bigger size, that has spread because of selection for it. It follows that this trait is an adaptation. But unlike the standard cases studied by evolutionary biologists, in this case selection has acted on envirotypically-caused variation rather than on genetically-caused variation. In this sense, bigger size is a nongenetic (or envirotypic) adaptation of the butterflies. In Dawkins� jargon (Dawkins [1982/1999], [1996]), we can say that this increase in size is not �for the good of� some genetic variant. There are no genetic variants in the butterflies, so no new adaptation can be for the good of genetic variants. The increase in size is �for the good of� a new envirotypic variant, �for the good of� a new intergenerationally-stable environmental trait.

In the standard cases studied by evolutionary biologists, the selection process is started by a genetic mutation. In the butterflies of my thought-experiment, the selection process is started by a mutation in plant of hatching, i.e. an envirotypic mutation, a mutation in an intergenerationally-stable environmental factor. Genetic mutation is usually random, in the sense that the probability that a mutation occurs is independent of the probability that the mutation is fitness-increasing. The envirotypic mutation in the butterfly is a random mutation too: the effects of developmental accidents are random with respect to fitness. Random mutations are not essential for selection. Many evolutionarily important envirotypic mutations are non-random: many envirotypic mutations are parental phenotypes acquired by the parents through learning or through some other mechanism designed to produce new adaptive phenotypes in ontogenetic time (Mousseau and Fox [1998]; Lacey [1998]; Avital and Jablonka [2001]; Lachmann and Jablonka [1996]). I shall discuss this issue in some of the following sections. But the point I want to make here is that the generation of nongenetic adaptation can be like the generation of genetic adaptation even with respect to randomness. Good

genetic mutations are cases of genetic luck. Envirotypic mutations like the one in the lucky butterfly are cases of envirotypic luck.

3 The Reality of Nongenetic Selection

Dawkins has written: �Where you find Darwinian adaptation there must have been genetic variation for the character concerned� (Dawkins [1982/1999], p. 20). And Lewontin has argued: �In order for a trait to evolve by natural selection, it is necessary that there be genetic variation in the population for such a trait� (Lewontin [1979], quoted in Dawkins [1982/1999], p. 20). According to one interpretation, Dawkins and Lewontin are saying that nongenetic selection is impossible. The thought-experiment of Section 1 shows that it is not. It is unlikely though that this interpretation is correct. Dawkins and Lewontin are aware of the in-principle possibility of nongenetic selection (Lewontin [1970], [1978]; Dawkins [1976/1989], [1983]). According to another interpretation, Dawkins and Lewontin are saying that, despite being possible, nongenetic selection does not occur in the actual world. But even on this interpretation, they are wrong. The story of the lucky butterfly is fictional because it is about a species with no genetic variation. In real species, there is always some genetic variation, and often there is a lot of it. But there is something non-fictional in the story of the lucky butterfly: the intergenerational stability of portions of fitness-relevant nongenetically-caused phenotypic variation is a widespread phenomenon. The existence of such variation indicates that nongenetic selection is a widespread phenomenon too. 8

Let us notice first that not all the genetically-caused phenotypic variation is intergenerationally stable. Phenotypic variation due to differences in the effects that alleles have independently of other alleles (additive genetically-caused variation) is intergenerationally stable. But within-population phenotypic variation due to differences in the effects that alleles have in combination with other alleles (non-additive genetically-caused variation) is not intergenerationally stable, at least not in general. So, not all genetically-caused phenotypic variation is intergenerationally stable. Not all environmentally-caused phenotypic variation is intergenerationally stable either. For each organism, there are environmental factors that affect its development but did not affect the development of its parents and will not affect the development of its offspring, at least not at the same moment in the life cycle and not in the same way. This does not mean though that none of the existing environmentally-caused variation is intergenerationally stable. Some environmental factors are envirotypes. Some phenotypic variation is envirotypically-caused variation. Such envirotypically-caused variation is intergenerationally-stable. Just like phenotypic variation in fitness caused by additive genetic variation, envirotypically-caused phenotypic variation in fitness is selectable.

Envirotypically-caused variation in fitness is a widespread phenomenon. In the rest of this section, I provide examples of this kind of variation.

3.1 Imprinting Mechanisms

Imprinting mechanisms are learning mechanisms that produce a strong attachment or preference for some particular object belonging to a (more or less well-defined) domain and during a (more or less well-defined) sensitive period. Imprinting mechanisms so defined are very common in nature.9 In the thought-experiment of Section 2, host-imprinting was mentioned. Host-imprinting is common in insects and parasitic birds (Immelmann [1975], pp. 19-20). Parasitic birds lay their eggs in the nests of other birds. In some cases, parasitic birds of one species lay their eggs in the nests of birds of a particular host-species. In others cases, different subspecies of parasitic birds belonging to the same species lay their eggs in the nests of different species. In still other cases, parasitic birds of the same species lay their eggs in the nests of different subspecies of the same species. Often, co-evolution and co-speciation of parasitic birds and their hosts take place (Paterson and Gray [1996]; Clayton and Moore [1996]; Rothstein and Robinson [1998]). What maintains the association between parasitic birds and their hosts? Parasitic birds imprint on their foster-parents and lay their eggs in the nests of birds that resemble as much as possible (in some respects specified by the imprinting mechanism)

their foster-parents. Avital and Jablonka describe the case of parasitic birds that use host-imprinting for both oviposition and mate selection purposes:

Female whydahs lay their eggs in the nests of species belonging to the Estrilidine finch sub-family. Each whydah species parasitises one particular species or subspecies of finch. The nestlings of the parasite and the host are very similar in appearance and, most importantly, the parasite nestling has the same species-specific mouth markings as the host nestling, which induces the finch parents to feed the young. A nestling that had deviant markings would not be fed and would die of starvation. There is therefore very strong selection for the parasite to faithfully mimic the host�s markings, and very strong selection against any mating that would disrupt the mimic�s genotype and lead to imprecise mouth markings. It is the strong imprinting of the parasite on their foster-parents that ensures matings are appropriate. Young female parasite nestlings recognise the host species as parents, from a search image of their appearance, and, when they are ready to lay, look for this host species and lay their eggs in the host�s nests. A female whydah becomes reproductively active and ovulates only when she sees the reproductive activity of members of her particular host species. But how does she find a compatible mate, one who was reared by the same parent-species and therefore is certain to have the genotype that will produce the right mouth-markings? It turns out that the song of the whydah male is made up of two major parts, one of which contains all the vocalisations of the host. This part of the song attracts a female reared by the same species because, as a nestling, the female became imprinted on her foster-father�s song. (Avital and Jablonka [2001], p. 129)

Imprinting on the host plays an important role in the development of oviposition and sexual preferences of female whydahs and in the development of the song in the males. These mechanisms cause the intergenerational stability of host in lineages of whydahs. Thereby, they cause the intergenerational stability of all those phenotypic differences caused by differences in host, they cause the intergenerational stability of differences in sexual and oviposition preferences and of all the phenotypic differences caused by such differences. Since phenotypic differences in sexual and oviposition preferences are responsible for differences in fitness, such phenotypic differences are under selection. So, selection can change the frequencies of sexual and oviposition preferences by changing the frequency of parasite-host associations, by changing the frequency of environmental traits of the kind being born in the nest of a host with such and such features.

Imprinting mechanisms are responsible for the intergenerational stability of many other environmental factors. Another example is locality-imprinting. Some organisms imprint on features of their natal site and, after having migrated somewhere else, they use this information to go back to the natal site. Locality-imprinting is common in many species of birds and is known to be present in fur seals and in salmons (Immelmann [1975], p. 17; Avital and Jablonka [2001], pp. 122-5). Salmons imprint on chemical features of the streams or rivers where they are born. They can detect these chemical features through their sense of smell. After spending many years at sea, they use the information obtained through olfactory imprinting to find the stream or river where they were born. By swimming against the current, they go back to the natal site and breed. So, natal site is intergenerationally stable in lineages of salmons, i.e. natal site is an envirotype for salmons. Thereby, differences in natal site among lineages of salmons are intergenerationally stable. This means that phenotypic differences due to differences in natal site are intergenerationally stable too. Many of these phenotypic differences are fitness-relevant, since some streams are better than others for breeding and development. Thus, these phenotypic differences are selectable. Selection can change phenotype frequencies in salmons by changing the frequencies of natal-site-related environmental traits, by changing the frequency of specific salmons-rivers associations.

Some organisms (e.g. herring gulls) imprint not on particular localities but rather on particular kinds of habitats. They imprint on features of the habitat where they are raised by their parents (e.g. they imprint on the kind of foliage) and they use this information to find an appropriate place where to breed and raise their own offspring (Immelmann [1975], p. 18). Differences in habitat in organisms of these species are intergenerationally stable and, thereby, phenotypic differences caused by differences in habitat are intergenerationally stable too. Since different habitats have different effects on fitness, some of these envirotypically-caused phenotypic differences are selectable. A case of nongenetic selection which involved habitat-imprinting for nesting purposes is that of the corralled dove (Strertopelia decaocto):

This species, which has a wide range in southern Asia, seems to have developed a very early and strong preference for human settlements and has been introduced by men into many hitherto uninhabited areas. In southeastern Europe, the spread of the species was correlated with Turkish rule over wide parts of the Balkan peninsula because the Turks tolerated the doves even when they were nesting on buildings in villages and towns. When, during the nineteenth century, the Turks left most of southeastern Europe, the doves lost their protectors and in many areas they quickly disappeared. Early during the 20th century, however, the species began to increase in numbers again and in an unparalleled expansion spread over most parts of southern, eastern, and central Europe within only few decades. Circumstantial evidence indicated that this expansion started with a shift from nesting on buildings to nesting in trees close to buildings, sites much safer from nest destruction by humans. Such imprinting to the relevant environmental features has enabled the species to rapidly spread over densely populated areas in large parts of Europe. (Immelmann [1975], p. 29)

Another common form of imprinting is food-imprinting. Many young organisms (e.g. mice) imprint on visual, olfactory, or gustatory features of the kinds of food their parents give them; many young organisms (e.g. many rodents and ruminants) imprint on those chemical features of the maternal milk that depend on what kinds of food the mother has been eating; and many young organisms (herbivorous mammals in particular) eat the maternal faeces and imprint on chemical features of the faeces that depend, again, on what kinds of food the mother has been eating (Marinier and Alexander [1995]; Immelmann [1975]; Avital and Jablonka [2001]). In all these organisms, the information obtained by means of imprinting is used in the development of food preferences: these organisms develop a strong preference for the foods they have come in contact with through maternal milk, or maternal faeces, or maternal feeding behaviour in general. Some organisms even �teach� their young what to eat and not to eat:

Early morning in the dry shrubland of the Judean hills finds a dozen day-old chukar chicks following their mother in single file across a large patch of wiry grasses, watching her closely and listening carefully. The mother stops by a tuft of short grass growing near the base of a mastic tree, lowers her head and explores some blades of grass with her bill, but the chicks do not try to peck at or eat anything yet. Eventually the mother points with a partly opened bill at a crowed colony of aphids occupying the blades of grass, and emits a special call. The day-old youngsters react as if invited to dine and enthusiastically peck several times at the aphids. More often than not most of them miss their living targets. They will need several weeks to perfect the art of accurate pecking. The mother marches on, and, every time she stops, she uses the same audio-visual display to introduce and encourage her youngsters to feed on particular food items, known by her to be both edible and rewarding. She introduces them to weevils on clover, caterpillars and grasshoppers on the grasses and a wide variety of seeds scattered on the ground. [�] Day-old chukar chicks are already physiologically capable of independent feeding, but they are almost completely ignorant [�] about [�] how edible and nutritious the potential food items they encounter are. By being constantly tutored by an experienced mother, the chicks gradually learn, over a period of a few weeks, to forage efficiently and securely. They limit their attention to the food items and sites preferred by their mother, adopting her sage list of food and site preferences, without having to resort to the much more dangerous and time-consuming method of individual learning through trial and error. (Avital and Jablonka [2001], pp. 66-7)

In some species, the food preferences acquired through imprinting on maternal foods remain stable during the whole life cycle. When this happens, the offspring imprint on the same kinds of foods imprinted on by the parents. In these organisms, nongenetically-caused variation in food preferences is intergenerationally stable, at least in female lineages. Variation in food preference is variation in fitness, since some foods are more easily found than others, some are more nutritious than others, some have more vitamins than others, etc. It follows that these environmentally-caused differences in food preferences�these differences in food preferences caused by differences in maternal food preferences�are selectable.

Another common form of imprinting is sexual imprinting (Immelmann [1972]; Bolhuis [1991], [2001]; Miller and Todd [1993]; Todd and Miller [1993]; Avital and Jablonka [2001]). Many birds (e.g. Japanese quails) imprint on features of the parent of the opposite sex. In this way, they develop a sexual preference for conspecifics that resemble their opposite-sex parent and, at the same time, they develop sexual preferences which resemble the sexual preferences of their same-sex parent. In the case of female birds, the mother chooses a mate according to her sexual preferences.

When a daughter is born, she comes in contact with a father with features that match the maternal sexual preferences. The daughter imprints on such features and uses this information to develop her own sexual preferences. So, the daughter develops a sexual preference for those very features her mother has used in order to choose a mate, i.e. the daughter develops sexual preferences that resemble those of her mother. Evidence for sexual imprinting of this kind has been found also in sheep and goats (Kendrick et al. [1998]). Obviously, sexual preferences are very important from the point of view of fitness. Sexual imprinting on features of the parents can generate intergenerationally-stable nongenetically-caused differences in sexual preferences. These environmentally-caused differences in sexual preferences�these differences in sexual preferences caused by differences in parental sexual preferences�are selectable.

Still another common form of imprinting in birds is song-learning. Many male birds imprint on features of the paternal song and use this information to develop their own song. Many female birds imprint on the paternal song and use this information to develop their sexual preferences. Moreover, there is variation in the song sung by birds belonging to the same species (Avital and Jablonka [2001], pp. 83-5). Environmental differences in paternal song are thereby intergenerationally stable. Such differences affect fitness, since they affect the ability of males and females to find appropriate mates. So, differences in paternal songs�which are environmental differences�can cause selectable phenotypic differences in the offspring generation. Intergenerationally-stable nongenetically-caused variation in vocalisations has also been found in killer whales (Whitehead [1998]; Rendell and Whitehead [2001]). In this case, the vocalisations are learned by the daughters from the mothers, i.e. they are intergenerationally stable in female lineages. Whitehead ([1998]) has argued that such variation has been selected and that the selection process has produced important changes in populations of killer whales.

3.2 Other Learning Mechanisms

Not only imprinting mechanisms, but learning mechanisms in general can cause intergenerationally-stable phenotypic variation. If the offspring learn the same things the parents have learned, and if there is variation in what the parents have learned, then variation in what is learned is intergenerationally-stable.10 Why did I spend so much time talking about imprinting then? By being constrained in timing and topic, imprinting mechanisms are particularly good at producing similarities between what is learned by the parents and what is learned by the offspring (Mameli [2002]). But learning mechanisms that do not count as imprinting mechanisms can lead to intergenerationally-stable phenotypic variation too. Many birds and mammals spend a significant portion of their early life with their parents (Avital and Jablonka [2001]). In this period of their life, they come in contact with many of the same environmental circumstances with which their parents have come in contact. In this way, these organisms learn many of the same things their parents have learned. Simply by following their parents around, they learn to eat the same foods as their parents do, to forage or to hunt the same things and in the same places as their parents do, etc. This is particularly true for those mammals and birds that produce behaviours designed to facilitate their offspring�s acquisition of these important skills. Learned phenotypes in these species are intergenerationally-stable and thereby selectable.

An example of learning that does not lead to intergenerationally-stable variation at the individual level is the one responsible for the transmission of food preferences in Norway rats (Galef [1996]; see also Laland et al. [1996b]; Boyd and Richerson [1996]). These rats� food preferences are influenced by the kinds of foods they smell on other rats: they prefer foods that they have smelled on their conspecifics. The conspecifics in question do not need to be their parents. Food preferences are transmitted horizontally, not only vertically. Because of this, there is no intergenerationally-stable within-population variation in learned food preference in Norway rats. So, such nongenetically-caused differences in food preferences cannot be selected, at least not by a process of Darwinian selection at the individual level. But the learning process may generate intergenerationally-stable variation at the group level rather than at the individual level. By means of the described learning mechanism, different food preferences may spread in different micro-populations and these group-

level differences may persist one generation after another. If this is the case, such learned between-group variation can lead�when some other conditions are in place, see Sober and Wilson [1998]�to nongenetic group-selection.

3.3 Other Nongenetic Mechanisms

Learning mechanisms are not the only mechanisms capable of producing envirotypic variation. Another important class of mechanisms of this kind is the class of mechanisms responsible for the vertical transmission of symbionts (Sterelny [2001], [forthcoming]). Many young herbivorous mammals (e.g. koalas, domestic horses, etc.) eat the maternal faeces and inoculate their own guts with the maternal gut flora (Avital and Jablonka [2001], p. 115). This flora is constituted by bacteria and protozoans. These endosymbionts are very important for the mammals, since these mammals are consumers of cellulose-rich plant material and without the endosymbionts they are unable to properly digest the plant material. Moreover, there is variation in the kinds and proportions of endosymbionts present in different individuals. This variation is responsible for differences in the kinds of diets different animals can sustain and in the efficiency with which they can extract important nutrients. Thus, variation in maternal gut flora is intergenerationally-stable (at least in female lineages) and the phenotypic differences caused by such environmental variation are fitness-relevant. Hence, the phenotypic variation caused by differences in maternal gut flora is selectable.

Symbiotic associations between insects and bacteria are also very common. Such associations are present in 10% of insect species. These associations are very important for the insects since the bacteria often play important metabolic functions. It has been shown that if the insects are stripped off their bacteria, they have reduced fitness. It is for this reason that many of these insects have adaptations with the function to make sure that there is a reliable vertical transmission of the bacteria. And it is for this reason that these associations are often very stable and very old. In many cases, there has been co-evolution and co-speciation of the insects and the bacteria (Sterelny [forthcoming]; Moran and Telang [1998]). Variation in the kinds and proportions of symbiotic bacteria is intergenerationally-stable in these insects. Given the important role played by the bacteria, such nongenetically-caused variation is responsible for selectable phenotypic variation in the insects.

Another example of envirotypically-caused variation is this: If female Mongolian gerbil embryos develop in a uterine environment in which most of the embryos are male, and they are therefore exposed to high levels of testosterone, they mature late and are more territorial than other females. [�] These females [�] in turn, produce litters with a grater proportion of males. Therefore, their daughters, who usually also develop in a testosterone rich environment, also mature late. The cycle perpetuates itself. (Avital and Jablonka [2001], p. 114)

Variation in features of the uterine environment of the mother (e.g. its levels of testosterone) is intergenerationally-stable in female gerbils. This environmental variation is responsible for phenotypic differences in maturation timing and sex ratio in the offspring. These differences are likely to affect fitness in important ways. So, the intergenerationally-stable variation in maternal uterine environment is responsible for selectable phenotypic differences.

There exist many other mechanisms responsible for envirotypically-caused phenotypic variation (Jablonka [2001]). An important class of mechanisms that I do not have time to discuss here is the class of mechanisms responsible for the transmission of nongenetic zygotic materials, e.g. chromatin marks, chemical gradients, etc. (Jablonka and Lamb [1995/1999]). A lot of environmental variation is intergenerationally stable. Moreover, a lot of this variation is responsible for differences in fitness. Hence, many phenotypic differences due to environmental differences are selectable. Hence, a lot of selection is selection of nongenetic variation. Given the pervasiveness of genetic variation, distinguishing between genetic and nongenetic selection may turn out to be empirically very difficult. But this does not mean that nongenetic selection is rare.

4 Genetic and Nongenetic Inheritance Mechanisms

Parents (together with their environment) cause their offspring�s existence. Moreover, parents (together with their environment) cause their offspring to have features similar to those the parents have. These two kinds of causal influence that parents exert on their offspring are�at least from a logical point of view�separable. Inheritance is the second kind of causal influence. Inheritance mechanisms are all those mechanisms that cause organisms to resemble their parents in phenotypic and/or genetic and/or environmental traits. That is, they are those mechanisms responsible for the fact that the offspring acquire some of the same phenotypic and/or genetic and/or environmental traits as the parents.11

One of the mechanisms that cause organisms to resemble their parents is genetic transmission. Genetic transmission causes children to have many (even though not all) of the same genes and gene complexes as their parents. That is, genetic transmission is responsible for genetic similarity between parents and offspring, it causes intergenerational resemblance in genetic traits. Moreover, since genes play an important role in the development of all phenotypes, genetic transmission is responsible for a lot of phenotypic similarity between parents and offspring.

Developmental systems theorists deny that genetic transmission is responsible for intergenerational resemblance in phenotypes (Oyama [1985/2000], [2000]; Griffiths and Gray [1994], [1997], [2001]). Phenotypes are the product of the interaction between genes and environmental factors. It follows that genetic similarity needs to be supplemented by environmental similarity in order to produce phenotypic similarity. The view that genetic similarity is sufficient for phenotypic similarity is equivalent to genetic determinism. And what we currently know about development entails that genetic determinism is wrong. From this, developmental systems theorists conclude that it is illegitimate to conceive of genetic transmission as a distinct mechanism involved in producing phenotypic similarity between generations. They conclude that the correct way to think about the intergenerational stability of phenotypic form is in terms of the whole developmental cycle which regenerates itself and all its parts one generation after another. My view is that we should not accept this conclusion. Genetic transmission causes genetic similarity. And genetic similarity is one of the two causes of phenotypic similarity, the other cause being environmental similarity. From the transitivity of causation, it follows that genetic transmission causes (even though not by itself) phenotypic similarity. By saying that all the features of the life cycle in one generation are involved in the reoccurrence of all the features of the life cycle in the following generation, developmental systems theorists are rejecting the distinction with which I have started the present section, the distinction between organisms causing their offspring to exist and organisms causing their offspring to have features similar to the parental ones. According to the strategy adopted by developmental systems theorists, this distinction is not theoretically interesting. It follows that, according to this strategy, the concept of inheritance mechanism is not theoretically interesting either. But, for example, the results of molecular biology show that it is theoretically very useful to focus on particular channels of intergenerational similarity, even in cases in which intergenerational similarity is due to the interaction of many different developmental factors. There is nothing wrong with talk of distinct inheritance mechanisms. The only thesis that we need to reject is the thesis that genetic transmission is the only existing inheritance mechanism (Jablonka 2001).

There are nongenetic (or envirotypic) inheritance mechanisms. All the mechanisms that I have described in Sections 2 and 3 produce intergenerational similarity by means other than genetic transmission. For example, the host-imprinting mechanism of the lucky butterfly is a nongenetic inheritance mechanism. This mechanism causes the offspring to resemble the parents in plant of hatching, which is an environmental trait. And (together with other developmental factors) it causes the offspring to resemble the parents in size, which is a phenotypic trait. That is, host-imprinting causes intergenerational similarity in environmental traits and it contributes to intergenerational similarity in phenotypes.

Genetic inheritance mechanisms cause intergenerational similarity in phenotypic traits by causing intergenerational similarity in genetic traits. Envirotypic inheritance mechanisms cause intergenerational similarity in phenotypic traits by causing intergenerational similarity in

environmental traits. Consider all those organisms that acquire the parental endosymbionts by eating the parental faeces. Eating the parental faeces causes intergenerational similarity in the kinds and proportions of endosymbionts an organism comes in contact with, i.e. it causes intergenerational similarity in environmental traits. Moreover, since endosymbionts are involved in digestive processes, eating the parental faeces contributes to the intergenerational similarity in the kinds and quantities of food an organism can digest, i.e. it contributes to the intergenerational similarity in phenotypes. Another example is the following. The sexual preferences of a female bird that has imprinted sexually on the features of her father resemble the sexual preferences of her mother not because (or not only because) the daughter has many genes in common with the mother. They resemble the sexual preferences of the mother partly because the mother�s sexual preferences have exerted a similarity-making causal influence on the daughter�s sexual preferences. They have exerted this influence by causing the mother to choose a mate with certain features and, thereby, by causing the daughter to imprint sexually on a father with those very features. This kind of sexual imprinting is a nongenetic inheritance mechanism which causes intergenerational similarity in phenotypes by causing intergenerational similarity in maternal sexual preferences, i.e. in an environmental trait.

The 20th century was dominated by a genocentric view of inheritance according to which genetic transmission is the only existing mechanism of inheritance. This view was defended clearly for the first time by August Weismann ([1892]) and it was expressed in modern genetic language for the first time by Wilhelm Johannsen in a paper called �The genotype conception of heredity�:

The personal qualities of any individual organism do not at all cause the qualities of its offspring; but the qualities of both ancestors and descendants are in quite the same manner determined by the nature of the �sexual substances��i.e. the gametes�from which they have developed. Personal qualities are then the reactions of the gametes joining to form a zygote; but the nature of the gametes is not determined by the personal qualities of the parents or ancestors in question. [�] Heredity may then be defined as the presence of identical genes in ancestors and descendants. (Johannsen [1911], pp. 130 and 159)

The picture in FIG.1 represents the genocentric view of inheritance.

This picture is also known as Weismann Diagram (Maynard-Smith [1975/1993], [1988/1998]). In this version, G stands for genetic traits and P for phenotypic traits. The horizontal arrows represent the causation of similarity from one generation to the next, while the oblique arrows represent the genetic contribution to the development of phenotypes. In this picture, only genetic factors are connected by horizontal arrows.12 The genocentric view of inheritance is wrong. Genetic transmission is not the only channel of intergenerational similarity. One way of representing the correct view of inheritance is the one in FIG.2.

FIG.1

P P P

G G G

Some (even though not all) parental phenotypes and some (but not all) aspects of the (extra-parental) environment are channels of intergenerational similarity.13 This picture represents these channels with the horizontal arrows that connect parental phenotypes and environments with the phenotypes and the environments of the offspring.14

It is important to keep in mind that these two pictures are not meant as representations of the whole of the causal connection between one generation and the next, but only as representations of the similarity-making causal connection between features of one generation and features of the following one. Parental phenotypes, parental environments, and parental genes have many effects on the phenotypes and the environments of the offspring. But not all these effects bring about a similarity between parents and offspring. The horizontal arrows do not just represent causation, they represent causation responsible for similarity. Here is a nice metaphor that tells us how to think about nongenetic inheritance mechanisms:

Consider a piece of music that is transmitted from generation to generation as a written score. If the score represents hereditary information in the DNA, the phenotype is a specific interpretation of this score at a certain time by certain artists. The interpretation does not affect the score. However if there is another transmission system - recordings - through which a particular interpretation can be transmitted from generation to generation along with the written score, the situation is rather different. There can be evolution of interpretations of this score, based on the influence that one interpretation has on a subsequent interpretation, and that this have on still later ones, and so on. Both the phenotype (the present interpretation) and the genotype (the written score) influence subsequent interpretations. (Jablonka and Lamb [1999], p. 19; see also Jablonka [2001]).

As this passage suggests, the existence of nongenetic inheritance mechanisms does not entail the truth of Lamarckism (as this doctrine is standardly conceived), i.e. the inheritance of acquired characters by means of germ-line genetic mutations. Nongenetic inheritance is entirely compatible with Weismann�s thesis that somatic mutations cannot be inherited by means of germ-line mutations. And it is entirely compatible with what Crick ([1958]) and Maynard-Smith ([1975/1993], [1988/1998]) call the Central Dogma of molecular biology.

5. Genetic and Nongenetic Inherited Factors

How do inheritance mechanisms give rise to parent-offspring similarity? They produce intergenerational similarity by causing the intergenerational stability of developmental factors. For example, genetic inheritance mechanisms cause intergenerational similarity by causing the intergenerational stability of genetic factors. Genetic transmission is responsible for the fact that some of kinds of the genes that affect the development of the parents affect the development of the

FIG.2

G G G

E E E

P PP

offspring too. By causing the intergenerational stability of genetic factors, genetic transmission results first of all in intergenerational similarity in genetic traits and, eventually, in intergenerational similarity in phenotypic traits. In contrast, nongenetic (envirotypic) inheritance mechanisms cause intergenerational similarity by causing the intergenerational stability of environmental factors. In this way, they result in intergenerational similarity in nongenetic traits and, eventually, in intergenerational resemblance in phenotypic traits. Host-imprinting produces intergenerational similarity by causing the intergenerational stability of host, i.e. by causing the offspring to interact with the same kind of host as the parents. Sexual imprinting produces intergenerational similarity by causing the intergenerational stability of parental sexual preferences, i.e. by causing the offspring to be affected by parental sexual preferences of the same kind as those by which their parents were affected. Symbiont-transmission produces intergenerational similarity by causing the intergenerational stability of symbionts. And so on.

Since inheritance mechanisms produce intergenerational similarity by causing the intergenerational stability of developmental factors, developmental factors that are intergenerationally stable can be said to be inherited. Obviously genes are inherited factors. But in organisms that acquire their sexual preferences by sexual imprinting, parental sexual preferences are inherited factors. And in organisms where symbionts are transmitted vertically, symbionts are inherited factors. Etc. Of course, many nongenetic factors are intergenerationally unstable and cannot thereby give rise to intergenerational similarity. So, many nongenetic factors are not inherited. But the same is true of many genetic factors. Some stretches of DNA and some combinations of such stretches are passed on intact from parents to offspring. But some DNA stretches are not inherited because of genetic mutation. And in many organisms (sexual organisms), there are mechanisms (segregation and recombination) that cause some combinations of genes to be broken up. Such combinations may not and often do not reappear in the following generation. For example, an homozygous organism may have heterozygous offspring. And an organisms with gene A at locus 1 and gene B at locus 2 may have offspring with gene A at locus 1 but without gene B at locus 2, or with gene B at locus 2 but without gene A at locus 1, or with neither gene A nor gene B. In general, in sexual species, gene combinations are not inherited factors.

One thing to notice is that no variation in a developmental factor is required for that factor to count as inherited. This holds for both genetic and nongenetic factors. Consider the butterflies of Section 2. They are all genetically identical. But genes are inherited factors for the butterflies and genetic transmission is an inheritance mechanisms for them. The reason is that, independently of any differences there may or may not be between the butterflies, it is still true that genes and genetic transmission are responsible for the genetic and (in part) for the phenotypic similarity between a butterfly and its offspring. Of course, since there is no genetic variation in the species, genes and genetic transmission cannot be responsible for intergenerationally-stable variation. In other words, genes and genetic transmission cannot be responsible for the butterflies resembling their parents more than they resemble the other butterflies. In real species, there is almost always genetic variation. It follows that genes are almost always responsible not only for the fact that the offspring resemble the parents, but also for the fact that the offspring resemble the parents more than they resemble other organisms, at least in genetic respects. The same is not true of other inherited developmental factors. Some nongenetic factors are like the genetic factors in the butterflies. They cause intergenerational similarity but they do not cause the offspring to resemble the parents more than other organisms. For example, the fact that the acceleration of gravity is roughly 9.8m/s2 on the surface of Planet Earth is an important developmental resource for the human phenotype of being able to walk around efficiently on two legs. If a human child were raised in an environment where the acceleration of gravity is greater (e.g. on Jupiter, where the acceleration of gravity is 26.0m/s2) or smaller (e.g. on Pluto, where the acceleration is 0.6m/s2), he would not develop normal legs and she would not develop normal walking skills (cf. Thelen and Smith [1994]). It follows that it is partly because both my father and I have been exposed to an acceleration of gravity of roughly 9.8m/s2 that we have developed similar (normal) legs and similar (normal) walking skills. This means that the acceleration of gravity is an inherited developmental factor for me. By the same argument, it is an inherited developmental factor for all humans. The causal processes responsible for the fact that,

generation after generation, humans remain exposed to an acceleration of gravity of 9.8 m/s2 is an inheritance mechanism for humans, even if it is a mechanism that we get �for free�. But since every human is exposed to roughly the same acceleration of gravity, this inheritance mechanism is not responsible for intergenerationally-stable and selectable variation.

Many organisms inherit ecological legacies, the result of niche-construction, from their parents (Laland et al. [1996a], [1999], [2000], [2001]). But in some cases all the members in a population inherit the same ecological legacies. So, these legacies are not responsible for intergenerationally-stable environmentally-caused within-population phenotypic variation. Ecological legacies of this kind can change the selection pressures acting on a population, but they are not responsible for within-population selectable variation. Nongenetic inheritance is not sufficient for nongenetic selection, variation in fitness in nongenetically inherited resources is also required. As my examples show, in many cases such variation exists. (But even when it does not produce intergenerationally-stable variation within populations, niche-construction and nongenetic inheritance in general may produce intergenerationally-stable variation at the group level and can thereby give rise to selection at the group level.)

In Section 4, I said that the 20th century was dominated by a genocentric view of inheritance. In the light of the remarks made in this section, we can distinguish two versions of the genocentric view of inheritance, a strong and a weak one. According to the strong version, genetic transmission is the only mechanism of inheritance (Johannsen [1911]). According to the weak version, genetic transmission is not the only mechanism of inheritance, but it is the only mechanism of inheritance responsible for intergenerationally-stable phenotypic variation in fitness, i.e. it is the only mechanism responsible for the vertical transmission of phenotypic differences and, thereby, it is the only inheritance mechanism to be evolutionarily significant (Dawkins [1982/1999]; Maynard-Smith [2000]). The arguments in Sections 2 and 3 show that there are nongenetic inheritance mechanisms responsible for fitness-relevant intergenerationally-stable phenotypic variation. Both versions of the genocentric view of inheritance are wrong.

6. Genetic and Nongenetic Heritability

The terms �inherited� and �heritable� are not co-referential (Sober [2001]). As we saw in the previous Section, �inherited� refers to a property of developmental factors and it does not require variation. In contrast, �heritable� refers to a property of phenotypic variation. If there is no phenotypic variation then there is no heritability. In order to understand heritability, one must therefore understand the way phenotypic variation can be measured and analysed. The standard way to measure the variation for a phenotypic trait is to calculate the trait�s variance, the mean of the squared deviations from the population mean. The variance of a phenotype can be analysed into different components:

VP = VG + VE + VGE + 2covGE

VP is the total variance of phenotype P in the population under study; it quantifies the total amount of variation for P in that population (from now on, reference to the population will be implicit). VG is the genetic variance of P; it quantifies the amount of variation for P due entirely to genetic differences. VE is the environmental variance of P; it quantifies the amount of variation for P due entirely to differences in nongenetic developmental factors. VGE is the gene-environment interaction variance; it quantifies the amount of variation for P due to differences in gene-environment combinations. covGE is the covariance of genetic and environmental factors for P; it quantifies the extent to which genetic factors that have a positive or negative effect on the deviation from the population mean are associated with environmental factors that have a positive or negative effect on the deviation from the population mean. Each of the components of phenotypic variance can itself be analysed into sub-components. In particular, the genetic variance can be analysed as follows:

VG=VA+VNA=VA+VD+VI

VA is the additive genetic variance and VNA is the non-additive genetic variance for phenotype P. VA quantifies the amount of variation for P due entirely to differences in genetic factors that are not broken up by segregation and recombination. That is, VA quantifies the variation for P due to differences in intergenerationally-stable (inherited) genetic factors; it quantifies the amount of intergenerationally-stable genetically-caused variation for P. In contrast, VNA quantifies the amount of variation for P due to differences in gene combinations that are broken up by segregation and recombination; it quantifies the amount of variation for P due to differences in genetic factors that are not intergenerationally-stable (not inherited), at least not in general.15 The non-additive genetic variance can be analysed into dominance variance, VD, and epistatic variance, VI. Both VD and VI measure portions of variation for P due to differences in non-inherited gene combinations. VD quantifies the amount of variation due to non-inherited differences in gene combinations where the relevant genes are at the same locus. VI quantifies the amount of variation due to differences in non-inherited gene combinations where the relevant genes are at different loci.

The standard definition of heritability distinguishes between narrow and broad heritability. The broad heritability of a phenotype P in a given population is:

H2 =VG/VP

H2 quantifies which fraction of the total variation for P is due entirely to genetic differences. It provides information about the extent to which existing deviations from the population mean are due exclusively to genetic factors. H2 does not tell anything about what is going to happen to the variation for P in the next generation. The reason is that VG includes components of variance due to genetic differences that will persist in the following generation as well as components of variance due to genetic differences that will not persist in the following generation, i.e. components of variance due to gene combinations that will be broken up by segregation and recombination. It is for this reason that some authors prefer to call H2 the �degree of genetic determination� of a phenotype�s variation (e.g. Falconer and Mackay [1960/1996]; Hartl and Clark [1997]). H2 has nothing to do with intergenerational similarity. Things are different with narrow heritability. The narrow heritability of a phenotype P in a population is defined as:

h2=VA/VP

h2 quantifies which fraction of the variation for P is both genetically-caused and intergenerationally-stable. It provides information about the extent to which existing deviations from the population mean are due entirely to intergenerationally-stable genetic factors. h2 provides information about deviations from the population mean that (ceteris paribus) will reappear in the following generation as a result of genetic transmission. It tells us the extent to which, as a result of genetic transmission (and ceteris paribus), the offspring are going to resemble their parents more than other organisms with respect to P. In order to understand the important role that the notion of narrow heritability plays in the received view of selection and evolution, three other notions need to be introduced. The first is the response to selection, R, the difference between the offspring population mean and the parental population mean for the phenotype under study. The second is the selection coefficient, S, the mean deviation of the selected parents from the parental population mean. And the third is the offspring-parent regression, bOP, defined as follows:

bOP=covOP/VP

covOP is the covariance of mean offspring value and mid-parental value of phenotype P. bOP quantifies the extent to which differences in P among the parents are associated with differences in P among the offspring. It quantifies the extent to which the offspring resemble the parents more than other organisms with respect to P. That is, bOP quantifies the amount of intergenerationally-stable variation for P. In standard textbooks of evolutionary biology (e.g. Futuyma [1997]; Ridley [1996]), it is claimed that the following equations are true:

(1) bOP=h2

(2) R=SbOP

(3) R=Sh2

Equation (1) entails that covOP=VA. That is, according to this equation, the offspring resemble their parents more than other organisms with respect to P only as a result of genetic transmission (accidental similarities on a side). This equation means that all the intergenerationally-stable phenotypic variation is additive genetically-caused variation.

Equation (2) entails that the more the offspring resemble their parents more than other organisms with respect to P, the higher the response to selection for P is going to be. And this is equivalent to saying that the more intergenerationally-stable variation for P there is, the more selection is going to change the mean value of P.

Equation (3) entails that the more genetically-caused intergenerationally-stable variation for P there is, the more selection can act on P. But it also entails that nongenetically-caused intergenerationally-stable variation for P has no effect on P�s response to selection. It entails that envirotypically-caused variation is irrelevant for selection and, thereby, only the additive genetic variance must be taken into account in order to predict the response to selection of a trait. Equation (3) follows from the conjunction of (1) and (2). As Futuyma puts it:

The additive genetic variance plays a key role in evolutionary theory because it is the basis for response to selection within populations. This is because the additive effects of alleles are responsible for the degree of similarity between parents and offspring�which [�] determines the magnitude of the response to selection. (Futuyma [1997], p. 414, italics in the original)

Equation (2) follows from the way R, S, and bOP have been defined (plus the assumption that the population mean does not change for reasons other than selection). But, if what I have said in this paper is correct, (1) and (3) are false. In many cases, and not by accident but for of the existence of nongenetic inheritance mechanisms, bOP>h2. So, equation (1) is false: for many phenotypic traits of many organisms, not all the intergenerationally-stable variation is additive genetically-caused variation. There exists a lot of nongenetically-caused intergenerationally-stable variation. And this variation is often responsible for variation in fitness. That is, selection can act on such variation. It follows that the response to selection of a phenotype is proportional not only to its narrow heritability. It is also proportional to the amount of nongenetically-caused intergenerationally-stable variation. The more envirotypically-caused variation for a trait there is, the more the trait can respond to selection. That is, equation (3) is false too.

Even if we reject (1) and (3), we should not reject (2). This equation tells us something important about the relation between response to selection and intergenerationally-stable variation. It tells us that the more intergenerationally-stable variation for a trait there is, the more the trait can evolve by natural selection. And, when this equation is interpreted correctly, it tells us that this is true independently of whether the causes of such intergenerationally-stable variation are genetic or not. Futuyma�s claim should be modified as follows:

The offspring-parent covariance, which is a measure of the intergenerationally-stable phenotypic variation, plays a key role in evolutionary theory because it is the basis for response to selection within populations. This is because the effects of intergenerationally-stable (i.e. inherited) developmental factors are responsible for the degree of similarity between parents and offspring�which determines the magnitude of the response to selection.

The definition of heritability in terms of h2 is the following: a phenotype P is heritable in a population to the extent that the existing variation for P in that population is additive genetically-caused variation, i.e. a phenotype P is heritable to the extent that the existing variation for P is caused by intergenerationally-stable (inherited) genetic factors. We can call this genetic heritability. The notion of heritability needed by the theory of selection is not this one but a more general one, one that takes into account all the intergenerationally-stable variation, whether genetically-caused or not. We can call such notion general heritability and we can define it as follows: a phenotype P is heritable in a population to the extent that the existing variation for P in that population is intergenerationally-stable, i.e. a phenotype P is heritable to the extent that it is caused by intergenerationally stable (inherited) genetic and nongenetic factors.16

I started this Section by saying that �inherited� and �heritable� are not coreferential. �Inherited� refers to a property of developmental factors. �Heritable� refers to a property of phenotypic variation. We can now see what is the relation between the two properties. An inherited factor is an intergenerationally-stable developmental factor. Variation in intergenerationally-stable developmental factors produces intergenerationally-stable phenotypic variation. That is, it produces heritable variation. The relation between general heritability and inheritance is that general heritability is the result of variation in inherited factors. Genetic heritability is the result of variation in inherited genetic factors. The assumption of the received view is that genetic heritability is all the heritability there is. This assumption follows from the genocentric view of inheritance (in all its versions). And, just like the genocentric view of inheritance, this assumption is false. Some heritability is nongenetic.

We already know how to measure genetic heritability. The standard definition of h2 tells us how:

h2(GENETIC)=VA/VP=VIN(GENETIC)/VP

VIN(GENETIC) is a variance that measures the variation due to inherited genetic factors, i.e. VIN(GENETIC)=VA. How can we measure general heritability? In this way:

h2(GENERAL)=VIN(GENERAL)/VP

VIN(GENERAL) is a variance that measures the variation due to inherited factors, genetic and nongenetic.17 We can now replace equation (1) with equation (1�) and, by using equation (2), we can derive equation (3�) in place of equation (3):

(1�) bOP=h2(GENERAL)

(2) R=SbOP

(3�) R=Sh2(GENERAL)

7. Conclusions

The beauty of Darwin�s theory of natural selection is that it allows us to explain very many important features of the living world by appealing to few conditions which can be characterised in very abstract terms. Darwin�s discovery�in the language of contemporary biology�was that phenotype frequencies can change as a result of intergenerationally-stable variation in fitness-related phenotypes. He realised that this kind of process can explain why certain phenotypes (those that confer a better ability to survive and reproduce) become more and more common in natural populations. And he realised that, when repeated many times over, such process could produce many of the features that we observe in living beings. Darwin did not know what mechanisms caused intergenerationally-stable phenotypic variation in fitness. He had evidence for the existence of such variation. And he knew that the existence of such variation was enough for natural selection to take place (Darwin [1859]).

Darwin tried to understand the mechanisms responsible for the observable intergenerationally-stable phenotypic variation. But he failed. His theory of inheritance, the theory of pangenesis (Darwin [1868], [1871]), was wrong. Many others tried to give a theory of inheritance. Mendel ([1866]) actually managed to discover something very important. What he discovered is nowadays called Mendelian inheritance. Mendelian inheritance is a particular kind of genetic inheritance. In 1900, Mendel�s results were rediscovered after being ignored for more than thirty years. In the same year, the term �gene� appeared for the first time in biology. The 20th century became the century of the gene (Fox-Keller [2001]). Many important features of genetic inheritance were discovered. In particular, Crick and Watson discovered that DNA has a double-helical structure and that genetic replication was obtained through template reproduction (Watson and Crick [1953a], [1953b]). This discovery confirmed the hypothesis that genetic transmission was a high-fidelity process, a process that could produce a lot of intergenerational similarity.

The 20th century was the century of the gene not only in molecular biology but in evolutionary biology too. During the first part of the century, many biologists and mathematicians tried to understand how particulate genetic inheritance could give rise to the observable continuous phenotypic variation. This effort resulted in the Modern Synthesis of Mendelian genetics and Darwinian evolutionary theory (Fisher [1918]; see also Levine [1971], Mayr [1982], Sarkar [1998]). Powerful models and theoretical tools were developed by Fisher, Wright, Haldane, Dobzhansky, Simpson, Mayr and many others. Other important ideas for studying genetic evolution were elaborated in the second half of the century by Hamilton, Price, Maynard-Smith, Trivers, and many others.

The enormous success of the study of genetic inheritance and genetically-caused phenotypic variation led people to ignore the possibility of other mechanisms of inheritance and, thereby, of other ways to produce intergenerationally-stable (selectable) phenotypic variation. The powerful genetic models led to the assumption that all the intergenerationally-stable phenotypic variation observed in natural populations was genetically caused. And they led to the assumption that all natural selection was at bottom genetic selection. Nongenetic channels of intergenerational similarity were never studied and nongenetic selection was never seriously considered. In this paper, I have argued that there exist nongenetic channels of intergenerational similarity, that some nongenetic mechanisms of inheritance are responsible for intergenerationally-stable phenotypic variation in fitness, and that natural selection can act on such variation. Nongenetic inheritance and its consequences need to become an official part of our theory of evolution. This may require giving up the mathematical elegance of population genetics. But the price is worth paying.

Many things remain to be done. In the received view there is no room for nongenetic inheritance. So, virtually no one has looked for it and for its evolutionary consequences. We need a systematic investigation of nongenetic inheritance mechanisms and of the kind of intergenerationally-stable phenotypic variation they can produce. Very likely, many nongenetic inheritance mechanisms have not been discovered yet. And those that have been discovered have not been investigated in depth. The problem is also that envirotypically-caused phenotypic variation is not easy to discover without some detailed knowledge of the relevant developmental processes. The assumption that genetic inheritance is the only mechanism responsible for intergenerationally-stable phenotypic variation simplifies things a lot. When that assumption holds, one can study intergenerationally-stable variation without knowing anything about developmental processes, genotype-phenotype mappings included. One can infer the amount of additive genetically-caused variation from responses to selection and from offspring-parents regressions. But when one realises that some intergenerationally-stable variation may be nongenetically-caused, things become more difficult. In order to distinguish the genetically-caused from the nongenetically-caused intergenerationally-stable phenotypic variation, experiments that reveal something about the developmental process (e.g. cross-fostering experiments) need to be made.

In order to understand the evolutionary significance of nongenetic inheritance, for each nongenetic inheritance mechanism we need to know (a) whether and to what extent it can generate phenotypic variation in fitness, (b) what processes are responsible for the production of new variants, (c) how intergenerationally stable is the phenotypic variation it can generate, and (d) how such variation interacts with the variation generated by other inheritance mechanisms, genetic transmission included. Such investigations will allow us to compare genetic and nongenetic inheritance.

Here are some preliminary considerations. Genetic transmission is evolutionarily very powerful (Sterelny [1996], [2001], [forthcoming]). One reason is that, given the combinatorial structure of DNA, genetic transmission can give rise to a lot of phenotypic variation, i.e. genetic transmission is an unlimited system of heredity (Maynard-Smith and Szathmáry [1995], [1999]; Szathmáry and Maynard-Smith [1995], [1997]; but for a critique of this notion see Griffiths [2001], Griffiths and Gray [2001]). Another reason is that, given that genetic transmission is high-fidelity (Dawkins [1976/1989], [1982/1999]), much genetically-caused phenotypic variation is intergenerationally stable to a high degree. It must be said though that new genetic mutations (new

variants) are random with respect to fitness. For this reason, adaptive evolution due to genetically-caused variation can be a slow process.

What about the evolutionary potential of nongenetic inheritance? Envirotypically-caused variation can mask genetically-caused variation (Avital and Jablonka [2001]) and can thereby �interfere� with genetic selection. Some mechanisms of nongenetic inheritance are very high-fidelity, almost like genetic transmission (Sterelny [2001], [forthcoming]). And many mutations in envirotypes are often produced by mechanisms (e.g. learning) designed to bring about adaptive changes in ontogenetic time. That is, in some nongenetic inheritance mechanisms, the generation of new variation is non-random with respect to fitness. This means that nongenetic inheritance can in some cases bring about adaptive evolution in a short time (Immelmann [1975]). It can bring about adaptive evolution even in cases in which the rate of mutation is higher than the relevant selection pressures. Pace Williams ([1966]) and Dawkins ([1976/1989], [1996], [1999]), high-fidelity transmission is not necessary for evolutionarily significant inheritance.

Moreover, the received view of natural selection focuses on within-population intergenerationally-stable variation, but selection can act on intergenerationally-stable variation among groups (Boyd and Richardson [1985], [2000]; Sober and Wilson [1998]; Wilson and Sober [1994]). There are reasons for thinking that nongenetic inheritance plays a big role in such between-groups variation. In so far as group-selection is concerned, it may well be that nongenetic inheritance is much more important than genetic inheritance.

In conclusion, just like genetic transmission (even though for different reasons), very likely some nongenetic inheritance mechanisms have a high degree of evolutionary significance.

Acknowledgements I am greatly indebted to David Papineau and Kim Sterelny for having encouraged me to explore the ideas I discuss in this paper and for having read and commented carefully on many different versions of this paper. Many thanks to my PhD examiners: John Maynard-Smith and John Worrall. Many thanks to Russell Gray, Paul Griffiths and Eva Jablonka for their very stimulating writings on nongenetic inheritance and for long and fruitful discussions. Many thanks also to the following people for very many useful comments and suggestions: Elliott Sober, Dan Dennett, Eva Jablonka, James Griesemer, Lisa Bortolotti, Finn Spicer, Katrina Sifferd, Alex Rosenberg, Danis Walsh.

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1 This is not the only possibility. Other scenarios are possible, e.g. a stable equilibrium between the butterflies of the old and of the new kind. But I am not concerned with these alternative scenarios here. 2 I write selection as short for Darwinian natural selection and fitness as short for Darwinian fitness. Notice that not every form of natural selection and not every kind of fitness is Darwinian. For example, selection that acts on horizontally-transmitted traits is not strictly speaking Darwinian since it does not necessarily cause the spread of traits that increase the Darwinian fitness of organisms. There have been attempts to elaborate theories of natural selection that can make sense of such processes (Dawkins [1976/1989]; Dennett [1995], [2001a], [2001b]; Cavalli-Sforza and Feldman [1981]; Boyd and Richerson [1985], [2000]). Such generalisations of Darwinian theory are not the topic of the present paper. 3 For similar fictions, see Avital and Jablonka ([2001]), Sterelny ([2000]), and Griffiths ([2001]). See also Mameli ([2001]) and Mameli ([2002]). The selection process that transforms the butterfly population is a selection process of type 2 in Sober�s classification of selection processes (Sober [1992], [1993/1999]). 4 The development of an organism can be indirectly affected by the genes of its mother, or by those of its father, or by the genes of other organisms. But those genes count as environmental factors for the development of the organism, even though they count as genetic factors for the development of the mother, father, etc. (Mousseau and Fox [1998]). 5 Since development is a hierarchical process, phenotypes contribute to the development of other phenotypes. For example, protein synthesis contributes to the development of tissues and the development of legs contributes to the development of the ability to walk. In spite of this, phenotypes do not count as developmental factors according to the terminology I am using. Only causes that pre-exist the developmental process count as developmental factors. 6 This definition of phenotypic traits includes extended as well as standard phenotypes. From the point of view of evolutionary theory, this is as it should be: evolutionary processes can act in the same way on standard as well as extended phenotypes (Dawkins [1982/1999], Mousseau and Fox [1998]). 7 Suppose two organisms O1 and O2 differ in a phenotype T: O1 has phenotype T1 and O2 has phenotype T2. Suppose that this phenotypic difference between O1 and O2 is due to the fact that the development of O1 is affected by developmental factor D1 but not by developmental factor D2 and the development of O2 is affected by D2 but not by D1. That is, the difference in T is due to the difference in D. Suppose now that D is very intergenerationally stable. This means that, in general, the development of O1�s descendants is affected by D1 but not by D2 and the development of O2�s descendants is affected by D2 but not by D1. Thus, ceteris paribus, O1�s descendants develop T1 and O2�s descendants develop T2. 8 Some of Dawkins� and Lewontin�s writings seem to suggest that nongenetic selection may occur in humans but not in other species. Dawkins� theory of memes ([1976/1989]) allows for the possibility that memes be transmitted vertically, from parents to offspring. Darwinian selection could in principle act on such memes. But meme-theorists never talk of such a process. They focus on horizontal transmission and stress that the selection processes operating on horizontally-transmitted memes do not necessarily cause the spread of memes that increase the fitness of organisms (Dawkins [1976/1989], [1982/1999]; Dennett [1995], [2001a], [2001b]; Blackmore [1999]). That is, the kind of selection that operates on horizontally-transmitted memes is not Darwinian selection as I have defined it (see footnote 2). Lewontin has claimed that, as it is obvious, not only genes but also money is inherited (Elliott Sober, personal communication). In principle, Darwinian selection could operate on traits that depend on this inheritance channel. But Lewontin thinks this is not a possibility

worth exploring. See Fracchia and Lewontin ([1999]) for a critique of applications of natural-selection theory to human cultural evolution. And see Cavalli-Sforza and Feldman ([1981]), Cavalli-Sforza ([2001]), Boyd and Richerson ([1985]), ([2000]), Durham ([1991]), and Mameli ([2001]) for an application of natural-selection theory to human culture. Studying cultural transmission is not the best way of studying nongenetic Darwinian selection because cultural transmission is a complex mix of vertical and horizontal transmission. For this reason, I avoid talking about cultural transmission in this paper. For a discussion of why horizontal transmission interferes with Darwinian selection see Sterelny�s discussion of outlaw replicators (Sterelny [2001], [forthcoming]). 9 There has been a long debate about the defining features of imprinting (Bateson [2000], Bolhuis [2001]). I do not need to deal with the details of this debate. 10 See Cavalli-Sforza and Feldman ([1981]), Boyd and Richerson ([1985]). Notice though that these accounts focus on humans. 11 This is not a general definition of inheritance mechanisms, it is only a definition of vertical inheritance mechanisms, those mechanisms that cause organisms to resemble their biological parents. But organisms can inherit traits from organisms other than their biological parents. When that happens, horizontal and oblique inheritance mechanisms need to be invoked. A general definition of inheritance mechanisms can be obtained by generalizing the parent/offspring relation. In this paper, I am concerned only with clarifying the role that inheritance plays in processes of Darwinian selection as it is standardly conceived. For this reason, I focus only on vertical inheritance mechanisms, since horizontal and oblique inheritance can lead to the spread of traits that are not fitness-increasing (Cavalli-Sforza and Feldman [1981], Boyd and Richerson [1985], Dennett [1995[, [2001a], [2001b]). So, I use inheritance as short for vertical inheritance. 12 This picture is, in a way, misleading because it suggests that, on the genocentric view, all genetic factors are transmitted from one generation to the next. But on this view, most gene complexes are not transmitted from one generation to the next, at least not in sexual species; only independent alleles are inherited. 13 FIG.2 is, in a way, misleading since it suggests that all parental phenotypic and environmental traits are inherited. This is not so. Only some parental phenotypes and some parental environmental traits are inherited by the offspring. (Compare with what said in the previous footnote.) 14 Parental phenotypes are themselves part of the offspring environment and can contribute to intergenerational similarity by modifying other parts of the offspring environment. This process is known as downstream niche constructions (Laland et al. [1996a], [1999], [2000], [2001]; Sterelny [2001]). 15 There are special cases in which the non-additive genetic variation can be inherited. 16 In this paper, I have talked about inherited genetic factors and inherited nongenetic factors. But intergenerationally-stable gene-environment combinations are also possible. Such combinations count as inherited. And they can generate selectable variation in fitness. 17 I must leave to another day the analysis of the various components of VIN. For some suggestions about how to proceed, see Kisdi and Jablonka ([manuscript]). It must also be noticed that in cases in which the mutation rate of the inherited factors for which there is variation is relatively high, the definition of general heritability must be modified as follows: h2(GENERAL)=(VIN/VP)µ, where µ stands for the probability of mutation.