e c o l o g i c a l m o d e l l i n g 2 0 6 ( 2 0 0 7 ) 166–178

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

Identification of the inland population dynamics of theEuropean eel using pattern-oriented modelling

Patrick Lambert ∗, Eric RochardCemagref, Unite Ecosystemes Estuariens et Poissons Migrateurs Amphihalins, 50 Avenue de Bordeaux, F-33612 Cestas Cedex, France

a r t i c l e i n f o

Article history:

Received 10 February 2006

Received in revised form

19 March 2007

Accepted 28 March 2007

Published on line 11 May 2007

a b s t r a c t

We propose a process-based model (GlobAng) for the population dynamics of the continen-

tal phase of the European eel based on an ecological pattern derived from knowledge in the

existing literature. This model simulates ageing, recruitment, sexual differentiation, silver-

ing, natural mortality and, for the first time, movement within a watershed. It demonstrates

that it is possible to simulate the pattern of density-dependent mortality, density-dependent

sexual determination and diffusive movements. The downstream part of the watershed

appears to be the area of maximum production for both males and females and where sex-

Keywords:

Anguilla anguilla

Population dynamics

Ecological modelling

ual differentiation takes place, especially when recruitment is low. The quality of the pattern

is discussed in relation to the modelling results and field observations. The consequences

of our findings for primary management are to advise concentrating mitigation efforts on

the downstream part of the catchment area.

eel population dynamics have been described in the literature,

Pattern-oriented model

1. Introduction

The European eel (Anguilla anguilla) is a diadromous fish whichprobably reproduces in the Sargasso Sea. After crossing theocean, the larvae reach the European coasts during winterand metamorphose into glass eels. As facultative catadromyis now accepted (Tsukamoto et al., 1998; Daverat et al., 2006),we know that a proportion of the larvae migrate up estuariesand freshwater streams where they become yellow eels andgrow for 5–12 years. They then start their downstream migra-tion from the watershed to the ocean, metamorphose intosilver eels and swim back to the spawning area, where theydie after reproduction. The glass eels arriving in an estuaryare the recruitment, and the silver eels that leave a watershedare called spawner escapement.

While this species is an important component of the

European inland fisheries (Dekker, 2000a), there is now clearevidence that the European eel stock, once abundant, isdecreasing dramatically throughout Europe (Brusle, 1990;

∗ Corresponding author. Tel.: +33 5 57 89 08 09; fax: +33 5 57 89 08 01.E-mail address: patrick.lambert@bordeaux.cemagref.fr (P. Lambert).

0304-3800/$ – see front matter © 2007 Published by Elsevier B.V.doi:10.1016/j.ecolmodel.2007.03.033

© 2007 Published by Elsevier B.V.

Chancerel, 1994; Moriarty and Dekker, 1997; Dekker, 2000a).The supposed causes of this collapse in numbers and intheir ranking remain open questions (Castonguay et al., 1994a;Knights, 2003; Dekker, 2004). As a result of this scarcity, thisspecies is now considered outside its safe biological limitsand fisheries are not sustainable (ICES, 1999). Managementplans to increase the quantity and quality of the spawn-ing biomass should therefore be implemented urgently (ICES,2001b, 2002; Lambert et al., 2003). In order to define such plansit is necessary to establish, at watershed level, the relationshipbetween the number of eel larvae arriving in the estuary andthe number of silver eels swimming back to the Sargasso Sea(Feunteun, 2002).

In view of the difficulty of direct field evaluations, mod-elling is a useful alternative. Different attempts at modelling

but most of these do not integrate fish movements (Gatto et al.,1982; Vollestad and Jonsson, 1988; Naismith and Knights, 1990;De Leo and Gatto, 1995; Dekker, 1996, 2000b,c; Adam, 1997;

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eunteun, 2002). Among those which do integrate fish move-ents, one covers exchanges between estuarine and stream

ompartments only (Gascuel and Fontenelle, 1994), two ignorether biological processes (Smogor et al., 1995; Ibbotson et al.,002) and one is limited to the estuarine migration of the glassel (Lambert et al., 1995). However, it is possible that fish move-ents interact significantly with mortality or maturation and

nfluence population dynamics, especially in a species likehe eel which is well known for having a great colonisationapacity and which is suspected to regulate density.

We therefore propose a model of eel population dynam-cs in a hydrographical network which includes all the mainiological processes, including fish movement. We based ourpproach on available knowledge, without reference to anyrecise geographical location. We thus summarized informa-ion from different contrasted populations and environmentso propose a paradigmatic ecological pattern of eel popula-ion dynamics. In doing so, we paid particular attention to theonsequences of density-dependence on population dynam-cs. From the simulated results we established the relationshipetween recruitment level and silver eel escapement, andetermined the area used by eels according to their age andiological state. We then went on to present the consequencesf our findings for management.

. Methods

.1. Modelling strategy and ecological patternefinition

e chose to use the pattern-oriented modelling approach pro-osed by Grimm et al. (1996) and Railsback (2001). Pattern isefined as clearly identifiable structures in nature itself or

n the data extracted from nature (Grimm et al., 1996). Thispproach allowed us to gather, in a single model, results fromeveral locations at different periods. We then followed theodelling process proposed by Wiegand et al. (2003). First, we

efined a pattern and implemented the population-dynamicsodel through which the pattern can arise. Second, we set

xed parameter values wherever possible and, for the remain-ng values, their likely variation range. Third, we defined threelternative hypotheses to be tested. Fourth, we performedll necessary simulations and systematically compared sim-lated results with the pattern in order to determine whichombinations of parameter values are compatible. This exper-mental approach to simulation enables us to identify thoseactors which have an effect and those which have no effectnder a given set of assumptions (Mullon et al., 2003). Lastly,xploring the model further enabled us to define secondaryomparative predictions.

A basic pattern with four characteristics was identifiedased on the literature relating to all eel species. An extendedattern was defined by adding a fifth characteristic which isn extension of point 2.

. Silver eel production in a watershed is not unlimited.

. A decrease in recruitment results in a sex ratio in the stand-ing stock or silver escapement in favour of females (Rossi etal., 1987). This modification can even invert sex ratio dom-

6 ( 2 0 0 7 ) 166–178 167

ination (Svardson, 1976; Parsons et al., 1977; Poole et al.,1990).

3. Eel abundance decreases exponentially the further the dis-tance from the sea (Smogor et al., 1995; Ibbotson et al.,2002).

4. Sex ratio evolves in favour of females, the further the dis-tance from the sea (Aprahamian, 1988; Oliveira, 1999).

5. Sex ratio evolves with increasing recruitment, from purelyfemale to purely male domination.

The first characteristic is easily acceptable even if no directobservation of such a limitation is available. There is clear evi-dence that a watershed cannot carry an infinite number ofeels. The second characteristic is based on sex ratio evolu-tion in systems where recruitment has decreased (Baltic Seain Svardson, 1976; Italian lagoons in Rossi et al., 1987; smallIrish river in Poole et al., 1990) or has been increased artificially(Irish lake in Parsons et al., 1977). Although heteromorphicsex chromosomes (Wiberg, 1983) have been identified, gen-der appears to be determined principally by environmentalfactors (Davey and Jellyman, 2005). Eel population densityseems to be an important factor in sex determinism (Kruegerand Oliveira, 1999) even if other factors like temperature(Holmgren, 1996) or available lacustrine habitats (Oliveira etal., 2001) can also affect the sex ratio. The third characteris-tic comes from results matching eel densities to the distancefrom the tidal limit in rivers in Virginia (Smogor et al., 1995)and England (Ibbotson et al., 2002). In many studies, distancefrom the ocean is also used to explain eel distribution quali-tatively (Aprahamian, 1988; Lobon-Cervia et al., 1995; Glova etal., 1998) however, this trend of less abundance with increas-ing distance from the sea is not systematic in short rivers(Laffaille et al., 2003). This general pattern is obviously modi-fied by dams (Feunteun et al., 1998; Goodwin and Angermeier,2003; Domingos et al., 2006) and also by specific habitat char-acteristics such as density of other fish (Wiley et al., 2004).The fourth pattern characteristic is a formulation of com-mon field observations in rivers where females and malesare present (Aprahamian, 1988; Oliveira, 1999). Males are usu-ally more abundant than females in downstream parts of thecatchment area, whereas they become rare in the upstreamreaches of rivers (Tesch, 2003). The fifth characteristic isan extrapolation of the second point and will be discussedlater.

2.2. Main model features and process representationchoices

We designed our model GlobAng by identifying the processesrequired to reproduce the pattern. The input process was inte-grated in order to choose recruitment level (points 1 and 2).Point 1 involved taking into account output processes (mortal-ity and silver eel escapement), including density-dependenceregulation. Points 2 and 4 led us to simulate the sexual dif-ferentiation process, which should depend on density. Points3 and 4 covered the modelling of movement within a catch-

ment area. The succession of biological processes is presentedin Fig. 1.

The model was structured with three states: undif-ferentiated, female yellow eel and male yellow eel. An

168 e c o l o g i c a l m o d e l l i n g

Fig. 1 – Flowchart of biological processes during a time step

nipulation results of Parsons et al. (1977) and the rearing

in GlobAng.

undifferentiated eel can become either a male or female yel-low eel. After sexual differentiation, the sex cannot changeany more. A yellow eel becomes a silver eel according to itsage and sex. A silver eel cannot revert to a yellow eel. Silvereels correspond to disappearance from the system and consti-tute the main model output. Growth is not explicitly taken intoaccount and states are structured by age. Details are providedin the online appendix.

The simulation of one trajectory is equivalent to monitor-ing the evolution of eel numbers Ni,j,k(t) from age class j (from0 to jmax), and from state k in compartment i (from 1 to imax)during time t. The time step is the week.

Based on existing information, we fixed seasonality or age-dependence parameters for each process.

2.2.1. Age and ageing of eelsSince we simulated only the continental life of the eel, glasseel age is equal to the 0 year class. We fixed the last yearlyage class jmax at 12 years, because, except in low produc-tive systems, eels older than 12 are rare (Adam, 1997). Dateof birth was fixed at the first week of May. This correspondsto the spawning period, usually considered to be from Marchto June (Schmidt, 1922; Boetius and Harding, 1985). Clas-sically, eel numbers for each age class were shifted everybirth week and the numbers of the last two classes wereadded.

We denoted the age of class j by aj(t) which was computedas the sum of the age class and the proportion of the yearbetween the current week and the birth week.

2 0 6 ( 2 0 0 7 ) 166–178

2.2.2. Basin topology and carrying capacityWe considered a simplistic hydrographical network consist-ing of a linear succession of 25 homogeneous compartments,without tributaries (imax = 25). We used upstream numbering,with number 1 corresponding to the mouth of the estuary andnumber 25 to the river source.

Based on Dhondt’s review (1988), carrying capacity wasdefined as the maximum weighted number (equivalent tobiomass) that can be supported in a given compartment for along period, independently of population dynamics. The car-rying capacity of each compartment was arbitrarily fixed at200 equivalent 13-year-old eels. Using the following formula,derived from a weight–growth curve, we calculated the contri-bution wj(t) of one individual of age class j to carrying capacitysaturation:

wj(t) =

⎧⎪⎨⎪⎩

0 if Aj(t) < 1(1 − exp(−˛w(aj(t) − 1)

1 − exp(−˛wjmax)

)3

if Aj(t) ≥ 1

Using this formulation, an eel contributed to saturation of thecarrying capacity from its second year. Its maximal contri-bution was at the end of its twelfth year. The saturation ofa spatial compartment si(t) corresponds to the ratio betweenthe number of eels Nj,k(i, t) weighted by wj(t) and the carryingcapacity ci.

All density-dependence mechanisms were expressed interms of saturation of carrying capacity as this can be con-sidered as actual suitability of the compartment.

2.2.3. RecruitmentRecruitment corresponded to incoming glass eels in an estu-ary. The proportion of arrivals in a given week was calculatedwith a beta function. This was combined with the seasonalrecruitment level to calculate, for each time step, the numberof 0-year-old animals added to the downstream compartment.

The beta function was limited to the period between thefirst week of October and the last week of April. Its two param-eters were fixed at 2. The simulated arrival of glass eels wastherefore symmetrical, with a maximum in the third week ofJanuary, which corresponds to the phenomenon observed onFrench coasts (Elie and Rochard, 1994).

2.2.4. Sexual differentiationThe change of state between sexually undifferentiated andsexually differentiated eels corresponded in the model to finalmasculinisation or feminisation (Bertin, 1951; Colombo andRossi, 1978; Grandi and Colombo, 1997).

We calculated a weekly mean rate of differentiation,assuming that the duration of the undifferentiated stage fol-lowed a lognormal distribution (Manly, 1990).

Sexual differentiation takes place before the age of 4, sinceonly a few older individuals could not be visually sexed (Adam,1997), and gonad differentiation is fixed only in fish longerthan 33 cm (Colombo and Grandi, 1996), corresponding to amean age of 4–5 years. To be in agreement with the bioma-

experiments of Roncarati et al. (1997) this process cannotoccur before the glass eel stage. We therefore fixed the meanduration of the undifferentiated stage to 2.69 years and the

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tandard deviation to 0.28 years. With these parameters, mostels differentiate between 2 and 4 years old. We also assumedhat this process takes place all year round.

.2.5. Sex determinismex determinism is considered to be environmental (i.e.ccurring during development in response to environmen-al factors, Bertin, 1951; Tesch, 1977; Wiberg, 1983). Fromasin scale observations, it is assumed that female produc-ion is favoured in low population density sectors (Krueger andliveira, 1999).

The proportion of males among the eels differentiating ingiven week t and compartment i, Mi(t) was calculated with a

ogistic function according to saturation of the compartment’sarrying capacity:

i(t) = 11 + exp(−�1(si(t) − �2))

2 corresponds to the saturation level that produces 50%f males among the differentiating eels. �1 measures the

nfluence of saturation on this process. A nil value for thisarameter is equivalent to simulating genotypic determinism

i.e. at or before conception) with an equilibrated recruitmentex ratio.

.2.6. Silveringhis process corresponds to the beginning of the meta-orphosis from yellow to silver eel. Silvering is a gradual

henomenon (Durif et al., 2000), the ultimate step beforeownstream migration takes place at the end of summer

Durif, 2003).As for the sexual differentiation process, the non-zero

eekly mean rate of silvering was calculated using a lognor-al distribution function between the first week of September

nd the last week of December.Tesch (1977) estimated that migration age varies from

to 12 years old for females and from 6 to 9 for males.rom a review of 38 European sites, Vollestad (1992) found

mean age of 8.73 years for females and a mean age of.66 years for males. Silvering parameters were determinedsing the results of Holmgren et al. (1997) monitoring silverel escapement from a Swedish lake. However, the 15-year-ange age structure was compressed to 12 years, given theow growth rate in this lake compared to other situationsVollestad, 1992). Using these parameters in the model, webtained a mean duration of 7.37 years and a standard devi-tion of 3.43 years for the yellow stage for females and 1.57ears and 1.38 years for males. With these parameter values,emales become silver after the age of 7 and males between 2nd 9.

.2.7. Movementmogor et al. (1995) and Ibbotson et al. (2002) demonstratedhat basin colonisation by eels is diffusive. The diffusion coef-cient decreases sharply with age (Ibbotson et al., 2002). Theolonisation process therefore occurs mainly during the first

ears of life. This kind of movement can be seen as a move-ent away from the compartment with the highest density of

els towards the compartment with the lowest density (Okubond Levin, 2001).

6 ( 2 0 0 7 ) 166–178 169

We assumed that this phenomenon concerned all yelloweels and took place all year round. We calculated Tj,t→t±1, theproportion of individuals of age class j leaving a compartmenti to go to an adjacent compartment i ± 1 by modulating themaximum movement rate dj for eels of age class j with thesaturation of the departure-compartment’s carrying capacity(si) and the saturation of the arrival-compartment’s carryingcapacity (st±1):

Tj,i→i±1(t) = dj(t)

(ˇsi(t)

ci + ˇsi(t)

)(ci+1

ci±1(t) + ˇsi±1(t)

)

This formulation generalizes the density-dependent move-ments proposed by Whitehead (2000) in the case of only onecategory of individuals. ˇ represents the relative influencebetween departure and arrival saturations on the transitionproportion (Whitehead, 2000). The higher the value of ˇ, themore movements from the higher density (usually observeddownstream) to the lower density (usually upstream) arefavoured. The maximal movement rate decreases with age,following a beta cumulative distribution. The maximum cor-responds to movements of glass eels �j0 and the minimum toolder individuals �j+.

The parameter values of the beta function simulating adecrease in maximum movement rate were arbitrarily fixed at6 and 20. In this case, eels older than 6 years have a maximummovement rate equal to �j+.

2.2.8. Natural mortalityMost studies have considered a mean rate for eel inland life.Only De Leo and Gatto (1995, 1996) and Adam (1997) haveproposed a more realistic decreasing relationship betweenmortality rate and age. Natural eel mortality increases withdensity in a reach or a hydrosystem (Vollestad and Jonsson,1988; De Leo and Gatto, 1996). Density dependence alsoexplains variations in a rate which combines mortality,emigration and immigration (Naismith and Knights, 1990;Bisgaard and Pedersen, 1991; Lobon-Cervia et al., 1995).

The natural mortality rate for eels aged j in compartmenti in week t was calculated with a Weibull distribution (De Leoand Gatto, 1995) whose scale parameter depends on the expo-nential of compartment saturation:

Zi,j(t) = 1 − exp

((aj(t)

v0 exp(−v1 max(si(t) − 1, 0))

)�

−(

aj(t + 1)

v0 exp(−v1 max(si(t) − 1, 0))

)�),

where � is the shape parameter, v0 the scale parameter whencompartment saturation is lower than 1, and v1 measuresthe decrease in the scale parameter according to saturation.Finally, we assumed that mortality process is equivalent allyear round. With this formulation, life expectancy decreases

when the saturation rate is higher than 1.

The shape parameter in the Weibull distribution was fixedat 0.1789, with reference to De Leo’s and Gatto’s (1995, 1996)studies.

170 e c o l o g i c a l m o d e l l i n g 2 0 6 ( 2 0 0 7 ) 166–178

Table 1 – Variables used in GlobAng computer simulations (see text for full explanation)

Symbol Definition Explored range

˛w Influence of age on the contribution of one eel to carrying capacity saturation (in year−1) [0.10, 1.00]v0 Scale parameter of the survival function when compartment saturation is lower than 1 [0.002, 0.050]v1 Decrease of scale parameter according to saturation [0, 30]�1 Influence of saturation on sex determinism [0, 2]�2 Carrying capacity saturation that produces 50% of males among differentiating eels [1, 10]�j0 Maximal movement rate for glass eels [0.1, 0.3]

uratio

�j+ Maximal movement rate for old eelsˇ Relative influence of departure and arrival sat

2.2.9. Experimental designAfter fixing the parameters for seasonality and age-dependence, eight parameters remained to be assessed(Table 1). Five were linked to saturation-dependence, eitherdirectly (˛w) or measuring its influence on sexual determinism(�1, �2), mortality (v0, v1) and movement (ˇ). Two concernedmovements at different ages (�j0, �j+). To assess these, weadopted an experimental approach (Grimm, 1999; Mullon etal., 2003) by considering three alternative hypotheses:

1. Genotypic sex determinism (˛w, v0, v1, �1 = �2 = 0, �j0,

�j+, ˇ)2. Saturation-independent mortality (˛w, v0, v1 = 0, �1, �2,

�j0, �j+, ˇ)3. Saturation-dependent mortality and environmental sex

determination (˛w, v0, v1, �1, �2, �j0, �j+, ˇ)

We computed 1000 combinations of parameter values forthe first hypothesis, 3000 for the second and 9000 for the thirdin order to take into account the different parameter numbersfor each hypothesis.

We fixed the range of likely values for each parameter. Forsome we used reference values based on the literature, suchas the density-independent scale parameter equal to 0.010used by De Leo and Gatto (1995, 1996) in their Italian lagoonmodel. Parameter b should be in the same order of magni-tude as compartment abundance (Whitehead, 2000), which, inour case, is equivalent to carrying capacity. Usually the range

was assessed based on our expertise, on preliminary trials andby respecting some biological constraints (aj0 ≥ aj+). For eachcombination, the values of the eight parameters were chosenrandomly within the value range.

Table 2 – Number of experiments compatible with different cha

Hypothesis 1, genotypicsex determinism (six

parameters) m

Number of combinations 1000Compatible with point 1 1000Compatible with point 2 0Compatible with point 3 999Compatible with point 4 991

Compatible with the basic pattern 0Compatible with the extended pattern

[0.,0, 0.1]ns on the transition proportion [50, 500]

The experiment was defined as the simulation of a tra-jectory with a given combination of parameter values over aperiod of 25 years for 15 different seasonal recruitment lev-els (from 10 to 1015 glass eels). Only results from the lastyear for each recruitment level – corresponding to equilib-rium – were compared to the patterns. A combination wasconsidered compatible with the basic pattern if (i) silver eelproduction did not increase for the two higher recruitmentlevels (pattern point 1), (ii) the proportion of females in the sil-ver eel run decreased with increasing recruitment level, andthis proportion exceeded 50% (pattern point 2), (iii) maximumeel abundance was found in the most downstream compart-ment, whatever the recruitment level (pattern point 3), and(iv) the proportion of females among the yellow eels was min-imum in the most downstream compartment, whatever therecruitment level (pattern point 4). A combination was com-patible with the extended pattern if the four previous pointswere respected and if the proportion of females was higherthan 95% for the lowest recruitment, and lower than 5% forthe highest recruitment.

3. Results

3.1. Model calibration according to the patterns

Experimental results and patterns are compared in Table 2.Genotypic sex determinism (hypothesis 1) produced moremale silver eels than female silver eels, whatever the recruit-

ment level. This observation was incompatible with patternpoint 2 and led us to reject this hypothesis. Saturation-independent mortality (hypothesis 2) systematically induced asilver eel production which increased indefinitely with recruit-

racteristics of the pattern for the three hypotheses

Hypothesis 2,saturation-independentortality (seven parameters)

Hypothesis 3, environmentaldeterminism + saturation-dependent mortality (eight

parameters)

3000 90000 9000

2828 10833000 89922995 2654

0 29128

e c o l o g i c a l m o d e l l i n g 2 0 6 ( 2 0 0 7 ) 166–178 171

r pat

m1

rpmaiioatotet

plp

tufp

3e

Aesfp

(Fig. 4). Undifferentiated eels older than 1 year were located indownstream basin compartments, whatever the recruitmentlevel. For medium and very large recruitments, they occupied amore downstream zone than male and female yellow eels. For

Fig. 2 – Histogram of values fo

ent. This observation was incompatible with pattern pointand led us to reject this hypothesis.

The model with saturation-dependent mortality and envi-onmental sex determinism (hypothesis 3) identified 291attern-compatible combinations. In this case, respecting theonotonic decrease in the proportion of silver eel females

ccording to recruitment caused us to reject 71% of the exper-ments, and this reached 87% if we also imposed a sex rationversion (point 2 of the pattern). We obtained a rejection ratef 71% for the changes in the proportion in favour of femaless distance from the sea increased (point 4 of the pattern). Allhe pattern-compatible combinations led to a null productionf silver eels for an extraordinarily large recruitment since inhat case the mortality induced by a huge number of youngels in the downstream compartments is sufficient to causehe death of all the eels before they reach age 2.

Only 28 of these 291 experiments presented a female pro-ortion higher than 95% for the lower recruitment level and

ess than 5% for the last recruitment before null silver eelroduction in the basin.

In the explored parameter space, the parameter values forhe 291 pattern-compatible experiments were not distributedniformly (Fig. 2). In particular, low values for ˛w and v1 wereavoured, high values for �j0 were more often accepted. Sur-risingly, high values for �j+ were not under-represented.

.2. Influence of recruitment level on silver eelscapement

ll the selected combinations led to the same escapement

volution according to recruitment level. An example is pre-ented in Fig. 3. Female production presented a maximumor low recruitment and a slight decrease afterwards. Maleroduction increased until medium recruitment and then

tern-compatible experiments.

stabilised. For a very large recruitment, nil escapement wasobtained.

3.3. Spatial structure

Figs. 4 and 5 show where eels with special features – stage orage – can be found in the virtual catchment area according torecruitment level.

Eel distribution in the basin varied according to stage

Fig. 3 – Evolution of silver escapement according to therecruitment level logarithm for one of thepattern-compatible experiments.

172 e c o l o g i c a l m o d e l l i n g 2 0 6 ( 2 0 0 7 ) 166–178

Fig. 4 – Upstream, downstream and quantile limits of stage distribution according to recruitment level logarithm (dark greygrey

area represents compartments where 50% of eels are found,

grey compartments are where fish are present).

low recruitment levels, the zone of high female production cor-responded to that of high male production. The maximum eelproduction zone moved upstream as recruitment increased,with a greater shift for females than for males.

We also observed an upstream shift in maximum eel abun-dance when recruitment became high, especially for eels over3 years old (Fig. 5).

Results for the location of sexual differentiation and mor-tality processes in the virtual catchment area are as follows.

Sexual differentiation took place in the first downstreamcompartments (Fig. 6). When recruitment increased, the max-imum female differentiation zone moved upstream while themaximum male differentiation zone remained downstream.

Fig. 5 – Upstream, downstream and quantile limits of age

area compartments are where 95% of eels are found, light

Natural mortality also occurred mainly in the downstreamcompartments (Fig. 7).

4. Discussion

4.1. Evaluation of the modelling approach

4.1.1. Comparison with other models of eel dynamics

Compared with other modelling approaches to eel dynamics,the GlobAng model explicitly integrates eel movements andlinks sex determinism and natural mortality with carryingcapacity saturation. This improvement in the representation

distribution according to recruitment level logarithm.

e c o l o g i c a l m o d e l l i n g 2 0 6 ( 2 0 0 7 ) 166–178 173

F w dil

ose

icalsFafb

4aOpa

ig. 6 – Upstream, downstream and quantile limits of the neogarithm.

f eel dynamics introduces an increase in complexity whichhows an original evolution in female and male spawnerscapement associated with recruitment.

However, this model cannot be considered complete, sincet does not cover the entire eel life cycle, being limited to theontinental part only. This limitation is relevant because (i)fter reproduction, eels die and do not contribute to popu-ation dynamics (Bertin, 1951; Fontaine et al., 1982), (ii) thetock–recruitment relationship is still putative (Gascuel andontenelle, 1994), even if Dekker (2004) has recently proposedfirst relationship between a recruitment index and landings

rom fisheries, and (iii) the distribution of leptocephali runsetween catchments is not well documented.

.1.2. Evaluation of the pattern-oriented modelling

pproachur modelling attempt is a successful application of theattern-oriented modelling approach proposed by Grimm etl. (1996). We have defined a pattern based on literature review

Fig. 7 – Upstream, downstream and quantile limits of dead e

fferentiated eel distribution according to recruitment level

and not on a specific well-documented situation. It shouldtherefore be considered as a potential paradigm for eel pop-ulation dynamics. This ecological pattern helps us designand calibrate the model. The fact that we found combina-tions that were compatible with the pattern shows that themodel is not incompatible with the present paradigm of eelpopulation dynamics, even though it does not prove thatthe simulated processes correspond to reality (Levin, 1992).Finally, by exploring the model further we were able to definesecondary comparative predictions (see later), the last step ofthe modelling cycle proposed by Wiegand et al. (2003).

The rejection of more than 95% of the combinations triedcould perhaps appear high. However, it also leads to recon-sider the selection criteria used. The monotonic relationshipbetween recruitment level and the proportion of females in the

silver eel run is very selective. A simple increasing trend couldallow us to retain experiments that are not basically incom-patible with our present knowledge of eel ecology. Similarly,we rejected experiments which did not respect, for at least

el distribution according to recruitment level logarithm.

i n g

174 e c o l o g i c a l m o d e l l

one recruitment level, the decreasing abundance as distancefrom the sea increases. In these cases, maximum abundanceswere situated one or two compartments away from the rivermouth, simply because of the co-action of diffusive move-ment and natural mortality. However, these situations wereobtained only for recruitments close to disappearance level,which have never been observed in reality. The position ofthis maximum is indeed not clear. Smogor et al. (1995) con-sider that this maximum is out at sea, but they were able toobserve eel density only 65 km upstream from the river mouth.Ibbotson et al. (2002) only consider density variations after thetidal limit. There is evidence that the maximum is locatedin the estuary (Tesch, 1977). In fact, glass eels using selec-tive tidal stream transport to cross the estuary (Creutzberg,1958; Gascuel, 1986; Wippelhauser and McCleave, 1988) shouldaccumulate near the tidal limit (McCleave and Wippelhauser,1987; Ciccotti et al., 1995). With this in mind, glass eel move-ment simulation should integrate an advective componentand a tidal zone should be clearly identified in the virtualbasin.

On the other hand, this high rejection rate, giving 291 or28 compatible combinations, could be seen as not selectiveenough because a combination is interpreted as a set of lifehistory traits for the single panmictic European eel stock. Onesolution is to introduce a fitness criterion into the pattern,and then consider only the combination which produces themaximum of female spawners.

4.2. Ecological consequences of modelling results

4.2.1. Sex determinism and sex ratioOur work argues in favour of environmental sex determinism(Krueger and Oliveira, 1999). In fact, the simulation of geno-typic determinism with an equilibrated recruitment sex ratioled systematically to a male-skewed silver eel run, due to theshorter inland life of the male. One way to compensate for thisskewing is to consider a higher natural mortality for malesthan for females, however a mortality difference betweensexes has never been demonstrated for the eel (Naismith andKnights, 1990). The mechanism underlying the relationshipbetween density and sex determinism is still an open ques-tion. It could be mediated by growth rate (Davey and Jellyman,2005) but the model should be improved (to take into accountgrowth and its spatial variability) in order to test this hypoth-esis.

The GlobAng model clearly highlights the fact that the sex-ual differentiation process takes place in the lower part of thebasin, which is in accordance with the downstream locationof undifferentiated eels older than 1 year (Figs. 4 and 5). It istherefore risky to assume a link between yellow eel densityand sex ratio in a specific sector. In particular, the presence offemales in the upper part of the basin results from movementover a long period (Aprahamian, 1988), rather than from sex-ual differentiation in this low-populated sector. On the otherhand, relationships at watershed range (Krueger and Oliveira,1999) are less suspect in that they provide information about

carrying capacity saturation in the lower part of the basinrather than across the whole watershed.

The selection of basic pattern-compatible combinationsgenerated either a male-skewed or female-skewed silver eel

2 0 6 ( 2 0 0 7 ) 166–178

production, in accordance with field observations with asmaller range of recruitment intensity (male-skewed observedby Vollestad and Jonsson, 1988; Castonguay et al., 1994b;De Leo and Gatto, 1995; female-skewed described by Lobon-Cervia et al., 1995; Adam, 1997). We also identified 28combinations which respect the extended pattern (evolu-tion from female-skewed to male-skewed as recruitmentincreases). This outcome should be of interest to eel spe-cialists, because it implies that hydrosystems like the St.Lawrence basin or Norwegian rivers, which currently producefemales only could produce males if recruitment increased.Similarly, if recruitment continues to decrease, femaleswill appear in Spanish rivers which today produce onlymales.

4.2.2. Migratory behaviourIn the GlobAng model structure, we did not separate yelloweels in the migratory and sedentary stages. Only the move-ment rate for older eels (�j+) gives information about eelsedentary level. The uniform distribution of selected values forthis parameter suggests that older eels may still move. How-ever, telemetry tracking demonstrates that individuals overa given length threshold adopt a homing behaviour (Parker,1995; Baras et al., 1998; Lamothe et al., 2000; Aoyama etal., 2002). The movements of older eels could therefore beassociated with home-site changes in response to differentfactors (lack of food, insecurity), as suggested by Baras et al.(1998).

4.2.3. Relation between recruitment and spawnerescapementAll experiments with density-independent mortality, cor-responding to the classical unlimited production with nodensity regulation, were rejected. However, no accepted exper-iment allows a sustained eel stock when recruitment is high,although the first pattern point leaves the possibility of anasymptotic evolution of silver eel production according torecruitment. However, these very high recruitment situationsare more theoretical than ecologically realistic.

In the model proposed by the ICES-EIFAC working group onthe American eel (ICES, 2001a), the relationship between elverand yellow eel is assumed to be either compensatory or over-compensatory according to the level of regulation inducedby habitat. Using our modelling approach, over-compensationappears to be observed for both sexes in the case of huge andunrealistic recruitments and with medium recruitment levelfor females.

4.2.4. Geography of eel population dynamicsEel population dynamics seem to be constrained by phe-nomena in the downstream part of the catchment area. Thecombination of low influence of density on mortality (lownon-null values of v1), low contribution to carrying capac-ity saturation by young eels (low value of ˛w) and highglass eel mobility (high values of �j0) could be interpreted assolutions to the problem of huge saturation compartments

caused by the arrival of large numbers of animals at a singlepoint.

In addition, the female differentiation zone is pushedupstream by the male differentiation zone when recruitment

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ncreases. When abundances are high, no female differen-iates in the first downstream compartments, even thoughome female yellow eel are observed in this zone (Figs. 4 and 6).his means that these eels differentiate upstream and laterolonize the downstream part, which thus accounts for thedownstream migration of estuarine eel” demonstrated bytrontium/calcium microanalysis of the otolith (Daverat et al.,005).

Lastly, even with a simulation of only diffusive eel move-ents, the zone of maximum older yellow eel abundanceoves upstream, especially when recruitment is high (Fig. 5).

he main silver eel production logically follows the samevolution, especially for females (Fig. 4). The upstream shift-ng of these zones is mainly due to a higher mortality inownstream compartments (Fig. 7), as well as to a higher dif-usion to the upstream lower-populated compartments. Byonstruction (pattern point 2) the percentage of females inilver escapement increases with recruitment.

.3. Secondary comparative predictions

his geography of population dynamics leads us to proposen interpretation tool for basin-scale observations. When theain production zone remains downstream, whatever the age

f the eels, the basin is not saturated and produces mainlyemales. Conversely, if we observe an upstream shifting oflder eels, then the basin is saturated in its downstream partnd will produce more and more males.

Furthermore, this tool could be considered as a firstecondary prediction to be compared with actual field obser-ations, some of which support our proposal. We can interprethe Severn results (Aprahamian, 1988; Ibbotson et al., 2002) byonsidering that this basin is not fully saturated, so that, forll eel age classes, there is a decrease in density from the tidalimit but it is sufficiently saturated to produce some males inhe lower part. This situation corresponds to a recruitmentevel in our figures of between 103 and 104 individuals per sea-on. Likewise, the observations of Lobon-Cervia et al. (1995)gree with our prediction. These authors show an increas-ng upstream density of the largest eels in the Esva River inccordance with the high density (probably close to carryingapacity saturation) and with the almost entirely male produc-ion. Our model simulates a comparable spatial organisationor high recruitment values (i.e. around 1010 individuals pereason).

On the other hand, the estimation of silver eel origins in thet. Lawrence River basin seems to contradict our prediction.he quasi-exclusive female production (Nilo and Fortin, 2001)uggests that recruitment is low compared with the basin’sarrying capacity and that therefore the maximum produc-ion zone should be in the lower part of the watershed. Inact, 60–70% of silver eel caught by fisheries seem to comerom Lake Ontario, 400 km from the river mouth (Dutil et al.,985; Couillard et al., 1997; Verreault and Dumont, 2003). Thisivergence could be explained by environmental characteris-ics (e.g. drastic winter conditions) or more likely by a lower

arrying capacity of the downstream part of the river thanhe Lake Ontario system. It could also be related to the exis-ence of more complex movement behaviours, as suggestedy Feunteun et al. (2003).

6 ( 2 0 0 7 ) 166–178 175

We can propose field experiments to validate other sec-ondary comparative predictions. For example, knowledge ofthe zone used by undifferentiated eels will clarify the effectof density dependence on sex determinism and enable us todefine more precisely the concept of carrying capacity in rela-tion to eels. Studies of stock identification and quantificationshould also be promoted in order to determine the contribu-tion of each tributary to global silver eel production. Silver eelrun quantification like that performed by Caron et al. (2003)or Feunteun et al. (2000) associated with geochemical signa-ture in otoliths (Wells et al., 2003) could help answer this andrelated questions.

4.4. Management advice

The GlobAng model was designed to summarize our knowl-edge of eel population dynamics and not specifically to answermanagement questions. Nevertheless, results from this workenable us to provide some information on the identification,location and evaluation of the potential efficiency of actionsand mitigation measures that could further European eelrecovery and future monitoring of the evolution of the statusof this species at risk.

It is clear that, for social or political reasons, basin-widemanagement could be justified (Casselman, personal commu-nication). However, our results show that in order to maximizethe effect of any actions that are implemented, eel manage-ment should now concentrate on the downstream part ofbasins because (i) sex determinism takes place there, and (ii)this sector appears to be the maximum production area forboth males and females, especially when recruitment is low,as in the current situation.

Secondly, an increase in female production could be a con-sequence of the decrease in recruitment and should be a cue toimplement a management plan quickly rather than postponeit. Likewise, a reduction in mortality could lead to a counter-intuitive reduction in female silver eel escapement, due to theenvironmental sex determinism hypothesis.

Thirdly, restocking with undifferentiated material inuncrowded sectors could help produce more females andcould therefore contribute to the restoration of eel stock. How-ever, the removal of fish for this purpose would reduce theregular upstream colonization in the source catchment area.The consequences of restocking should be carefully weighedbefore implementation.

Finally, this population dynamics model confirms the clas-sical result (Feunteun, 2002) concerning the delay betweenincreases in recruitment and escapement (unpublishedresult) and therefore highlights the fact that manage-ment efforts should be implemented over a long period oftime.

It is clear that the conclusions of such a paradigmaticmodel have only a theoretical usefulness and have to becompared with field reality. However, the validity of theseconclusions is confirmed by our present knowledge of eelecology. They can certainly be used to assist in management

decision-making (Johnson, 1995). In future, the GlobAng modelshould test precise alternative management options (Gatto etal., 1982), especially watershed planning and spatial fisherymanagement.

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176 e c o l o g i c a l m o d e l l

5. Conclusions

This approach to population dynamics modelling (GlobAng)is the first to integrate movement at the watershed scale.Because of our incomplete knowledge of some of the pro-cesses, especially those dependent on density, we chose tocarry out a theoretical exploration with a paradigmatic patternof continental eel population dynamics.

We identified parameter combinations that are compati-ble with the ecological pattern established from a literaturereview and produced the modelling cycle by analysing thegeography of eel dynamics. We then defined secondary com-parative predictions which can be used to validate the modelvia field observations. Our approach is based on a simplifiedassumption about the river structure. Results will have to beconfirmed, using a more complex hydrological network in afuture work.

This work also poses questions about pattern quality,showing above all that it is necessary to document the patternin actual watersheds.

Acknowledgements

This study was funded by the European Union (Feder), theMinistere de l’ecologie et du developpement durable (GRISAMprogram), the Conseil Regional d’Aquitaine and the Agence del’eau Adour Garonne (ECOBAG program). We thank ChristianMullon for his valuable advice on a preliminary version of thismanuscript and two anonymous referees for their construc-tive suggestions.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version, at doi:10.1016/j.ecolmodel.2007.03.033.

e f e r e n c e s

Adam, G., 1997. L’anguille europeenne (Anguilla anguilla L. 1758):dynamique de la sous-population du lac de Grand-Lieu enrelation avec les facteurs environnementaux et anthropiques.Doctorat de l’universite en hydrobiologie, Universite PaulSabatier, Toulouse, 353 pp.

Aoyama, J., Sasai, S., Miller, M.J., Shinoda, A., Nakamura, A.,Kawazu, K., Tsukamoto, K., 2002. A preliminary study of themovements of yellow and silver eels, Anguilla japonica, in theestuary of the Fukui River, Japan, as revealed by acoustictracking. Hydrobiologia 470, 31–36.

Aprahamian, M.W., 1988. Age structure of eel (Anguilla anguilla L.)population in the rivers Severn (England) and Dee (Wales).Aquacult. Fish. Manage. 19, 365–376.

Baras, E., Jeandrain, D., Serouge, B., Philippart, J.C., 1998. Seasonalvariations in time and space utilization by radio-tagged

yellow eels Anguilla anguilla (L.) in a small stream.Hydrobiologia 372, 187–198.

Bertin, L., 1951. Les anguilles, variation, croissance, euryhalinite,toxicite, hermaphrodisme, juvenile, sexualite, migrations,metamorphoses. Payot, Paris, 188 pp.

2 0 6 ( 2 0 0 7 ) 166–178

Bisgaard, J., Pedersen, M.I., 1991. Mortality and growth of wildand introduced cultured eels (Anguilla anguilla (L)) in a Danishstream, with special reference to a new tagging technique.Dana 9, 57–69.

Boetius, J., Harding, E.F., 1985. List of Atlantic and MediterraneanAnguilla anguilla leptocephali: Danish material up to 1966. Dana4, 163–249.

Brusle, J., 1990. L’anguille europeenne (Anguilla anguilla), uneespece jugee commune jusqu’a la derniere decennie,merite-t-elle d’acquerir aujourd’hui le statut d’especemenacee ? Bull. Soc. Zool. France 114, 61–73.

Caron, F., Verreault, G., Rochard, E., 2003. Estimation of thepopulation size, exploitation rate, and escapement ofsilver-phase American eels in the St. Lawrence watershed. In:Dixon, D.A. (Ed.), Proceedings of the Biology, Management,and Protection of Catadromous Eels, American FisheriesSociety Symposium. Bethesda, MD, USA, pp. 235–242.

Castonguay, M., Hodson, P.V., Moriarty, C., Drinkwater, K.F., Jessop,B.M., 1994a. Is there a role of ocean environment in Americanand European eel decline? Fish. Oceanogr. 3, 197–203.

Castonguay, M., Hodson, P.V., Couillard, C.M., Eckersley, M.J.,Dutil, J.D., Verreault, G., 1994b. Why is recruitment of theAmerican eel, Anguilla rostrata, declining in the St. LawrenceRiver and Gulf? Can. J. Fish. Aquat. Sci. 51, 479–488.

Chancerel, F., 1994. Distribution de l’anguille europeenne enFrance. Bull. Francais Peche Piscicult. 335, 289–294.

Ciccotti, E., Ricci, T., Scardi, M., Fresi, E., Cataudella, S., 1995.Intraseasonal characterization of glass eel migration in theRiver Tiber—space and time dynamics. J. Fish Biol. 47,248–255.

Colombo, G., Rossi, R., 1978. Environmental influences on growthand sex ratio in different eel populations (Anguilla anguilla L.)of Adriatic coasts. In: McLusky, D.S., Berry, A.J. (Eds.),Physiology and Behaviour of Marine Organisms. PergamonPress, Oxford, pp. 313–320.

Colombo, G., Grandi, G., 1996. Histological study of thedevelopment and sex differentiation of the gonad in theEuropean eel. J. Fish Biol. 48, 493–512.

Couillard, C.M., Hodson, P.V., Castonguay, M., 1997. Correlationsbetween pathological changes and chemical contamination inAmerican eels, Anguilla rostrata, from the St. Lawrence River.Can. J. Fish. Aquat. Sci. 54, 1916–1927.

Creutzberg, F., 1958. Use of tidal streams by migrating elvers(Anguilla vulgaris Turt). Nature 181, 357–358.

Daverat, F., Tomas, J., Lahaye, M., Palmer, M., Elie, P., 2005.Tracking continental habitat shifts of eels using otolith Sr/Caratios: validation and application to the coastal, estuarine andriverine eels of the Gironde–Garonne–Dordogne watershed.Marine Freshwater Res. 56, 619–627.

Daverat, F., Limburg, K.E., Thibault, I., Shiao, J.C., Dodson, J.D.,Caron, F., Tzeng, W.-N., Iizuka, Y., Wickstrom, H., 2006.Phenotypic plasticity of habitat use by three temperate eelspecies Anguilla anguilla, A. japonica and A. rostrata. MarineEcol. Progr. Ser. 308, 231–241.

Davey, A., Jellyman, D., 2005. Sex determination in freshwatereels and management options for manipulation of sex. Rev.Fish Biol. Fish. 15, 37–52.

De Leo, G.A., Gatto, M., 1995. A size and age-structured model ofthe European eel (Anguilla anguilla L.). Can. J. Fish. Aquat. Sci.52, 1351–1367.

De Leo, G.A., Gatto, M., 1996. Trends in vital rates of the Europeaneel: evidence for density dependence? Ecol. Appl. 6, 1281–1294.

Dekker, W., 1996. A length-structured matrix population modelused as a fish stock assessment tool. In: Cowx, I.G (Ed.), Stock

Assessment in Inland Fisheries. Fishing News Books, pp.245–259.

Dekker, W., 2000a. The fractal geometry of the European eelstock. Ices J. Marine Sci. 57, 109–121.

g 2 0

D

D

D

D

D

D

D

D

E

F

F

F

F

F

G

G

G

G

e c o l o g i c a l m o d e l l i n

ekker, W., 2000b. A Procrustean assessment of the European eelstock. Ices J. Marine Sci. 57, 938–947.

ekker, W., 2000c. Impact of yellow eel exploitation on spawnerproduction in lake IJsselmeer, vol. 12. Dana, The Netherlands,pp. 17–32.

ekker, W., 2004. Slipping through our hands. Populationdynamics of the European eel. Ph.D., University ofAmsterdam, 186 pp.

hondt, A.A., 1988. Carrying capacity: a confusing concept. ActaOecol. 9, 337–346.

omingos, I., Costa, J.L., Costa, M.J., 2006. Factors determininglength distribution and abundance of the European eel,Anguilla anguilla, in the River Mondego (Portugal). FreshwaterBiol. 51, 2265–2281.

urif, C., 2003. La migration d’avalaison de l’anguille europeenneAnguilla anguilla: Caracterisation des fractions devalantes,phenomene de migration et franchissement d’obstacles.Doctorat de l’universite en Ecologie Aquatique, UniversitePaul Sabatier, Toulouse III, Toulouse, 359 pp.

urif, C., Elie, P., Dufour, S., Marchelidon, J., Vidal, B., 2000.Analyse des parametres morphologiques et physiologiqueslors de la preparation a la migration de devalaison chezl’anguille europeenne (Anguilla anguilla) du lac de Grand-Lieu(Loire-Atlantique). Cybium 24, 63–74.

util, J.D., Legare, B., Desjardins, C., 1985. Discrimination d’unstock de poisson, l’anguille (Anguilla rostrata), basee sur lapresence d’un produit chimique de synthese, le mirex. Can. J.Fish. Aquat. Sci. 42, 455–458.

lie, P., Rochard, E., 1994. Migration des civelles d’anguilles(Anguilla anguilla L.) dans les estuaires, modalite duphenomene et caracteristiques des individus. Bull. FrancaisPeche Piscicult. 335, 81–98.

eunteun, E., 2002. Management and restoration of European eelpopulation (Anguilla anguilla): an impossible bargain. Ecol.Eng. 18, 575–591.

eunteun, E., Acou, A., Laffaille, P., Legault, A., 2000. European eel(Anguilla anguilla): prediction of spawner escapement fromcontinental population parameters. Can. J. Fish. Aquat. Sci. 57,1627–1635.

eunteun, E., Acou, A., Guillouet, J., Laffaille, P., Legault, A., 1998.Spatial distribution of an eel population (Anguilla anguilla L.)in a small coastal catchment of northern Brittany (France).Consequences of hydraulic works. Bull. Francais PechePiscicult. 349, 129–139.

eunteun, E., Laffaille, P., Robinet, T., Briand, C., Baisez, A., Olivier,J.M., Acou, A., 2003. A review of upstream migration andmovements in inland waters by anguillid eels. Towards ageneral theory. In: Aida, K., Tsukamoto, K., Yamauchi, K.(Eds.), Eel Biology. Springer-Verlag, Tokyo, pp. 191–213.

ontaine, M., Delerue-Le Belle, N., Lallier, F., Lopez, E., 1982.Biologie generale. Toutes les anguilles succombent-elles apresla reproduction et frayent-elles necessairement en mer?Comptes Rendus de l’Academie des Sciences-SeriesIII-Sciences de la Vie 294, 809–811.

ascuel, D., 1986. Flow carried and active swimming migration ofthe glass eel (Anguilla anguilla) in the tidal area of a smallestuary on the French Atlantic coast. HelgolanderMeeresuntersuchungen 40, 321–326.

ascuel, D., Fontenelle, G., 1994. Approche conceptuelle de lamodelisation de la dynamique du stock d’anguilles dans unbassin versant: interet et adaptation du modele de rendementpar recrue. Bull. Francais Peche Piscicult. 332, 43–56.

atto, M., Laniado, E., Rossi, R., 1982. The management of eels inthe Valli di Comacchio lagoon. Oceanol. Acta, sp, 303–307.

lova, G.J., Jellyman, D.J., Bonnett, M.L., 1998. Factors associatedwith the distribution and habitat of eels (Anguilla spp.) inthree New Zealand lowland streams. NZ J. Marine FreshwaterRes. 32, 255–269.

6 ( 2 0 0 7 ) 166–178 177

Goodwin, K.A., Angermeier, P.L., 2003. Demographiccharacteristics of American eel in the Potomac River drainage,Virginia. Trans. Am. Fish. Soc. 132, 524–535.

Grandi, G., Colombo, G., 1997. Development and earlydifferentiation of gonad in the European eel (Anguilla anguilla[L.], Anguilliformes, Teleostei): a cytological andultrastructural study. J. Morphol. 231, 195–216.

Grimm, V., 1999. Ten years of individual-based modelling inecology: what have we learned and what could we learn inthe future? Ecol. Model. 115, 129–148.

Grimm, V., Frank, K., Jeltsch, F., Brandl, R., Uchmanski, J., Wissel,C., 1996. Pattern-oriented modelling in population ecology.Sci. Total Environ. 183, 151–166.

Holmgren, K., 1996. Effect of water temperature and growthvariation on the sex ratio of experimentally reared eels. Ecol.Freshwater Fish 5, 203–212.

Holmgren, K., Wickstrom, H., Clevestam, P., 1997. Sex-relatedgrowth of European eel, Anguilla anguilla, with focus onmedian silver eel age. Can. J. Fish. Aquat. Sci. 54, 2775–2781.

Ibbotson, A., Smith, J., Scarlett, P., Aprahamian, M.W., 2002.Colonisation of freshwater habitats by the European eelAnguilla anguilla. Freshwater Biol. 47, 1696–1706.

ICES, 1999. Report of the ICES Advisory Committee on FisheriesManagement. ICES Cooperative Research Report, pp. 393–405.

ICES, 2001a. Report of the ICES/EIFAC Working Group on Eels,ICES/EIFAC, St Andews, Canada, 87 pp.

ICES, 2001b. Report of the ICES Advisory Committee on FisheryManagement, 2001. European eel ICES Cooperative ResearchReport, pp. 357–366.

ICES, 2002. Report of the ICES Advisory Committee on FisheryManagement, 2002. ICES Cooperative Research Report, pp.940–948.

Johnson, B.L., 1995. Applying computer simulation as learningtools in fishery management. North Am. J. Fish. Manage. 15,736–747.

Knights, B., 2003. A review of the possible impacts of long-termoceanic and climate changes and fishing mortality onrecruitment of anguillid eels of the Northern Hemisphere. Sci.Total Environ. 310, 237–244.

Krueger, W.H., Oliveira, K., 1999. Evidence for environmental sexdetermination in the American eel, Anguilla rostrata. Environ.Biol. Fishes 55, 381–389.

Laffaille, P., Feunteun, E., Baisez, A., Robinet, T., Acou, A., Legault,A., Lek, S., 2003. Spatial organisation of European eel (Anguillaanguilla) in a small catchment. Ecol. Freshwater Fish 12,254–264.

Lambert, P., Rochard, E., Elie, P., 1995. A Study of the EstuarialMigration of Civelles (Anguilla anguilla L., 1758) usingIndividual based Simulation. ICES/CIEM, Anacat Committee,Aalborg, Danemark, 8 pp.

Lambert, P., Feunteun, E., Crivelli, A.J., 2003. L’anguille, un defipour les scientifiques. Compte rendu des journees du Grisam,La Tour du Valet, 26–29 mars 2001. Bull. Francais PechePiscicult. 368, 1–8.

Lamothe, P.J., Gallagher, M., Chivers, D.P., Moring, J.R., 2000.Homing and movement of yellow-phase American eels infreshwater ponds. Environ. Biol. Fishes 58, 393–399.

Levin, S.A., 1992. The problem of pattern and scale in ecology.Ecology 73, 1943–1967.

Lobon-Cervia, J., Utrilla, C.G., Rincon, P.A., 1995. Variations in thepopulation dynamics of the European eel Anguilla anguilla (L.)along the course of a Cantabrian river. Ecol. Freshwater Fish 4,17–27.

Manly, B.F.J., 1990. Stage-structured Populations. Sampling,

Analysis and Simulation. Chapman and Hall, London, 187 pp.

McCleave, J.D., Wippelhauser, G.S., 1987. Behavioural aspects ofselective tidal stream transport in juvenile American eels.Am. Fish. Soc. Symp. 1, 138–150.

i n g

American eel abundance in five river basins in Maryland.

178 e c o l o g i c a l m o d e l l

Moriarty, C., Dekker, W. (Eds.), 1997. Management of the EuropeanEel, p. 110.

Mullon, C., Freon, P., Parada, C., van der Lingen, C.D., Huggett, J.,2003. From particles to individuals: modelling the early stagesof anchovy (Engraulis capensis/encrasicolus) in the southernBenguela. Fish. Oceanogr. 12, 396–406.

Naismith, I.A., Knights, B., 1990. Modelling of unexploited andexploited populations of eels Anguilla anguilla (L.), in theThames estuary. J. Fish Biol. 37, 975–986.

Nilo, P., Fortin, R., 2001. Synthese des connaissances etetablissement d’une programmation de recherche surl’anguille d’Amerique (Anguilla rostrata). Universite du Quebeca Montreal, Departement des Sciences biologiques pour laSociete de la faune et des parcs du Quebec, Direction de larecherche sur la faune, Quebec, 298 pp.

Okubo, A., Levin, S.A., 2001. Diffusion and Ecological Problems:Modern Perspectives. Springer-Verlag, New York, USA, 467 pp.

Oliveira, K., 1999. Life history characteristics and strategies of theAmerican eel, Anguilla rostrata. Can. J. Fish. Aquat. Sci. 56,795–802.

Oliveira, K., McCleave, J.D., Wippelhauser, G.S., 2001. Regionalvariation and the effect of lake: river area on sex distributionof American eels. J. Fish Biol. 58, 943–952.

Parker, S.J., 1995. Homing ability and home range of yellow phaseAmerican eels in a tidally dominated estuary. J. Marine Biol.Assoc. U.K. 75, 127–140.

Parsons, J., Vickers, K.U., Warden, Y., 1977. Relationship betweenelver recruitment and changes in the sex ratio of silver eelsAnguilla anguilla L. migrating from Lough Neagh, NorthernIreland. J. Fish Biol. 10, 211–229.

Poole, W.R., Reynolds, J.D., Moriarty, C., 1990. Observations on thesilver eel migrations of the Burrishoole River system, Ireland,1959 to 1988. Int. Rev. Gesamten Hydrobiol. 75, 807–815.

Railsback, S.F., 2001. Concepts from complex adaptive systems asa framework for individual-based modelling. Ecol. Model. 139,47–62.

Roncarati, A., Melotti, P., Mordenti, O., Gennari, L., 1997. Influenceof stocking density of European eel (Anguilla anguilla, L.) elverson sex differentiation and zootechnical performances. J. Appl.Ichthyol. 13, 131–136.

Rossi, R., Carrieri, A., Franzoi, P., Cavallini, G., Gnes, A., 1987. Astudy of eel (Anguilla anguilla L.) population dynamics in theComacchio lagoons (Italy) by mark-recapture method. Oebalia

XIV, 1–14.

Schmidt, J., 1922. The breeding places of the eel. Philos. Trans. R.Soc. Lond. B: Biol. Sci. 211, 179–208.

Smogor, R.A., Angermeier, P.L., Gaylord, C.K., 1995. Distributionand abundance of American eels in Virginia Streams—tests of

2 0 6 ( 2 0 0 7 ) 166–178

null models across spatial scales. Trans. Am. Fish. Soc. 124,789–803.

Svardson, G., 1976. The decline of the Baltic eel population.Report of the Institute of Freshwater Research Drottningholm,55: 136–143.

Tesch, F.W., 1977. The Eel. Chapman and Hall, London, 434 pp.Tesch, F.W., 2003. The Eel. Blackwell Publishing, 408 pp.Tsukamoto, K., Nakai, I., Tesch, F.W., 1998. Do all freshwater eels

migrate? Nature 396, 635–636.Verreault, G., Dumont, P., 2003. An estimation of American eel

escapement from the Upper St. Lawrence River and LakeOntario in 1996 and 1997. In: Dixon, D.A. (Ed.), Proceedings ofthe Biology, Management, and Protection of CatadromousEels, American Fisheries Society Symposium. Bethesda, MD,USA, pp. 243–251.

Vollestad, L.A., 1992. Geographic variation in age and length atmetamorphosis of maturing European eel—environmentaleffects and phenotypic plasticity. J. Animal Ecol. 61, 41–48.

Vollestad, L.A., Jonsson, B., 1988. A 13-year study of thepopulation dynamics and growth of the European eel Anguillaanguilla in a Norwegian river: evidence for density-dependentmortality, and development of a model for predicting yield. J.Animal Ecol. 57, 983–997.

Wells, B.K., Rieman, B.E., Clayton, J.L., Horan, D.L., Jones, C.M.,2003. Relationships between water, otolith, and scalechemistries of westslope cutthroat trout from the Coeurd’Alene River, Idaho: the potential application of hard-partchemistry to describe movements in freshwater. Trans. Am.Fish. Soc. 132, 409–424.

Whitehead, H., 2000. Density-dependent habitat selection andthe modeling of sperm whale (Physeter macrocephalus)exploitation. Can. J. Fish. Aquat. Sci. 57, 223–230.

Wiberg, U.H., 1983. Sex determination in the European eel(Anguilla anguilla, L.). A hypothesis based on cytogeneticresults, correlated with the findings of skewed sex ratios ineel culture ponds. Cytogenet. Cell Genet. 36, 589–598.

Wiegand, T., Jeltsch, F., Hanski, I., Grimm, V., 2003. Usingpattern-oriented modeling for revealing hidden information:a key for reconciling ecological theory and application. Oikos100, 209–222.

Wiley, D.J., Morgan II, R.P., Hilderbrand, R.H., Raesly, R.L.,Shumway, D.L., 2004. Relations between physical habitat and

Trans. Am. Fish. Soc. 133, 515–526.Wippelhauser, G.S., McCleave, J.D., 1988. Rhythmic activity of

migrating juvenile American eels Anguilla rostrata. J. MarineBiol. Assoc. U.K. 68, 81–91.