Patterns in time
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Transcript of Patterns in time
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Patterns in time
-3-2-10123
1964 1968 1972 1976 1980
Oulu-3-2-10123
1964 1968 1972 1976 1980
Vaasa
-3-2-10123
1964 1968 1972 1976 1980
Häme-3-2-10123
1964 1968 1972 1976 1980
Turku-Pori
-3-2-10123
1964 1968 1972 1976 1980
Central Finland
-3-2-10123
1964 1968 1972 1976 1980
Uusimaa
-3-2-10123
1964 1968 1972 1976 1980
Lapland-3-2-10123
1964 1968 1972 1976 1980
Kuopio-3-2-10123
1964 1968 1972 1976 1980
North Karelia
-3-2-10123
1964 1968 1972 1976 1980
Mikkeli-3-2-10123
1964 1968 1972 1976 1980
Kymi
Population dynamics (1964 to 1983) of the red squirrel in 11 provinces of Finland (Ranta et al. 1997)
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Number of ly
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tra
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Study time (years)
Ab
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nc
e i
nd
ex
Lynx fur in Canada
Voles in Norway
Mean abundance
Upper limit (carrying capacity)
Lower limit (extinction treshold)Elton and Nicholson (1942 )
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GenerationSpecies1.00 0.71 1.25 1.27 6.36 12.50 14.52 50.84 49.072.00 0.93 1.10 3.43 0.55 14.30 15.06 31.47 27.853.00 0.09 0.83 2.08 2.45 12.34 15.45 26.01 61.754.00 0.97 0.06 0.35 3.51 13.08 27.56 5.57 44.995.00 0.14 0.60 0.56 4.33 13.47 9.86 28.64 30.706.00 0.33 1.44 3.22 4.89 15.39 27.84 34.93 39.657.00 0.63 0.41 0.94 0.87 14.89 2.87 49.46 61.228.00 0.96 0.06 2.31 6.81 12.76 28.50 48.08 60.169.00 0.20 1.48 0.90 3.43 8.08 25.14 60.29 51.97
10.00 0.30 1.49 2.80 4.60 15.75 1.52 46.60 24.2611.00 0.96 0.36 2.49 1.40 7.67 25.94 51.83 48.5712.00 0.38 0.19 3.52 5.56 1.64 28.19 24.89 4.7813.00 0.09 1.52 2.39 7.02 9.82 5.54 18.72 12.0614.00 0.88 1.10 0.43 1.23 6.92 24.29 55.69 34.6615.00 0.16 1.30 3.69 1.43 4.06 1.99 1.03 10.1516.00 0.45 1.76 2.24 4.43 8.46 17.37 7.02 36.2517.00 0.20 1.27 0.11 6.41 9.32 6.64 12.77 1.6318.00 0.83 1.60 0.12 0.04 9.55 17.38 19.19 22.0819.00 0.97 0.99 0.59 4.49 14.33 6.77 46.32 47.9120.00 0.36 0.59 1.29 0.32 0.40 4.29 46.40 7.69
Mean 0.53 0.97 1.74 3.51 10.24 15.34 33.29 33.87Variance 0.12 0.30 1.48 5.40 20.10 98.09 334.99 380.96
Taylor’s power law
Assume an assemblage of species, which have different mean abundances and fluctuate at random but proportional to their abundance.
The relationship between variance and mean follows a power function of the form
2 2a
Going Excel
Taylor’s power law; proportional rescaling
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Abu
ndan
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z
y = 0.34x2.0
R2 = 0.99
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Var
ianc
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Taylor’s power law
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0.35
0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4
Variance category
Per
cent
age
Taylor’s power law in aphids (red), moths (green) and birds (blue). In all three groups the exponent z of the relation s2 = a mz peakes around 2.
Data from Taylor et al. (1980).
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Major results from this database are that
The variance – mean relationship of most populations follows Taylors power law
z = 2 is equivalent to a random walk
Z =<< 2 is required for population regulation
2 zN
The majority of species has 1.5 < z < 2.5
Long term studies of population variability
Most populations, in particular invertebrate populations are not regulated!
They are not in equilibrium
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0.00
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ndan
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z
0.001.002.003.004.005.006.00
0.00 5.00 10.00 15.00 20.00Generation
Abu
ndan
ce
z
0.001.002.003.004.005.006.007.00
0.00 5.00 10.00 15.00 20.00Generation
Abu
ndan
ce
z
2 1a
2 2a
2 0a
Ecological implications
2 za
Temporal variability is a random walk in time
Abundances are not regulated
Extinctions are frequent
Temporal species turnover is high
Temporal variability is intermediate
Abundances are or are not regulated
Extinctions are less frequent
Temporal species turnover is low
Temporal variability is low
Abundances are often regulated
Extinctions are rare
Temporal species turnover is very low
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2ln( ) ln( )(ln( )) ln( )2E
R
N NT N KVar
Mean time to extinction Extinction probability
Under the assumption of Taylor’s power law (a simple random walk in time without density dependent population regulation and lower extinction boundary)
we can calculate the frequency of local extinction
1.42)2
)20000ln(100000(ln42.5
)20000ln(2 ET
)(ln1 NTt
tEeP
02.01 1.421
1 eP
)(ln2
1
1
rsVar
NNr
rNN
R
t
t
tt
Abundances (ind.m-2)
Year Eustochus atripennis
Exallonyx ater
1981 1.78 1.81982 4.15 2.51983 5 2.71984 36 1.31985 0.8 0.81986 8.8 0.81987 2 0.5
K 10 3
Abundances (ind.ha-2)
Eustochus atripennis
Exallonyx ater
17800 1800041500 2500050000 27000360000 130008000 8000
88000 800020000 5000
100000 30000
Reproduction rate
ln r ln r
0.85 0.330.19 0.081.97 -0.73-3.81 -0.492.40 0.00
-1.48 -0.47
Variance 5.42 0.17
TE 42.101 1056.342
K 0.023 0.001
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Number if individuals
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mal
ized
num
ber o
f ex
tinct
ions
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Mean number of nesting pairs
Ext
inct
ion
prob
abili
ty
y = 0.06 / x y = 0.96x + 0.55R2 = 0.46
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ln (e
xtin
ctio
n tim
e)
How many individuals do populations need to survive (lower extinction boundary)?
Orb web spiders on the Bahama islands (Schoener 1983)
Birds on small islands off the British coast (Pimm 1991)
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inct
ion
prob
abili
ty
Number of patchesEmigrationrate
Parasitic Hymenoptera (Hassell et al. 1991)
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The species – time relationshipLocal species area and species time relationships in a temperate Hymenoptera community
studied over a period of eight years.
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0 5 10t
Turn
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S = S0Az S = S0ttS = S0Aztt
The accumulation of species richness in space and time follws a power function model
S = (73.0 ± 1.7)A(0.41 ± 0.01) t(0.094 ± 0.01)
The mean extinction probability per year is about 9%
Photo E. G. Vallery
Coeloides pissodis (Braconidae)
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-3-2-10123
1964 1968 1972 1976 1980
Oulu-3-2-10123
1964 1968 1972 1976 1980
Vaasa
-3-2-10123
1964 1968 1972 1976 1980
Häme-3-2-10123
1964 1968 1972 1976 1980
Turku-Pori
-3-2-10123
1964 1968 1972 1976 1980
Central Finland
-3-2-10123
1964 1968 1972 1976 1980
Uusimaa
-3-2-10123
1964 1968 1972 1976 1980
Lapland-3-2-10123
1964 1968 1972 1976 1980
Kuopio-3-2-10123
1964 1968 1972 1976 1980
North Karelia
-3-2-10123
1964 1968 1972 1976 1980
Mikkeli-3-2-10123
1964 1968 1972 1976 1980
Kymi
Population dynamics (1964 to 1983) of the red squirrel in 11 provinces of Finland
The Moran effect
Regional sychronization of local abundances due to correlated environmental effects
Patrick A.P. Moran 1917-1988
t t 1 t 2 A
t t 1 t 2 B
N (A) f (N (A), N (A))N (B) f (N (B), N (B))
A B
Moran assumed:1. Linear density dependence2. Density dynamics are identical3. Stochastic effects are correlated
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0100000200000300000400000500000600000700000
Acr
es D
efol
iate
d Maine
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es D
efol
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Acr
es D
efol
iate
dVermont
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New Hampshire
Massachusetts
Year20 30 40 50 60 70 80 90
Defoliation by gypsy moths in New England states
Lymantria dispar
Data from Williams and Liebhold (1995)
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Species turnover rates differ between groups of animals and plants
Larger animal species have lower turnover rates
Despite high turnover rates total species numbers of
habitats remain largely constant.
This constancy holds for ecological, historical and
evolutionary times
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E-04 1.E-03 1.E-02 1.E-01 1.E+001.E+011.E+021.E+03
Generation time
Turn
over
rate
(%/y
r)Protozoa
Sessile marine organisms
Arthropoda
Birds
Lizards
Vascular plants
Body weight
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1977 1982 1987 1992 1997
YearN
umbe
r of s
peci
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02000400060008000
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Num
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f spe
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f spe
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Year
Num
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Desert rodents
Birds
Plants
Plants
Species turnover rates (Brown et al. 2001)
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Speciation rates, latitudinal gradients, and macroecology
What causes the latitudinal gradient in species diversity?TemperatureHow does temperature influences species richness?SpeciationExtinction
Metabolic theory predicts that generation time t should scale to body weight and temperature to
1/ 4 E / kTW e
The theory predicts further that mutation rate should scale to
body weight and temperature to
How does mean generation time decreases if we increase mean
environmental temperature from 5º to 30 º?
Mutation rates are predicted to increase by the same factor
Evolutionary speed can be seen as the product of mutation rates and generation turnover (1/t).
Still unclear is how temperature influences extinction rates.
E1/ 4 kTt w e 11.0
38.91
)5()30(
)2735/(7541
)27330/(7541
ee
tt
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Today’s reading
Minimum viable population size: http://en.wikipedia.org/wiki/Minimum_viable_population
Long term ecological research: http://www.lternet.edu/
Kinetic effects of temperature on speciation: http://www.pnas.org/content/103/24/9130.full.pdf
Paleobiology: http://findarticles.com/p/articles/mi_m2120/is_n5_v77/ai_18601045