Slajd 1

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Patterns in time
Population dynamics (1964 to 1983) of the red
squirrel in 11 provinces of Finland (Ranta et al.
1997)
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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Taylors power law
Assume an assemblage of species, which have
different mean abundances and fluctuate at random
but proportional to their abundance.
Going Excel
The relationship between variance and mean
follows a power function of the form
Taylors power law proportional rescaling
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Taylors power law
Taylors 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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In a second example the variability is
independent from the mean abundance
The relationship between variance and mean is
constant
5
Long term studies of population variability
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 ltlt 2 is required for
population regulation
The majority of species has 1.5 lt z lt 2.5
Most populations, in particular invertebrate
populations are not regulated! They are not in
equilibrium
The frequency of extinction
Mean time to extinction
Extinction probability
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Ecological implications
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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Return times and population stability
N
Exponential population growth
K
dN
dt
t
Tangent at K
Characteristic return rate
Return rates gtgt 2 chaotic fluctuations (no
density dependences Return rates lt 0 population
goes extinct Return rates 1 density
dependence fast return to equilibrium
Bony fish
Birds
Mammals
Insects
Figure from Sibly et al. 2007
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The Moran effect Regional sychronization of
local abundances due to correlated environmental
effects
Population dynamics (1964 to 1983) of the red
squirrel in 11 provinces of Finland
Patrick A.P. Moran 1917-1988
Moran assumed 1. Linear density dependence 2.
Density dynamics are identical 3. Stochastic
effects ? are correlated
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Defoliation by gypsy moths in New England states
700000
Maine
600000
500000
400000
Acres Defoliated
300000
200000
100000
0
2500000
New Hampshire
2000000
1500000
Acres Defoliated
1000000
500000
0
140000
120000
Vermont
100000
Lymantria dispar
80000
Acres Defoliated
60000
40000
20000
0
3000000
Massachusetts
2500000
2000000
Acres Defoliated
1500000
1000000
500000
0
Year
Data from Williams and Liebhold (1995)
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How many individuals do populations need to
survive?
Orb web spiders on the Bahama islands (Schoener
1983)
Parasitic Hymenoptera (Hassell et al. 1991)
Birds on small islands off the British coast
(Pimm 1991)
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Species turnover rates (Brown et al. 2001)
Species turnover rates differ between groups of
animals and plants Larger animal species have
lower turnover rates
Desert rodents
Plants
Despite high turnover rates total species numbers
of habitats remain largely constant. This
constancy holds for ecological, historical and
evolutionary times
Birds
Plants
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The species time relationship
Local species area and species time relationships
in a temperate Hymenoptera community studied over
a period of eight years.
S S0Az
S S0tt
S S0Aztt
The accumulation of species richness in space and
time follws a power function model
Coeloides pissodis (Braconidae)
Photo E. G. Vallery
S (73.0 1.7)A(0.41 0.01) t(0.094 0.01)
The mean extinction probability per year is about
9
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Speciation rates, latitudinal gradients, and
macroecology
What causes the latitudinal gradient in species
diversity? Temperature How does temperature
influences species richness? Speciation Extinction
Metabolic theory predicts that generation time t
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?
The theory predicts further that mutation rate a
should scale to body weight and temperature to
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.
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Todays reading
Minimum viable population size
http//en.wikipedia.org/wiki/Minimum_viable_popula
tion Long term ecological research
http//www.lternet.edu/ Kinetic effects of
temperature on speciation http//www.pnas.org/con
tent/103/24/9130.full.pdf Paleobiology
http//findarticles.com/p/articles/mi_m2120/is_n5_
v77/ai_18601045