Metapopulation and Intertrophic Dynamics. From single species population dynamics (and how to harvest them) to complex multispecies (predprey) dynamics in time and space . Metapopulation and Intertrophic Dynamics. abiotic factors? ( density independence ). Herons, UK. stability.
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Metapopulation and Intertrophic Dynamics
From single species population dynamics (and how to harvest them) to complex multispecies (predprey) dynamics in time and space.
Metapopulation and Intertrophic Dynamics
abiotic factors?
(density independence)
Herons, UK
stability
fluctuations
biotic factors?
(density dependence)
BHT: fig. 10.17
Metapopulation and Intertrophic Dynamics
A+B+C
A
Density
C
B
SdrJylland
DK
Populationlevel analysis!
Then again … where is the populationlevel?
Metapopulation and Intertrophic Dynamics
Dispersal – an important population process
Searocket
(Cakile edentula)
BHT: fig. 15.19
Metapopulation and Intertrophic Dynamics
(1) Metapopulations: living in a patchy environment
(2) Intertrophic dynamics: squeezed from above and below
Do animals occupy all suitable habitats within their geographic range?
39 sites
water vole
Slope, vegetation,
heterogeneity
human disturbance
10 core, 15 peripheral & 14 novisit
Lawton & Woodroffe 1991
core sites
Increase in % grass
novisit sites
reduced colonization rates
Increasing bank angle and structural heterogeneity
predation
Do animals occupy all suitable habitats within their geographic range?
PCA performed
water vole
55% with suitable habitats ...
...30% lack voles because...
Know your species...!
Lawton & Woodroffe 1991
Equilibrium “population” of species
(extinction  recolonization)
Metapopulation theory
The MacArthurWilson Equilibrium theory
Metapopulation
Metapopulation theory
MainlandIsland model
(Singlespecies version of the MW multispecies model)
Metapopulation
Metapopulation theory
MainlandIsland model
(Singlespecies version of the MW multispecies model)
Levins’s metapopulation model
(no mainland; equally large habitat patches)
P : fraction of patches occupied
(1P) : fraction not occupied
Metapopulation theory
Levins’s model
(equal patch size)
m : recolonization rate
e : extinction rate
recolonization – increases with BOTH the no of empty patches (1P) AND with the no of occupied patches (P).
extinction – increases with the no of patches prone to extinction (P).
Metapopulation theory
Levins’s model
P : fraction of patches occupied
(1P) : not occupied
m : recolonization rate
e : extinction rate
P
1e/m
time
Metapopulation theory
Levins’s model
P : fraction of patches occupied
(1P) : not occupied
m : recolonization rate
e : extinction rate
Given that (m – e)> 0, the metapop will grow until equlibrium:
(trivial: P* = 0)
dP/dt = 0 => P* = 1 – e/m
Melitaea cinxia
local patches
the metapop persists:
ln(1991) = ln(1993)
Hanski et al. 1995
Metapopulation theory
NOTE: the metapop persists, stably, as a result of the balance between m and edespite unstable local populations!
Levins
MI
Metapopulation theory
MainlandIsland model
Levins’s metapopulation model
Metapopulation theory
MainlandIsland model
Variable patch size
Levins’s metapopulation model
Metapopulation theory
MainlandIsland model
a = 0
Variable patch size model
a =
Levins’s metapopulation model
Increasinga, the freq of larger patches decreases
Melitaea cinxia
dP/dt = 0 => P1* = 1 – e/m
P2* = 0
Hanski et al. 1995
Metapopulation theory
Levins’s model:
Value ofa!
Hanski & Gyllenberg (1993) Two general metapopulation models and the coresatellite species hypothesis. American Naturalist142, 1741
across metapops
(i) Predation on prey are biased
Thomson’s Gazelle
BHT: fig. 8.9
(2) Intertrophic dynamics: squeezed from above and below
mates
territories
There is density dependence (crowding), which may influence or be influenced buy predation!
(2) Intertrophic dynamics: squeezed from above and below
(ii) Predators AND prey are also ”squeezed from the side”
Hokkaido
Long winter
DD intense
Short winter
DD weak
Demonstrating the effect of predation is NOT straight forward
multiannual cyclic
seasonal fluctuations
Italian matphys
The Lotka  Volterra model
% pred fish
Vito Volterra
(18601940)
American matbiol
Alfred J Lotka
(18801949)
q: mortality
The LotkaVolterra model
Predator (P)
a': hunting eff.
per predator
 qP
fa’PN
f: ability to convert
food to offspring
 a’PN
+ fa’PN
r: intrinsic rate of
increase
rN
 a’PN
Prey(N)
 qP*
fa’P*N*
= 0
= 0
rN*
 a’P*N*
predator
mortality
offpring/prey
= qP*
fa’P*N*
hunting
effeciency
rN*
= a’P*N*
prey
reproduction
The LotkaVolterra model
isoclines,dN/dt = dP/dt = 0
(Predator isocline)
(Prey isocline)
=>
N* = q/fa’
=>
P* = r/a’
P
P*
predator
mortality
N*
N
offpring/prey
P
P*
hunting
effeciency
prey
reproduction
N*
N
The LotkaVolterra model
isoclines,dN/dt = dP/dt = 0
N* = q/fa’
P* = r/a’
BHT: fig. 10.2
P*
N*
The LotkaVolterra model
P
N* = q/fa’
Predator isocline:
P* = r/a’
Prey isocline:
N
P
Crowding in predators:
Hunting effeciency (a’ ) decreases with increasing P
P*
N*
N
N* = q/fa’
Predator isocline:
P* = r/a’
Prey isocline:
Crowding in the LotkaVolterra model
Crowding in prey:
Reproduction rate (r ) decreases with increasing N
N* = q/fa’
Predator isocline:
P* = r/a’
Prey isocline:
Crowding in the LotkaVolterra model
P
Crowding in predators:
Hunting effeciency (a’ ) decreases with increasing P
P*
N*
N
Crowding in prey:
Reproduction rate (r ) decreases with increasing N
N* = q/fa’
Predator isocline:
P* = r/a’
Prey isocline:
Crowding in the LotkaVolterra model
P
Crowding in predators:
Hunting effeciency (a’ ) decreases with increasing P
P*
KN
N*
N
Combining DD in predator and prey
Predator isocline
Prey isocline
Less effecient predator
Predator isocline
Prey isocline
Strong DD in predator
Prey isocline
N* = q/fa’
Predator isocline:
Predator isocline
P* = r/a’
Prey isocline:
Crowding in the LotkaVolterra model
BHT: fig. 10.7
The greater the distance from Eq, the quicker the return to Eq!
Functional response and preyswitching
Switch of prey
P
eat another prey
eat this prey
N(this prey)
P
KN
N (this prey)
Switch of prey
At low N there’s no effect of predator
P
N (this prey)
Functional response and preyswitching
P
eat another prey
eat this prey
N(this prey)
P
KN
N (this prey)
Switch of prey
At low N there’s no effect of predator
Degree of DD determines level
Functional response and preyswitching
P
eat another prey
eat this prey
N(this prey)
P
Independent of prey
(DD still in work)
P
KN
N (this prey)
N (this prey)
Predator isocline (high DD)
Stable pattern with prey density below carrying capacity
Functional response and preyswitching
BHT: fig. 10.9
Predator isocline
Prey isocline
Combining DD in predator and prey
BHT: fig. 10.7
Predator isocline
Prey isocline
Less effecient predator
Predator isocline
Prey isocline
Strong DD in predator
Prey isocline
Predator isocline
Functional response and preyswitching
Many other combinations! Despite initial settings they all become stable!
Crowding in practice
Indian Meal moth
Heterogeneous media
Log density
Structural simple media
time
BHT: fig. 10.4
Crowding in practice
Indian Meal moth
Intrinsic and extrinsic causes of population cycles (fluctuations)
Heterogeneous media
Structural simple media
Population cycles and their analysis
lynx
+
Sunspot
Lynx – hare interactions
(2) harelynx
(3) vegetationharelynx
(4) sunspots

Lynx – hare interactions
(2) harelynx
(3) vegetationharelynx
(4) sunspots
lynx
Sunspot
+
Lynx – hare interactions
(2) harelynx
(3) vegetationharelynx
(4) sunspots
lynx
Sunspot
Lynx – hare interactions: The Kluane Project
Factorial design largescale experiment:
(1) control blocks
(2) ad lib supplemental food blocks
(3) predator exclusion blocks
(4) 2+3 blocks
(pred, + food)
(pred)
(+food)
10fold
(control)
Hare density
year
Vegetationharepredator
Lynx – hare interactions: The Kluane Project
… but neither food addition and predator exclosure prevented hares from cycling  Why?
Lynx – hare interactions: A spatial perspective
NAO
Openforest
Continental
Atlantic
Closed forest
Pacific
Forest/Grassland
f(Nt1,Nt2)
increase
Nt =
density
f(Nt1,Nt2)
decrease
year
Lynx – hare interactions: the lynx perspective
Kluane indicates that harepredator interactions are central.
Nt = f(Nt1,Nt2,..., Nt11)!...
… dynamics nonlinear!
High dependence (80%) on hare density ...
hare
lynx
Lemmus
Clethrionomys
27 populations
Microtus
BHT: fig. 15.13
A geographical gradient in rodent fluctuations: a statistical modelling approach
Ottar Bjørnstad
Effect of predators?
Bjørnstad et al. 1995
Hanski et al. 1991
Lemmus
Clethrionomys
Microtus
AR(2): Nt = f(Nt1,Nt2)
AR(1): Nt = f(Nt1)
efficiency
no of pred
BHT: fig. 15.16
A geographical gradient in rodent fluctuations: a statistical modelling approach
Two hypotheses
delayed effect on prey
direct effect on prey
Analysis of prey population dynamics:
Bjørnstad et al. 1995
Hanski et al. 1991
Lemmus
17 (89%) time series best described by:
Clethrionomys
AR(2): Nt = f(Nt1,Nt2)
Nt2
Microtus
Nt1
A geographical gradient in rodent fluctuations: a statistical modelling approach
Ottar analysed 19 time series (>15 years) using autoregression (AR):
Increasing no of gen pred increases the direct negative effect on prey
The generalist predator hypothesis
Bjørnstad et al. 1995
Metapopulation and Intertrophic Dynamics
Combining metapopulation and predatorprey theory
BHT section 10.5.5
Comins et al. (1992) The spatial dynamics of hostparasitoid systems. Journal of Animal Ecology61, 735748
(1) Harvesting natural populations
Niels
Toke
(2) Cohort variation and life histories
(3) Climate and density dependence in
population dynamics
Mads
Max 34 pax/group
Max 1015 pp + figs/tabs