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Metapopulation and Intertrophic Dynamics. From single species population dynamics (and how to harvest them) to complex multi-species (pred-prey) 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 multi-species (pred-prey) dynamics in time and space.


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Metapopulation and Intertrophic Dynamics

abiotic factors?

(density independence)

Herons, UK

stability

fluctuations

biotic factors?

(density dependence)

BHT: fig. 10.17


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Metapopulation and Intertrophic Dynamics

A+B+C

A

Density

C

B

SdrJylland

DK

Population-level analysis!

Then again … where is the population-level?


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Metapopulation and Intertrophic Dynamics

Dispersal – an important population process

Searocket

(Cakile edentula)

BHT: fig. 15.19


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Metapopulation and Intertrophic Dynamics

(1) Metapopulations: living in a patchy environment

(2) Intertrophic dynamics: squeezed from above and below


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Metapopulation Dynamics

Do animals occupy all suitable habitats within their geographic range?

39 sites

water vole

Slope, vegetation,

heterogeneity

human disturbance

10 core, 15 peripheral & 14 no-visit

Lawton & Woodroffe 1991


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Metapopulation Dynamics

core sites

Increase in % grass

no-visit 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


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Metapopulation Dynamics

...and know your landscape!

Hanski & Gilpin 1997


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Metapopulation Dynamics

Equilibrium “population” of species

(extinction - recolonization)

Metapopulation theory

The MacArthur-Wilson Equilibrium theory


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Metapopulation Dynamics

Metapopulation

Metapopulation theory

Mainland-Island model

(Single-species version of the M-W multi-species model)


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Metapopulation Dynamics

Metapopulation

Metapopulation theory

Mainland-Island model

(Single-species version of the M-W multi-species model)

Levins’s metapopulation model

(no mainland; equally large habitat patches)


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Metapopulation Dynamics

P : fraction of patches occupied

(1-P) : 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 (1-P) AND with the no of occupied patches (P).

extinction – increases with the no of patches prone to extinction (P).


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Metapopulation Dynamics

Metapopulation theory

Levins’s model

P : fraction of patches occupied

(1-P) : not occupied

m : recolonization rate

e : extinction rate


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Metapopulation Dynamics

P

1-e/m

time

Metapopulation theory

Levins’s model

P : fraction of patches occupied

(1-P) : 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


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Metapopulation Dynamics

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!


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Metapopulation Dynamics

Levins

M-I

Metapopulation theory

Mainland-Island model

Levins’s metapopulation model


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Metapopulation Dynamics

Metapopulation theory

Mainland-Island model

Variable patch size

Levins’s metapopulation model


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Metapopulation Dynamics

Metapopulation theory

Mainland-Island model

a = 0

Variable patch size model

a = 

Levins’s metapopulation model

Increasinga, the freq of larger patches decreases


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Metapopulation Dynamics

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 core-satellite species hypothesis. American Naturalist142, 17-41

across metapops


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Intertrophic Dynamics

(i) Predation on prey are biased

Thomson’s Gazelle

BHT: fig. 8.9

(2) Intertrophic dynamics: squeezed from above and below


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Intertrophic Dynamics

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”


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Intertrophic Dynamics

Hokkaido

Long winter

DD intense

Short winter

DD weak

Demonstrating the effect of predation is NOT straight forward

multiannual cyclic

seasonal fluctuations


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Intertrophic Dynamics

Italian mat-phys

The Lotka - Volterra model

% pred fish

Vito Volterra

(1860-1940)

American mat-biol

Alfred J Lotka

(1880-1949)


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Intertrophic Dynamics

q: mortality

The Lotka-Volterra 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)


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Intertrophic Dynamics

- 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 Lotka-Volterra model

isoclines,dN/dt = dP/dt = 0

(Predator isocline)

(Prey isocline)

=>

N* = q/fa’

=>

P* = r/a’


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Intertrophic Dynamics

P

P*

predator

mortality

N*

N

offpring/prey

P

P*

hunting

effeciency

prey

reproduction

N*

N

The Lotka-Volterra model

isoclines,dN/dt = dP/dt = 0

N* = q/fa’

P* = r/a’


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Intertrophic Dynamics

BHT: fig. 10.2

P*

N*

The Lotka-Volterra model

P

N* = q/fa’

Predator isocline:

P* = r/a’

Prey isocline:

N


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Intertrophic Dynamics

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 Lotka-Volterra model


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Intertrophic Dynamics

Crowding in prey:

Reproduction rate (r ) decreases with increasing N

N* = q/fa’

Predator isocline:

P* = r/a’

Prey isocline:

Crowding in the Lotka-Volterra model

P

Crowding in predators:

Hunting effeciency (a’ ) decreases with increasing P

P*

N*

N


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Intertrophic Dynamics

Crowding in prey:

Reproduction rate (r ) decreases with increasing N

N* = q/fa’

Predator isocline:

P* = r/a’

Prey isocline:

Crowding in the Lotka-Volterra model

P

Crowding in predators:

Hunting effeciency (a’ ) decreases with increasing P

P*

KN

N*

N


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Intertrophic Dynamics

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 Lotka-Volterra model

BHT: fig. 10.7

The greater the distance from Eq, the quicker the return to Eq!


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Intertrophic Dynamics

Functional response and prey-switching

Switch of prey

P

eat another prey

eat this prey

N(this prey)

P

KN

N (this prey)


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Intertrophic Dynamics

Switch of prey

At low N there’s no effect of predator

P

N (this prey)

Functional response and prey-switching

P

eat another prey

eat this prey

N(this prey)

P

KN

N (this prey)


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Intertrophic Dynamics

Switch of prey

At low N there’s no effect of predator

Degree of DD determines level

Functional response and prey-switching

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)


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Intertrophic Dynamics

Predator isocline (high DD)

Stable pattern with prey density below carrying capacity

Functional response and prey-switching

BHT: fig. 10.9

Predator isocline

Prey isocline


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Intertrophic Dynamics

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 prey-switching

Many other combinations! Despite initial settings they all become stable!


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Intertrophic Dynamics

Crowding in practice

Indian Meal moth

Heterogeneous media

Log density

Structural simple media

time

BHT: fig. 10.4


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Intertrophic Dynamics

Crowding in practice

Indian Meal moth

Intrinsic and extrinsic causes of population cycles (fluctuations)

Heterogeneous media

Structural simple media


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Intertrophic Dynamics

Population cycles and their analysis


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Intertrophic Dynamics

lynx

+

Sunspot

Lynx – hare interactions

  • pattern: the distinct 10-year cycle (hunting data!)

  • processes?: obscure!

  • hypotheses: (1) vegetation-hare

(2) hare-lynx

(3) vegetation-hare-lynx

(4) sunspots


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Intertrophic Dynamics

-

Lynx – hare interactions

  • pattern: the distinct 10-year cycle (hunting data!)

  • processes?: obscure!

  • hypotheses: (1) vegetation-hare

(2) hare-lynx

(3) vegetation-hare-lynx

(4) sunspots

lynx

Sunspot


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Intertrophic Dynamics

+

Lynx – hare interactions

  • pattern: the distinct 10-year cycle (hunting data!)

  • processes?: obscure!

  • hypotheses: (1) vegetation-hare

(2) hare-lynx

(3) vegetation-hare-lynx

(4) sunspots

lynx

Sunspot


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Intertrophic Dynamics

Lynx – hare interactions: The Kluane Project

Factorial design large-scale experiment:

(1) control blocks

(2) ad lib supplemental food blocks

(3) predator exclusion blocks

(4) 2+3 blocks

  • monitored everything over 15 years (species composition, population dynamics, life histories ...)


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Intertrophic Dynamics

(-pred, + food)

(-pred)

  • Non-additive response

(+food)

10-fold

(control)

Hare density

year

Vegetation-hare-predator

  • Increased cycle period ...

Lynx – hare interactions: The Kluane Project

… but neither food addition and predator exclosure prevented hares from cycling - Why?


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Intertrophic Dynamics

Lynx – hare interactions: A spatial perspective

NAO

Openforest

Continental

Atlantic

Closed forest

Pacific

Forest/Grassland


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Intertrophic Dynamics

f(Nt-1,Nt-2)

increase

Nt =

density

f(Nt-1,Nt-2)

decrease

year

Lynx – hare interactions: the lynx perspective

Kluane indicates that hare-predator interactions are central.

Nt = f(Nt-1,Nt-2,..., Nt-11)!...

… dynamics non-linear!

High dependence (80%) on hare density ...

hare

lynx


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Intertrophic Dynamics

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


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Intertrophic Dynamics

  • The specialist predator hypothesis

  • (predator numerically linked to prey, that is through reproduction; variations come from variations in predator efficiency)

Lemmus

Clethrionomys

  • The generalist predator hypothesis

  • (more generalist predators in south than north)

Microtus

AR(2): Nt = f(Nt-1,Nt-2)

AR(1): Nt = f(Nt-1)

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


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Intertrophic Dynamics

Lemmus

17 (89%) time series best described by:

Clethrionomys

AR(2): Nt = f(Nt-1,Nt-2)

Nt-2

Microtus

Nt-1

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


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Metapopulation and Intertrophic Dynamics

Combining metapopulation and predator-prey theory

BHT section 10.5.5

Comins et al. (1992) The spatial dynamics of host-parasitoid systems. Journal of Animal Ecology61, 735-748


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Fagprojekter

(1) Harvesting natural populations

Niels

Toke

(2) Cohort variation and life histories

(3) Climate and density dependence in

population dynamics

Mads

Max 3-4 pax/group

Max 10-15 pp + figs/tabs


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