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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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slide1

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.

slide2

Metapopulation and Intertrophic Dynamics

abiotic factors?

(density independence)

Herons, UK

stability

fluctuations

biotic factors?

(density dependence)

BHT: fig. 10.17

slide3

Metapopulation and Intertrophic Dynamics

A+B+C

A

Density

C

B

SdrJylland

DK

Population-level analysis!

Then again … where is the population-level?

slide4

Metapopulation and Intertrophic Dynamics

Dispersal – an important population process

Searocket

(Cakile edentula)

BHT: fig. 15.19

slide5

Metapopulation and Intertrophic Dynamics

(1) Metapopulations: living in a patchy environment

(2) Intertrophic dynamics: squeezed from above and below

slide6

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

slide7

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

slide8

Metapopulation Dynamics

...and know your landscape!

Hanski & Gilpin 1997

slide9

Metapopulation Dynamics

Equilibrium “population” of species

(extinction - recolonization)

Metapopulation theory

The MacArthur-Wilson Equilibrium theory

slide10

Metapopulation Dynamics

Metapopulation

Metapopulation theory

Mainland-Island model

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

slide11

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)

slide12

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).

slide13

Metapopulation Dynamics

Metapopulation theory

Levins’s model

P : fraction of patches occupied

(1-P) : not occupied

m : recolonization rate

e : extinction rate

slide14

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

slide15

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!

slide16

Metapopulation Dynamics

Levins

M-I

Metapopulation theory

Mainland-Island model

Levins’s metapopulation model

slide17

Metapopulation Dynamics

Metapopulation theory

Mainland-Island model

Variable patch size

Levins’s metapopulation model

slide18

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

slide19

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

slide20

Intertrophic Dynamics

(i) Predation on prey are biased

Thomson’s Gazelle

BHT: fig. 8.9

(2) Intertrophic dynamics: squeezed from above and below

slide21

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”

slide22

Intertrophic Dynamics

Hokkaido

Long winter

DD intense

Short winter

DD weak

Demonstrating the effect of predation is NOT straight forward

multiannual cyclic

seasonal fluctuations

slide23

Intertrophic Dynamics

Italian mat-phys

The Lotka - Volterra model

% pred fish

Vito Volterra

(1860-1940)

American mat-biol

Alfred J Lotka

(1880-1949)

slide24

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)

slide25

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’

slide26

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’

slide27

Intertrophic Dynamics

BHT: fig. 10.2

P*

N*

The Lotka-Volterra model

P

N* = q/fa’

Predator isocline:

P* = r/a’

Prey isocline:

N

slide28

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

slide29

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

slide30

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

slide31

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!

slide32

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)

slide33

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)

slide34

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)

slide35

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

slide36

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!

slide37

Intertrophic Dynamics

Crowding in practice

Indian Meal moth

Heterogeneous media

Log density

Structural simple media

time

BHT: fig. 10.4

slide38

Intertrophic Dynamics

Crowding in practice

Indian Meal moth

Intrinsic and extrinsic causes of population cycles (fluctuations)

Heterogeneous media

Structural simple media

slide39

Intertrophic Dynamics

Population cycles and their analysis

slide40

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

slide41

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

slide42

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

slide43

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 ...)
slide44

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?

slide45

Intertrophic Dynamics

Lynx – hare interactions: A spatial perspective

NAO

Openforest

Continental

Atlantic

Closed forest

Pacific

Forest/Grassland

slide46

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

slide47

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

slide48

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

slide49

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

slide50

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

slide51

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