ibm meets traditional population ecology ibm behavioural patterns life history variation ...

IBM meets traditional population ecology

Born Judging environment

Death

Environmental evaluation

Behavioural Allocation

Nursing Parturition Pregnant

Mating

Growth IBM

behavioural patterns

life history variation

population level responses (ecology, genetics)

What are the characteristicsof population-level responsesto different IBM scenarios?

Analytical tools



Death




Mating

Growth IBM

individual behaviour patterns

individual life history variation


Matrix populationmodel:

nt+1 = A nt

abundance vector

projection matrix

sensitivityCaswell, H (2001) Matrix population models



Death




Mating

Growth IBM

individual behaviour patterns

individual life history variation


Abundance in time andspace:

synchrony

structural dynamics density dependence

Matrix populationmodel:

nt+1 = A nt

abundance vector

projection matrix

sensitivityCaswell, H (2001) Matrix population models


Analysis of patterns: fox abundance in time and space

IBM space

7

7.5

8

8.5

9

9.5

100 150 200 250 300

time (years)

ab

un

dan

ce

regional

34

IBM time

Many IBM modellers look for cyclic population level responses (?) ...



10.4

10.6

10.8

11

11.2

1 11 21 31 41

time (years)

ab

un

dan

ce

regional

time (years)

abu

ndan

ce

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41 local

IBM spaceIBM time

10.4

10.6

10.8

11

11.2

1 11 21 31 41



time (years)

ab

un

dan

ce

time (years)

abu

ndan

ce

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41

regional

local

IBM spaceIBM time



cross

corr

ela

tion

distance

-1

-0.5

0

0.5

1

0 2 4 6 8 10

spatial fox dynamics IBM space

migration, predation and climate

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41



time (years)

abu

ndan

ce

local

temporal fox dynamics: fluctuations

lag (years)

corr

ela

tion

corr

ela

tion

lag (years)

24

ACF

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41



time (years)

abu

ndan

ce

local

corr

ela

tion

lag (years)

spect

rum

frequency (1/years)

22

6 2

24

temporal fox dynamics: fluctuations

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41



time (years)

abu

ndan

ce

local

temporal fox dynamics: structure

Xt=f (Xt-1, ..., Xt-n)

Xt = 1.14Xt-1 – 0.48Xt-

2

Xt = 0.66Xt-1+0.22Xt-2

autoregression

Royama, T (1992) Analytical population dynamics

Tong, H (1990) Non-linear time series


Fox abundance in time and space: connecting patterns and processes

intra-specific

inter-specific

inter-specific

Xt=f (Xt-1, ..., Xt-n)fox AR structure:



Xt=f (Xt-1)intra-specific

inter-specific

inter-specific

fox AR structure:



Xt=f (Xt-1, Xt-2)intra-specific

inter-specific

inter-specific

fox AR structure:



intra-specific

inter-specific

inter-specific

Xt=f (Xt-1, Xt-2, Xt-3)

dimension indicates no of trophic interactions

fox AR structure:

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41



time (years)

abu

ndan

ce

local

Xt = 0.66Xt-1+0.22Xt-2

Xt = 1.14Xt-1 – 0.48Xt-

2

2-dimensional AR models


Bornholm

Jylland

FynSjælland

-1-0.8-0.6-0.4-0.20

0.20.4

1 11 21 31 41

time (years)

abu

ndan

ce

local

Xt = 0.66Xt-1+0.22Xt-2

Xt = 1.14Xt-1 – 0.48Xt-

2

Indeed, ...


The interface between IBM and analytical population ecology may ...

... provide information on how populations will behave – in time and space – over a range of IBM scenarios... focus on key variables potentially responsible, otherwise muddled by the numerous IBM variables and their syngistic effects

ibm meets traditional population ecology ibm behavioural patterns life history variation ...

Documents

matrix population modelsibm

time andspace

time seriesibm

specificfox ar structure

spaceibm spaceibm timeibm

dimensional ar modelsibm

nt sensitivitycaswell

analytical toolsibm