1. IBM meets traditional population ecology IBM  behavioural patterns  life history variation  population level responses (ecology, genetics) What are the characteristics of population-level responses to different IBM scenarios? Analytical tools

2. IBM meets traditional population ecology IBM  individual behaviour patterns  individual life history variation  population level responses (ecology, genetics) Matrix population model: n t+1 = A n t abundance vector projection matrix  sensitivity Caswell, H (2001) Matrix population models

3. IBM meets traditional population ecology IBM  individual behaviour patterns  individual life history variation  population level responses (ecology, genetics) Abundance in time and space:  synchrony  structural dynamics density dependence Matrix population model: n t+1 = A n t abundance vector projection matrix  sensitivity Caswell, H (2001) Matrix population models

4. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space IBM space time (years) abundance regional 34 IBM time Many IBM modellers look for cyclic population level responses (?)...

5. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space time (years) abundance regional time (years) abundance local IBM space IBM time

6. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space time (years) abundance time (years) abundance regional local IBM space IBM time

7. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space cross correlation distance spatial fox dynamics IBM space migration, predation and climate

8. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space time (years) abundance local temporal fox dynamics: fluctuations lag (years) correlation lag (years) 24 ACF

9. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space time (years) abundance local correlation lag (years) spectrum frequency (1/years) 22 6 2 24 temporal fox dynamics: fluctuations

10. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space time (years) abundance local temporal fox dynamics: structure X t =f (X t-1,..., X t-n ) X t = 1.14X t-1 – 0.48X t-2 X t = 0.66X t-1 +0.22X t-2 autoregression Royama, T (1992) Analytical population dynamics Tong, H (1990) Non-linear time series

11. IBM meets traditional population ecology Fox abundance in time and space: connecting patterns and processes intra-specific inter-specific X t =f (X t-1,..., X t-n ) fox AR structure:

12. IBM meets traditional population ecology Fox abundance in time and space: connecting patterns and processes X t =f (X t-1 ) intra-specific inter-specific fox AR structure:

13. IBM meets traditional population ecology Fox abundance in time and space: connecting patterns and processes X t =f (X t-1, X t-2 ) intra-specific inter-specific fox AR structure:

14. IBM meets traditional population ecology Fox abundance in time and space: connecting patterns and processes X t =f (X t-1, X t-2 ) intra-specific inter-specific fox AR structure:

15. IBM meets traditional population ecology Fox abundance in time and space: connecting patterns and processes intra-specific inter-specific X t =f (X t-1, X t-2, X t-3 ) dimension indicates no of trophic interactions fox AR structure:

16. IBM meets traditional population ecology Analysis of patterns: fox abundance in time and space time (years) abundance local X t = 0.66X t-1 +0.22X t-2 X t = 1.14X t-1 – 0.48X t-2 2-dimensional AR models

17. IBM meets traditional population ecology Bornholm Jylland Fyn Sjælland time (years) abundance local X t = 0.66X t-1 +0.22X t-2 X t = 1.14X t-1 – 0.48X t-2 Indeed,...

18. IBM meets traditional population ecology 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