Presentation at SMB2014/MPDE14
- 1. Stuart Nattrass s.nattrass@abdn.ac.uk @StuNattrass ANALYTIC MEASURES FOR PREDICTING POPULATION CONSEQUENCES OF DISTURBANCE
- 2. CONTRIBUTORS Aberdeen -David Lusseau UCSC -Dan Costa -Liza Schwarz -Patrick Robinson
- 3. CONSEQUENCES OF DISTURBANCE ACUTE BEHAVIOR VITAL RATES DISTURBANCE PHYSIOLOGY HEALTH ACUTE CHRONIC PROBABILITY OF PERSISTENCE CHRONIC New et al 2004
- 4. TOOLS TO PREDICT PCOD LIKELIHOOD •Can we find tools that allow us to predict whether population effects occur following disturbance? •Measures must be •Based on behavioural ecology •Influenced by both environmental conditions and life history strategies
- 5. BEHAVIOUR AS MODEL SYSTEM •Behavioural patterns can be thought of a system •Certain behavioural patterns can be stable with positive outputs
- 6. RESILIENCE •Two measures of resilience •ENGINEERING RESILIENCE – how quickly you recover from a disturbance •ECOLOGICAL RESILIENCE (REACTIVITY) – how far system can be perturbed before behaviour is permanently disrupted ECOLOGICAL RESILIENCE ENGINEERING RESILIENCE Barros & Lusseau in prep
- 7. RESILIENCE •ECOLOGICAL RESILIENCE (REACTIVITY) – how far system can be perturbed before behaviour is permanently disrupted Barros & Lusseau in prep
- 8. RESILIENCE Definitions of resilience • Jacobian matrix of system 퐽 gives fixed point stability and resilience • ENGINEERING RESILIENCE 휆푖 eigenvalues of 퐽 • ECOLOGICAL RESILIENCE 휅푖 eigenvalues of 퐽+ 퐽푇 2 max(| Re( ) |) i max(| Re( ) |) i
- 9. RESILIENCE IN A GENERAL, SIMPLE MODEL •Simple ODE model where individual can alter feeding behaviour 퐹′ 퐶′ 퐸′ = −푎1−푎2푎3 푏1−푏20−푐10푐3 퐹 퐶 퐸 •Gives a single fixed point at the origin
- 10. RESILIENCE IN A GENERAL, SIMPLE MODEL •Engineering Resilience varies with fixed point type • Stable equilibria have higher engineering resilience than the unstable equivalent • Nodes have higher engineering resilience than foci with the same stability Unstable node Unstable focus Saddle Stable node Stable focus
- 11. RESILIENCE IN A GENERAL, SIMPLE MODEL •Ecological resilience does not show same variety, equilibrium type has little effect Unstable node Unstable focus Saddle Stable node Stable focus
- 12. RESILIENCE IN A GENERAL, SIMPLE MODEL •How does this resilience affect individuals who are perturbed? •Compare systems with stable fixed points but different resilience values •Higher engineering resilience results in the system returning to the fixed point faster
- 13. GROUNDPROOFING WITH DATA (1) • Model based on elephant seals data • Variables • Condition (lipid stores L) • Transit rates T • Number of drift dives V • Time step of 1 day 0 1 1 2 3 1 0 1 1 2 1 3 1 1 1 1 0 1 2 3 ~ ~ ~ t t t t t t t t t t t t t t V V T L T L V T R L L L T V
- 14. GROUNDPROOFING WITH DATA (1) Female elephant seals with higher resilience will have more consistent weight gain across multiple season Using El Nino as a disturbance event, we can compare female weight gain in El Nino years and ‘normal’ years •Resilience calculated from ‘normal’ conditions
- 15. GROUNDPROOFING WITH DATA (1) •Limited data suggests prediction holds •More resilience individuals perform better in El Nino conditions
- 16. GROUNDPROOFING WITH DATA (2) •Can increase number of data points by using dive scale model •4 types of dive •Foraging •Drift •Benthic •‘Other’ – mostly assumed to be transit •Disturbance: dives over 5000 seconds (1 hour 23 minutes)
- 17. GROUNDPROOFING WITH DATA (2) •Do disturbances affect behaviour at short time scale? •Dive patterns of a disturbed individual suggest yes
- 18. GROUNDPROOFING WITH DATA (2) •Assume Markovian process to assess behaviour patterns •Transition Intensity matrices vary before and after the disturbance dive vary Transit Forage Drift Benthic Transit Forage Drift Benthic
- 19. GROUNDPROOFING WITH DATA (2) •Resilience in a Markov Chain model based on pre disturbance behaviour •Convert intensity matrix to transition probability matrix (average dive length) .549.325.125.825.071.055.029.021.132.220.159.260.578.060.068.515 •Damping ratio ln 휆1 휆2=0.5427285 gives estimate of return rate (engineering resilience)
- 20. GROUNDPROOFING WITH DATA (2) •Look at groups of 10 dives following disturbance: how likely is it this behaviour came from the same transition matrix as pre disturbance behaviour •See major change between 9-10 dives after disturbance
- 21. CURRENT CHALLENGES •However, when extended, peak may be anomaly •Therefore, may need alternative measure to assess return time following disturbance at the dive scale •Can we assess reactivity, or ecological resilience in this dive scale MC system?
- 22. CONCLUSIONS •Resilience can be useful measure in predicting which individuals are most at risk from disturbance •Elephant seals with higher resilience appear to perform better in stressed years •Possible to extrapolate from these individuals to population level to determine where to focus protective efforts
- 23. THANK YOU FOR LISTENING •s.nattrass@abdn.ac.uk •@StuNattrass