Multiple Season Model Part I. 2 Outline  Data structure  Implicit dynamics  Explicit dynamics  Ecological and conservation applications.

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Presentation transcript:

Multiple Season Model Part I

2 Outline  Data structure  Implicit dynamics  Explicit dynamics  Ecological and conservation applications

3 Recap Season 1 12k1k1... Surveys 2 12k2k2... T 12kTkT Closure

4 Encounter histories Season Unit 12…T … s

5 Implicit Dynamics  Can introduce structure to model systematic changes in occupancy.  Does not model the dynamic processes of occupancy; local-extinctions and colonizations.  Implicit dynamics are non-Markovian (random): Pr(occupancy at t ) is independent of state at t -1.

6 Multiple season- probability statements  Detection/nondetection data Pr(h 1 = ) =  1 p 1,1 p 1,2 (1-p 1,3 ) x

7 Explicit Dynamics  Model the biological processes of change in occupancy.  Model occupancy as a first order Markov process: Pr(occupancy at t ) depends on occupancy state at t -1.

8 Explicit Dynamics  t = probability unit occupied in season t  t = probability a unit becomes unoccupied between seasons t and t +1  t = probability a unit becomes occupied between seasons t and t +1 p t,j = probability species detected at a unit in survey j of season t (given presence)

9 Explicit Dynamics S1S2S3 Occupied Unoccupied

10 Explicit Dynamics S1S2S3 Occupied Unoccupied Not Ext. Ext.

11 Explicit Dynamics S1S2S3 Occupied Unoccupied Not Ext. Ext. Not Col. Col.

12 Explicit Dynamics S1S2S3

13 Explicit Dynamics For example, h 1 = Mathematical translation: Pr(h 1 = ) =  1 p 1,1 (1-p 1,2 )p 1,3 X { 1 + (1- 1 )  (1-p 2,j )} 3 j=1

14 Model selection Model AICc wK (1)(Disturb)(Disturb)p(t,.) (1)(Disturb+hare)(Disturb+hare)p(t,.) (1)(.)(.)p(t,.) (1)(hare)(hare)p(t,.) Notes: AICc: Akaike information criterion; AICc for the ith model is computed as AICc i – min(AICc); w: AICc weight; K: number of parameters. From 1 st ever use of adap mgmt on a national park. Occupancy of golden eagles at Danali nat. park in AK. Disturb=human disturbance at site, hare=index of snowshoe hare presence at site.

15 Models of occupancy dynamics : probability of local desertion (pi10) : probability of local colonization (pi01) Occupied 1 Unocc. 0 State variable

16 Optimal decisions

17 Summary and Perspectives  Multi-season models allow us to make inference about changes in occupancy and the underlying dynamic processes, while accounting for imperfect detection.  A suite of flexible methods are now available that account for: detectability Covariates Finite population Spatial correlation

18 What you should know  Purpose of single species multi season models  Definition of psi, prob of extinction and colonization  Can be used to project the consequences of environmental changes (including management decisions) on occupancy dynamics