Pollock’s Robust Design: Extensions II

Quick overview 1.Separation of Recruitment Components in a single patch context (Source-Sink) 2.Separation of Recruitment Components in a Metapopulation context (Multistate Reverse-time Modeling)

1. Separation of Recruitment Components Single patch

Motivations Recruitment = new individuals arriving in a population Recruitment = new individuals arriving in a population 2 sources: 2 sources: in situ Reproduction in situ Reproduction Immigration (from an outside source) Immigration (from an outside source) Important to distinguish for population projection models Important to distinguish for population projection models

Problem Adult survivors In situ recruits Immigrants Can be estimated with open models

Problem

Solution

Model parameters 2-age model with young (age 0) and adult (age 1+) N i (a) = abundance for age a at period i N i (a) = abundance for age a at period i  i (a) = survival rate (i to i+1) for age a  i (a) = survival rate (i to i+1) for age a B i (1)’ = new recruits via in situ reproduction entering adult population between i and i+1, and present at i B i (1)’ = new recruits via in situ reproduction entering adult population between i and i+1, and present at i B i (1)’’ = new recruits via immigration entering adult pop between i and i+1, and present at i B i (1)’’ = new recruits via immigration entering adult pop between i and i+1, and present at i

Model Estimate in situ recruits as surviving young Estimate in situ recruits as surviving young Estimate immigrant recruits: Estimate immigrant recruits: subtract surviving adults and in situ recruits from total abundance

Parameter Estimation Multinomial likelihoods Multinomial likelihoods Data: numbers of animals with each capture history Data: numbers of animals with each capture history Model: probability structure for each capture history Model: probability structure for each capture history Maximum likelihood (e.g., programs RDSURVIV, MARK) Maximum likelihood (e.g., programs RDSURVIV, MARK)

1. Separation of Recruitment Components Metapopulation

Motivation Rather than source-sink dichotomy, consider the contribution of any local population to an entire metapopulation system (Runge et al. 2006) Rather than source-sink dichotomy, consider the contribution of any local population to an entire metapopulation system (Runge et al. 2006) Contribution metric should include recruits to both the focal local population and other local populations in the system Contribution metric should include recruits to both the focal local population and other local populations in the system

Two possible approaches Demographic parameter estimates for each patch (just showed) : Demographic parameter estimates for each patch (just showed) : patch-specific survival (young and adults), patch-specific survival (young and adults), patch-specific reproduction, patch-specific reproduction, patch-specific dispersal-recruitment (young and adults of focal patch) with respect to all system patches patch-specific dispersal-recruitment (young and adults of focal patch) with respect to all system patches Multisite Reverse-time CR Multisite Reverse-time CR patch-specific abundance patch-specific abundance patch-specific contribution parameters patch-specific contribution parameters

Multistate Reverse-time Modeling (Robust Design) Situation: capture-recapture sampling at multiple locations (multistate model) Situation: capture-recapture sampling at multiple locations (multistate model) Question: For any site, what is the relative contribution (to population growth) of: (1) surviving animals (adults and young) from the same location vs. (2) migrants from the other site(s) Question: For any site, what is the relative contribution (to population growth) of: (1) surviving animals (adults and young) from the same location vs. (2) migrants from the other site(s)

Data

Model Parameters

Inference

Derived parameters: Abundance (Local and Metapopulation)

Metapopulation Growth Rate

Contributions to Metapopulation Growth Rate Proportion of adults (immigrants) that came from site s Proportion of young that were born in site s

Contribution from Extra-system Immigration

Includes contribution from: - All surveyed sites (r itself and others) - All age classes

Contribution from Extra-system Immigration Proportional contribution to metapopulation grtowh from extra-system immigration: Proportional contribution to metapopulation grtowh from extra-system immigration: = contributions to any site r

As a conclusion

Metapopulation dynamics Sources of variation to consider (for the contributions of local populations to the metapopulation) Sources of variation to consider (for the contributions of local populations to the metapopulation) Animal age Animal age Distance between populations Distance between populations Local population size Local population size Location (centrality) of local population Location (centrality) of local population

Other Extensions (Combining Methods/Data) Robust design (closed + open CR) Robust design (closed + open CR) Open CR + band recovery (Burnham 1993) Open CR + band recovery (Burnham 1993) Separate permanent emigration and mortality Separate permanent emigration and mortality Open CR + ancillary sightings (Barker 1997) Open CR + ancillary sightings (Barker 1997) Allows sightings between sampling occasions Allows sightings between sampling occasions Open CR + genetic assignment test (Wen et al. 2011) Open CR + genetic assignment test (Wen et al. 2011) Separation of immigration/reprod. recruitment Separation of immigration/reprod. recruitment Open CR + telemetry (Powell et al. 2000) Open CR + telemetry (Powell et al. 2000) Separate detection and temporary emigration Separate detection and temporary emigration