10/21/2011 1 Estimating Population Size using Mark-Recapture techniques Why use capture methods? • Allows for estimation of density •Allows for estimation of birth and mortality rates •More practical method for small, fast, hard to spot species10/21/2011 2 There are variety of models for mark-recapture studies that attempt to account for different assumptions of the base model. These deal with: • Capture rates • Individual variation • Post-trap response • Time General Mark-Recapture methods: • Population sampled 2 or more times • Captured individuals marked and released in first session • Additional session(s) to follow, in some cases new unmarked individuals marked • Capture can be physically trapped, photographs, DNA samples, etc10/21/2011 3 Lincoln-Petersen method: • Population sampled 2 times (1 recapture event) • Captured individuals marked and released in first session • Closed population • Probability of catching individuals equal in both session • Marks not lost, gained, or overlooked • Marks needn’t be unique to individuals Lincoln-Petersen method: n1 = # captured and marked in 1st session n2 = Total # captures in 2nd session m2 = # of marked animals captured in 2nd session Remember our general model for abundance estimates: Estimate of abundance = Count / estimated probability of detection N-hat = n1 / (m2 / n2) or N-hat = n1 * n2 / m210/21/2011 4 Lincoln-Petersen method: n1 = # captured and marked in 1st session n2 = Total # captures in 2nd session m2 = # of marked animals captured in 2nd session Chapman modified this original formula to account for bias due to small samples: N-hat = (n1 +1)/ (m2 +1) / (n2 +1) or N-hat = (n1 +1) * (n2 +1) / (m2 +1) Session 1 Session 2 Lincoln-Petersen method: = marked individual = unmarked individual10/21/2011 5 Marks can be unique patterns on individuals capture in images. An example of this is Calambokidis & Barlows study of Humpback Whales Closed models w/ >1 recapture periods: • Population sampled 2 times (1 recapture event) • Captured individuals marked and released in first session • Closed population • Probability of catching individuals equal within a sampling period but can vary between sampling periods • Marks not lost, gained, or overlooked • For some models/purposes Marks need must be unique to individuals, unique encounter histories created • Calculation intensive, use programs such as CAPTURE or Program MARK for analyses10/21/2011 6 Different models address different sources of variation in capture probabilities: • M0 = Equal Catchability Model (null model) -- Assumes every animal in the population has the same p-hat for each sampling period in the study. • Mh = The Heterogeneity Model -- Assumes that each animal has a unique p-hat that remains constant over all trapping occasions. Furthermore, capture probabilities are assumed to be a random sample of all individuals in the population. • Mb = The Trap Response Model -- Adjusts for a change in capture probabilities caused by a response to trapping. An assumption of the Mb model is that the initial p-hat for all animals is the same (equal catchability). Different models address different sources of variation in capture probabilities: • Mbh = The Heterogeneity and Trap Response Model-- Based on the assumption that each animal has its own unique pair of potential capture probabilities, pj and cj (j = 1, ..., N animals in the population), where pj is the initial capture probability and cj is the recapture probability. • Mt = The Time Variation (Schnabel) Model -- Based on the assumption that every individual in the population has the same p-hat for a given sampling occasion, but capture probabilities can vary at each sampling time. • Other Time-Dependent Models: Mth, Mtb, and Mtbh (various combinations of the above models).10/21/2011 7 Open Models: •Cormack-Jolly-Seber models (based on k>2) in Program MARK. •Combination of open and closed models (Pollock's Robust Design) in Program
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