Capture-recapture Models for Open Populations Abundance, Recruitment and Growth Rate Modeling 6.15 UF-2015

Population Growth Model

Estimated from capture-recapture data = “finite rate of population increase” Closely related to population changes Difference with the obtained from projection matrices –It does not rely on asymptotics (e.g., temporal constancy of vital rates, stable age distribution) –It incorporates movement as well as birth and death

3 approaches Jolly-Seber Superpopulation Reverse-time

Jolly-Seber Model

Concept of the JS model Same kind of modeling as CJS model, but extended to abundance (N) Idea: apply the p estimated based on marked animals to unmarked animals => allows modeling Pr(animal never caught)

Data u m m 0 m u m 0 0 m u m m 0 0 Etc…

Conceptual model

Estimation of Abundance Apply the p estimated based on marked animals to unmarked animals as well Abundance is estimated as: (marked + unmarked caught) / (estimated capture probability)

Estimation of Abundance, N i, and Recruitment From i to i+1, B i n i = number of animals caught/detected at sample period i p estimated from marked animals # of survivors

2 important assumptions In addition to ‘classic’ CJS assumptions, we assume: Same survival for marked and unmarked animals Same detection for marked and unmarked animals

Superpopulation Model (called POPAN in MARK)

Superpopulation Approach B0B0 N 1 = B 0 N 1 –S 1 N 2 = S 1 + B 1 N3N3 N4N4 B1B1 N 2 –S 2 B2B2 N 3 –S 3 B3B3 k=1k=2k=3 K=4

Special Application: Estimation of Birds Passing Through a Migration Stopover Site

Superpopulation and JS models Data: marked animals and unmarked animals detected Key Assumption: Marked and unmarked animals have similar capture probabilities

...a backward process with recruitment and no mortality is statistically equivalent to a forward process with mortality and no recruitment Pollock et al. (1974) Reverse-time Model

Reverse time modeling  i = seniority parameter = probability that an animal in the sampled population at period i was already in the sampled population at i-1

Reverse time modeling

Reverse-time Modeling: Potential Uses

Pradel’s Full Likelihood 2 ways to write expected number of animals alive in 2 successive sample periods:

Pradel’s Full Likelihood Simultaneous forward- and reverse-time modeling (called temporal-symmetry model)

Pradel’s Full Likelihood: 3 Parameterizations  i = seniority parameter i = population growth rate f i = recruitment rate (recruits at i+1 per animal at i) = B i / N i

Relationships Reminder:  i = seniority parameter = probability that an animal in the sampled population at period i was already in the sampled population at i-1 = contribution to pop growth due to survival

Pradel’s Full Likelihood: Potential Uses Direct estimation of and its temporal variance This should correspond more closely than projection matrix ’s to observed population changes because: –It does not rely on asymptotics (e.g., temporal constancy of vital rates, stable age distribution) –It incorporates movement as well as birth and death Can model as a function of covariates and specific vital rates (proper way to do “key factor analysis”)

Remember: Jolly-Seber annual population size (one value/year) Superpopulation N* is # animal ever in population (summed over years…) Reverse-time (gives you estimate of λ or recruitment directly)