Open-Population Mark-Recapture Models - Introduction to Ecological Sampling - page 114

a similar manner, and the construction of the likelihood function is therefore
in principle straightforward.
An important feature of this approach for modeling is the focus on the
estimation of survival and capture probabilities instead of population sizes.
One justification for this is that mark-recapture estimation works better for
estimating these parameters than it does for the estimation of population
sizes. Another justification is that it is survival probabilities that are impor-
tant for population dynamics, and population size is just the outcome of sur-
vival and reproduction rates.
Of course, in some cases it really will be estimates of population size that
are needed. These can, however, always be derived using the estimation
equation

ˆ

/ ˆ

i i i , where N i is the estimated population size, n i is the num-
ber of animals captured, and ˆ i is the probability of capture, all for the i th
sample. This estimator is valid, providing that the probability of capture is
the same for marked and unmarked animals, which is an assumption that
is not required for the estimation of survival probabilities. The variance can
then be estimated using an equation provided by Taylor et al. (2002) and dis-
cussed in Chapter 9 of Amstrup et al. (2005, p. 244).

Nnp

8.6.1 Models for Capture and Survival Probabilities

In Chapter 7, in the section on the Huggins (1991) models, the advantages
of modeling the probabilities of capture by means of a logistic function of
the form

p i = exp( u i )/{1 + exp( u i )}. (8.20)

were discussed. Those same advantages apply here to both capture and sur-
vival probabilities of the form

ϕ i = exp( v i )/{1 + exp( v i )} (8.21)

Incorporating these logistic functions of external covariates into the CJS like-
lihood was formally proposed by Lebreton et al. (1992) and makes it easy
to model effects associated with time or individual differences because of
age, weight, sex, and so on. For example, if x i is a measure of the severity
of the weather from year j to year j + 1 and y i is a measure of the effort put
into recapturing animals in year j , then it may be considered appropriate to
model the probabilities of capture and survival by

ϕ j = exp(α 0 + α 1 x j )/{1 + exp(α 0 + α 1 x j )} (8.22)

and

p j = exp(β 0 + β 1 y j )/{1 + exp(β 0 + β 1 y j )}. (8.23)