## Mark-Recapture Estimates of Population Size

### Mark-recapture Methods

1. Lincoln-Petersen method: Closed populations, single marking event

2. Schnabel method: Closed populations, multiple marking and recapture events, equal probability of capture within a given sampling occasion but probabilities can vary between sampling periods.

3. CAPTURE: Closed populations, multiple marking and recapture events, unequal probability of capture due to:

• Individual differences in capture probabilities

• Differences in capture probabilities associated with a behavioral response to trapping

• Differing capture probabilities between sampling periods (Schnabel model)

1. Jolly-Seber method: Open populations, equal probability of capture, multiple marking and recapture events

### A. Fundamental concepts of Jolly -Seber method

• Jolly (1965) and Seber (1965) submitted idea separately.

• Model estimates population size, "mortality" rates (i.e., deaths + emmigration), and "births" (i.e., births + immigration)

### B. Notation for the Jolly-Seber model:

mt = Number of marked animals caught in sample t

ut = Number of unmarked animals caught in sample t

nt = Total number of animals caught in sample t

= mt + ut

st = Total number of animals released after sample t

= nt - accidental deaths or removals

Rt = Number of the st individuals released at sample t and caught again in some later sample

Zt = Number of individuals marked before sample t, not caught in sample t, but caught in some sample after sample t

### C. Estimate of Population Size

Example From Krebs, C. J. 1989. Ecological Methodology.

#### The Jolly-Seber model can also be used to estimate the loss rate and the addition rate of the population.

Øt = Loss rate.  Probability of survival from sample time t to sample time t + 1.

= Staying alive in the study area.  Individuals which emigrate are counted as losses just as individuals that die.

### D. Assumptions

1. Population is geographically closed.

2. Every animal present in the population (marked and unmarked) has the same probability of capture in sample t.

3. Every marked animal present in the population immediately after the ith sample has the same probability of survival (Øi) until the (t + 1)th sampling time.

4. Marks are not lost or overlooked.

5. Sampling time is negligible in relation to intervals between samples (i.e., demographic closure is satisfied during each sampling occasion) and each release is made immediately after the sample.