Mark-Recapture Estimates of Population Size

• Population is sampled 2 or more times with previously unmarked individuals receiving a unique mark

• 'Captured' individuals are released back into the population

** Capture may be accomplished by physical capture, photography, DNA fingerprinting, etc.

Mark-recapture Methods

1. Lincoln-Petersen method:

• 1 recapture event

• Closed population

• Equal capture probability of individuals during BOTH capture events

• Marks are not lost, gained, or overlooked

2. K-sample Closed Population Models:

• >1 (K) recapture/marking events

• Closed population

• Equal probability of capture within a given sampling occasion BUT probabilities can vary between sampling periods

• Capture history for each individual is recorded

• Program CAPTURE

        Models to accommodate different capture probabilities:

1. Equal capture model (M₀): Every animal has the same capture probability every time.

2. Heterogeneity model (M_h):  Each animal (j) has a unique capture probability (p_j)

 

2. 'Trap' response model (M_b):  All individuals have same initial capture probability (p) and all marked individuals in subsequent captures have a constant recapture probability (c).  p and c can be different 

 

3. Behavior heterogeneity model (M_bh):  Each animal has its own unique pair of initial capture (p_j) and recapture probabilities (c_j)

 

4. Time variation (Schnabel) model (M_t):  Every individual in the population has the same (re)capture probabilities that can vary over time (t).  Thus, capture probabilities are (p_t) for t = 1, 2, ..., K sampling occasions.

 

5. Time-heterogeneity model (M_th):  Each individual has a unique capture probability that can vary through time (p_tj)

 

6. Time-behavioral response model (M_tb):  Every animal that has not been previously marked has an initial capture probability that can vary with time (p_t) and every animal that has been previously caught has a recapture probability that can vary with time (c_t) 

 

7. Time-behavioral-heterogeneity model (M_tbh):  Each individual has a unique initial capture probability that can vary with time (p_tj) and each individual has a unique recapture probability that can vary with time (c_tj). 

** Each of these models have substantially different number of parameters that need to be estimated

** Use BOTH biological and statistical (e.g., AIC) arguments for model selection (additional notes on AIC)

3. Jolly-Seber method:

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

• Every animal present in the population (marked and unmarked) has the same probability of capture during each sampling occasion (p_t)

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

• Marks are not lost or overlooked.

• 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.

• Every animal in the population is equally likely to emigrate and emigration is permanent 

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

Notation for the Jolly-Seber model:

N_t = total number of animals in the population at time (t) of the sample

M_t = total number of marked animals in the population at time (t) of the sample

m_t = Number of marked animals caught in sample t

n_t = Total number of animals caught in sample t

R_t = Total number of animals released after sample = n_t - accidental deaths or removals

r_t = Number of individuals released at sample t and caught again in some later sample

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

        To estimate population size:  Program JOLLY (http://www.mbr-pwrc.usgs.gov/software)

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

Capture history for field voles: