brief introduction to robust design capture-recapture

BRIEF INTRODUCTION TOBRIEF INTRODUCTION TOROBUST DESIGN ROBUST DESIGN

CAPTURE-RECAPTURE CAPTURE-RECAPTURE

Original MotivationOriginal Motivation

CJS models permit estimation of survival and are robust to heterogeneity in capture probabilities.

JS models allow abundance estimation and recruitment but…

• Are not robust to capture heterogeneity/ behavioral effects

• Potential for serious bias in the estimates of abundance and recruitment

SolutionSolution

Estimate survival using CJS between periods when the population is considered open

Estimate abundance using closed capture models over shorter periods when the population is considered closed.

Combine the estimates to estimate recruitment

Sample designSample design

Sampling at 2 temporal scales:

Primary periods

Periods longer-term sampling over which population is assumed to be open (gains and losses may occur, birth death, emigration)

Secondary periods

Periods short-term sampling during which the population is assumed to be closed (no birth, death, emigration)

The best of both worlds: Robust Design

Combination of open and closed population models

Parameters: survival, emigration, immigration, detection, population size

Survival, emigration, immigration

Population size, capture probability

The Robust Design

Robust design capture Robust design capture histories histories

Encounter history ordered by primary period and secondary period within primary period

e.g., 3 primary periods, 4 secondary periods

0001 1001 1100 0000 note: NO SPACES in MARK data file

Interpretation:

In primary period 1: caught only in secondary sample period 4

In primary period 2: caught in secondary sample periods 1 and 4

In primary period 3: caught in secondary sample periods 1 and 2

In primary period 4: never caught

Likelihood based approach in Likelihood based approach in program MARKprogram MARK

Full likelihood using data from both primary and secondary periods

ModelsCan include virtually any of the open modelsAdditional parameter temporary emigration

Closed abundance estimationMaximum likelihood models, including

Huggins variationCovariates, time, and individual effects

Temporary emigration

Super population of animals Ni0

Subset of population Ni in sample area and available for capture with probability p*i

e.g., spawning sturgeon

All adult SturgeonSpawning

and non spawning

Ni0

Spawning sturgeonavailable for captureNi

Temporary emigration

Parameters ”i: probability that the animal leaves the study area(an estimate for each interval)

’i: probability stays away (i.e., is not available for capture), given that the animal was not present during primary trapping period i—1 (no estimate for the first interval)

No emigration: ”i = ’i= 0

Immigration only: ”i = 0

Random emigration: ”i = ’i

Advantages of Robust Design

In comparison with designs with dispersed effort:Permits the assumptions of closed population to be satisfied closely during the secondary periods with concentrated effort

The separation between primary periods is more appropriate for estimating survival and other parameters of population dynamics

Dispersed sampling effort frequently will result in a failure of the study estimates Insufficient data to estimate parameters with precisionFailure to satisfy assumptions of either the closed or open modelRD is recommended over dispersed sampling

Multiple options in MARK

Robust Design in MARK

We’ve barely scratched the surface

Planning a CMR study

How many marked fish needed?

How many capture occasions (primary/secondary)?

Effort per occasion?

“Power” to detect differences/change or precision of estimates?

Planning a CMR study

Evaluate tradeoffs via simulationvalues from previous studiespreliminary databest guesscosts constraints

Simulations in MARKSimulations in MARK

ON TO MARK