BRIEF INTRODUCTION TOBRIEF INTRODUCTION TOROBUST DESIGN ROBUST DESIGN
CAPTURE-RECAPTURE CAPTURE-RECAPTURE
Original MotivationOriginal MotivationCJS 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 openEstimate 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 periodsPeriods longer-term sampling over which population is assumed to be open (gains and losses may occur, birth death, emigration)Secondary periodsPeriods 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 4In primary period 2: caught in secondary sample periods 1 and 4In primary period 3: caught in secondary sample periods 1 and 2In 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 periodsModelsCan 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 dynamicsDispersed 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