Pollock’s Robust Design: Model Extensions

Estimation of Temporary Emigration Temporary Emigration: = individual emigrated from study area, but only temporarily (e.g., for one or a few years) “emigrated”: individual is outside the study area during entire primary period => NOT available for detection “temporary”: animal will come back => not confounded with mortality, but bias detection low

Estimation of Temporary Emigration Temporary Emigration (TE) = individual unavailable for detection a given year We distinguish:

Estimation of Temporary Emigration Robust Design: closed + open models

TE: Two possible directions Exiting vs. remaining outside study area (from one year to the next) We define 2 distinct parameters: γ ' = Probability that an individual that was not present in the previous sampling period become present in the current sampling period γ '' = Probability that an individual that was present in the previous sampling period remains present in the current sampling period

Temporary emigration p1p1 p2p2 p3p3 p4p4 ’’ 1-  ” ’’

Models for temporary emigration No temporary emigration γ’ = γ’’ = 1 Random movement – emigration does not depend on last period γ’ = γ’’ Markovian movement – emigration depends on last period γ’ ≠ γ’’

Temporary Emigration: Biological Relevance Sometimes just local movement Breeding ground sampling: equates with P(nonbreeding) in various taxa (sea turtles, many bird species, some marine mammals, some toads)

Open Robust Design

Closed Robust Design p1p1 p2p2 p3p3 p4p4 ’’ 1-  ” ’’ Closure assumption within primary periods (closed model) No gain/loss

Open Robust Design p1p1 p2p2 p3p3 p4p4 ’’ 1-  ” 00 11 33 22 11 22 33 We model “staggered entries and departures” between secondary sampling occasions = Each indiv. can enter (  ) and depart (  ) only once each year = Super-Population model applied inside primary periods ’’ 1-  ”

Open Robust Design Deals with the fact that an individual might: -not be available yet at first sampling occasion and it might become = has not entered the sampled area yet -might become unavailable before the last occasion = has departed the sampled area

Kendall and Bjorkland (2001) Hawksbill Sea Turtle ( Eretmochelys imbricata )

Hawksbill Sea Turtle (Eretmochelys imbricata) Jumby Bay, Long Island, Antigua Collected 15 June – 15 November Female arrives, lays clutch returns to surf, lays up to 4 more clutches every 14 days Captured/resighted on nest, flipper tag applied and shell notched.

Hawksbill Sea Turtle (Eretmochelys imbricata) Breeding season divided into 10 half-month periods to approximate 14-day cycle of egg deposition Females are available for detection between first and last clutch NEVER breed in two consecutive years (Non-breeding = TE)

How do we account for no breeding in consecutive years? Why do we need an OPEN robust design model here? How do we interpret the ‘super-population’ estimate? p1p1 p2p2 p3p3 p4p4 ’’ 1-  ” ** 00 11 33 22 11 22 33 ’’ **

Hawksbill Sea Turtles (Parameters involved) 1. Between breeding seasons:  i * = prob. of survival/fidelity from year i to i+1  i ” = prob. turtle is a breeder in year i if turtle was a breeder in year i-1 Never happens =>  i ” = 0 ; (1 -  i ”) = 1  i ’ = prob. turtle is a breeder in year i if turtle was a non-breeder in year i-1

Hawksbill Sea Turtles (Parameters involved) 2. Inside breeding season:  ij = probability breeder in year i enters study area between sample j and j+1 (first clutch)  ij = prob. breeder in year i lays last clutch between samples j and j+1 p ij = prob. breeder is detected in sample j of year i

How do we account for no breeding in consecutive years? We fix:  i ” = 0 ; (1 -  i ”) = 1 p1p1 p2p2 p3p3 p4p4 ’’ 1-  ” ** 00 11 33 22 11 22 33 ’’ **

p1p1 p2p2 p3p3 p4p4 ’’ ** 00 11 33 22 11 22 33 ’’ ** Use of the OPEN robust design? Turtle only available between first and last clutch. Dates of arrival/departure vary. We use the  j and  j to model arrival/departures.

p1p1 p2p2 p3p3 p4p4 ’’ 1-  ” ** 00 11 33 22 11 22 33 ’’ ** Super-population?

Multistate Robust Design Combine methods to improve estimates of state transitions (Nichols and Coffman 1999, Coffman et al. 2001) Reverse-time example in next section –Allows contributions of survival, reproduction, and emigration to be separated