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: = Pr(presence in sampled area) and = Pr(detection | presence in sampled area)

We have:

Estimation of Temporary Emigration

Robust Design: closed + open models

Closed model: Pr(detection | availability)

Open model:

= Pr(detection | availability) * Pr(availability)

We can thus estimate as =>

TE: Two possible directionsExiting 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

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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

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Closure assumption within primary periods (closed model)

No gain/loss

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Open Robust Design

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1 2 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 1987-96• 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 depositionFemales 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?

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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 betweensamples j and j+1

pij = 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

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*

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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.

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0 1 32

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Super-population?

= Total number of turtles that bred (in sampled area) this year

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