Capture-recapture Models for Open Populations Multiple Ages

Context Single-age models: assume that survival is the same for all age classes But often survival varies with age: –Higher mortalities of young? –Senescence? How do we estimate different survival rates?

Multiple Age Models Age-specific survival 1.2-age class (Pollock 1981) 2.Age-0 cohort Models (full age) Age-specific breeding probabilities

2-Age Model of Pollock (1981)

Pollock’s 2-Age Model CJS-type model for multiple age classes developed by Ken Pollock (1981)  allows survival and recapture rates to vary with both time and age Developed for situation where animal can be aged on capture (young/juv. vs. adult)

Sampling Design Open-population capture-recapture study Animal identified as young or adult at capture ; then, marked and released Time interval between sampling period must be the same as the time interval required to make transition from young to adult (e.g., annual samples for birds)

Multiple-Age Model of Pollock (1981): Notation for 2 Ages  i (0) = survival probability for young animals, from sample period i to period i+1 (transition between young and adult occurs during this period)  i (1) =survival probability for adults, i to i+1 p i (1) = capture probability for adults in i

Capture History Probabilities P(0 A A 0 A | released as adult in 2) = P(0 Y A 0 A | released as young in 2) = first capture/release at occ. 2

Multiple-Age Model of Pollock (1981): Additional Modeling Additional modeling abilities with multiple- age models are the same as those for single age models –Multiple groups –Capture-history dependence –Time-specific and group-specific covariates –Individual covariates

Assumptions Similar to those of single-age models Homogeneity of rate parameters now applies within age classes Time interval between sample periods corresponds to time needed to make age class transition (usually ‘annual’)

Age-0 Cohort Model

Framework Age is known with certainty only for animals marked at birth (age 0) If an animal is first caught as adult, age is unknown => we don’t use these data here ! Now, age specific survival can be estimated for all ages: 1,2,3,4,5,… (not only “age classes”)

Age-0 cohort models Age is known with certainty only for animals marked at birth (age 0) If an animal is first caught as adult, age is unknown Limit data to known age individuals, then age specific survival can be estimated

What is a cohort ? Sampling Occasion t1t2t3t4t5t6 cohort 1a0a1a2a3a4a5 cohort 2a0a1a2a3a4 cohort 3a0a1a2a3 cohort 4a0a1a2 cohort 5a0a1 cohort 6 a0 Cohort = all individuals born in a same year Age = unique combination “cohort*time” => Age specific can be expressed in 2-ways: - time-specific - cohort-specific

Notation – age and time  i (a) = probability that animal survives from age a to a+1 for the sample period i to period i+1 p i (a) = capture probability for individuals of age a in sample period i P(01101 | released as young in sample 2) =

Notation – age and cohort  c (a) = probability that animal survives from age a to a+1 for an individual from cohort c p c (a) = capture probability at age a for an individual from cohort c P(01101 | released as young in sample 2) =

Linear functions for age-specific survival Linear logistic Account for processes like senescence Or ‘quadratic’

Implementing the model Easily done in MARK “Age effect” models Can be combined with time/cohort effect But remember that you assume ‘known age’ for all individuals in your data

Age-specific breeding model

Context Young are marked at breeding area and not expected to return until they are adult breeders Age not relevant once adults start breeding Focus is on the age at which individuals return and start breeding

Notation k – earliest age an individual can breed m – age at which all are assumed to breed - probability breeder is detected - probability breeder survives - probability young survive to age k - probability non-breeder becomes breeder at age a (transition)

Example of C.H. Assume earliest age 2 and all breed by age 3 Pr(10011|released at period 1 as young of age 0) Started breeding at age 2, but not detected Did not started breeding at age 2, Survived to age k=2

Example of C.H Assume earliest age 2 and all breed by age 3 Pr(01001|adult released in period 2)

Some Assumptions No breeding <k and everyone is a breeder by m All non-breeders and breeders have same survival and detection (homogeneity assumption) Non-breeders greater than age > 0 not recorded as detected Breeding probability is constant (over time, among indiv.)