calc_POP: Predict the probability of CKMR kinship pairs

In multiSA: Multi-Stock Assessment

Predict the probability of CKMR kinship pairs

Description

Calculate the probability of observing a parent-offspring pair (calc_POP) and half-sibling pair (calc_HSP) for closed-kin mark recapture (CKMR) for an age-structured model.

Usage

calc_POP(t, a, y, N, fec)

calc_HSP(yi, yj, N, fec, Z)

Arguments

t	Vector, capture year of parent i
a	Vector, age at capture of parent i
y	Vector, birth year of offspring j
N	Abundance of mature spawners. Matrix by ⁠[y, a]⁠
fec	Fecundity schedule of mature spawners. Matrix by ⁠[y, a]⁠
yi	Vector, birth year of sibling i. Must be older than sibling j.
yj	Vector, birth year of sibling j.
Z	Instantaneous total mortality rate. Matrix by ⁠[y, a]⁠

Value

Numeric, vector of probabilities

Parent-offspring pairs

The parent-offspring probability is calculated from Bravington et al. 2016, eq 3.4:

p_{\textrm{POP}} = 2 \times \dfrac{f(y_j,y_j - (t_i - a_i))}{\sum_a f(y_j,a) N(y_j,a)}

where y_j - (t_i - a_i) is the parental age in year y_j. Scalar 2 accounts for the fact that the parent could be either a mother or a father. calc_POP is vectorized with respect to t, a, and y.

Half-sibling pairs

The half-sibling probability is calculated from Bravington et al. 2016, eq 3.10, and expanded by Hillary et al. 2018, Supplement S2.8.1 for age-specific survival and fecundity of the parent:

p_{\textrm{HSP}} = 4 \times \sum_a\left( \dfrac{N(y_i, a)f(y_i, a)}{\sum_{a'} N(y_i, a')f(y_i,a')}\times \exp(-\sum_{t = 0}^{y_j - y_i - 1} Z(y_i + t,a + t))\times \dfrac{f(y_j,a+y_j-y_i)}{\sum_{a'} N(y_j,a')f(y_j,a')} \right)

• The first ratio is the probability that a fish at age a in year y_i is the parent of i.

• The exponential term is that fish's survival from year y_i to y_j.

• The second ratio is the probability that the parent of i, age a+y_j-y_i in year y_j, is the parent of j.

The parent is not observed in the HSP, so we sum the probabilities over all potential ages in year y_i. calc_HSP is vectorized with respect to yi and yj.

Author(s)

Q. Huynh with contribution from Y. Tsukahara (Fisheries Research Institute, Japan)

References

Bravington, M.V. et al. 2016. Close-Kin Mark-Recapture. Stat. Sci. 31: 259-274. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/16-STS552")}

Hillary, R.M. et al. 2018. Genetic relatedness reveals total population size of white sharks in eastern Australia and New Zealand. Sci. Rep. 8: 2661. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1038/s41598-018-20593-w")}

See Also

like_CKMR()

multiSA documentation built on March 21, 2026, 1:06 a.m.