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\begin{document}

\title{Age is not just a number: how incorrect ageing impacts close-kin
mark-recapture estimates of population size}



\author[1]{Felix Petersma}%
\author[1]{Len Thomas}%
\author[1]{Danielle Harris}%
\author[2]{Darcy Bradley}%
\author[3]{Yannis P.  Papastamatiou}%
\affil[1]{University of St Andrews}%
\affil[2]{University of California Santa Barbara}%
\affil[3]{Florida International University}%


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  \date{May 25, 2024}


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\begin{abstract}
Population size is a key parameter for the conservation of animal
species. Close-kin mark-recapture (CKMR) relies on the observed
frequency and type of kinship among individuals sampled from the
population to estimate population size. This approach requires being
able to determine the age of sampled individuals. One common approach,
particularly in fish studies, is to measure animal length and using an
assumed age-length relationship (a `growth curve'). We used simulation
to test the effect of misspecifying the length measurement error and the
growth curve on population size estimation. Simulated populations
represented two fictional shark species, one with a relatively simple
life history and the other with a more complex life history based on the
grey reef shark (Carcharhinus amblyrhynchos). We estimated sex-specific
adult abundance, which we assumed to be constant in time. We observed
small median biases in these estimates ranging from 1.35 to 2.79\% when
specifying the correct measurement error and growth curve, with true
coefficients of variation between 21.56 and 28.50\%. Introducing error
via misspecified growth curves resulted in changes in the magnitude of
the estimated total population, with upwards shifts negatively biasing
abundance estimates. Over- and underestimating the length measurement
error did not introduce a bias and had negligible effect on the variance
in the estimates. Our findings show that assuming an incorrect length
measurement error has little effect on estimation, but having an
accurate growth curve is crucial for CKMR whenever ageing is based on
length measurements. If ageing could be biased, researchers should be
cautious when interpreting CKMR results and consider the potential
biases arising from inaccurate age inference.%
\end{abstract}%



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