Temporal Variability in Effective Size ( N ̂ e $$ {\hat{N}}_e $$ ) Identifies Potential Sources of Discrepancies Between Mark Recapture and Close Kin Mark Recapture Estimates of Population Abundance.

Although efforts to estimate effective population size, census size and their ratio in wild populations are expanding, few empirical studies investigate interannual changes in these parameters. Hence, we do not know how repeatable or representative many estimates may be. Answering this question requires studies of long-term population dynamics. Here we took advantage of a rich dataset of seven brook trout (Salvelinus fontinalis) populations, 5 consecutive years and 5400 individuals genotyped at 33 microsatellites to examine variation in estimates of effective and census size and in their ratio. We first estimated the annual effective number of breeders ( $\hat{N}$ _b) using individuals aged 1+. We then adjusted these estimates using two life history traits, to obtain ${\hat{N}}_{b\left(\mathrm{adj}2\right)}$ and subsequently, ${\hat{N}}_{e\left(\mathrm{adj}2\right)}$ following Waples et al. (2013). ${\hat{N}}_{e\left(\mathrm{adj}2\right)}$ was estimated for the years 2014 to 2019. Census size was estimated by mark recapture using double-pass electrofishing ( ${\hat{N}}_{c\left(\mathrm{MR}\right)}$ ) (years 2014-2018) as well as by the Close Kin Mark Recapture approach ( ${\hat{N}}_{c\left(\text{CKMR}\right)}$ ) (years 2015-2017). Within populations, annual variation in ${\hat{N}}_{e\left(\mathrm{adj}2\right)}$ (ratio of maximum to minimum ${\hat{N}}_{e\left(\mathrm{adj}2\right)}$ ) ranged from 1.6-fold to 58-fold. Over all 7 populations, the median annual variation in ${\hat{N}}_{e\left(\mathrm{adj}2\right)}$ was around 5-fold. These results reflect important interannual changes in the variance in reproductive success and more generally in population dynamics. Within population ${\hat{N}}_{c\left(\mathrm{MR}\right)}$ varied between years by a (median) factor of 2.7 with a range from 2 to 4.3. Thus, estimated effective size varied nearly twice as much as did estimated census size. Our results therefore suggest that, at least in small populations like those examined in the present study, any single annual estimate of ${\hat{N}}_{e\left(\mathrm{adj}2\right)}$ is unlikely to be representative of long-term dynamics. At least 3-4 annual estimates may be required for an estimate of contemporary effective size to be truly representative. We then compared ${\hat{N}}_{c\left(\mathrm{MR}\right)}$ to ${\hat{N}}_{c\left(\text{CKMR}\right)}$ . For five of the seven populations, the estimates of population abundance based on mark recapture ( ${\hat{N}}_{c\left(\mathrm{MR}\right)}$ ) were indistinguishable from those based on close kin mark recapture ( ${\hat{N}}_{c\left(\text{CKMR}\right)}$ ). The two populations with discordant ${\hat{N}}_{c\left(\mathrm{MR}\right)}$ and ${\hat{N}}_{c\left(\text{CKMR}\right)}$ exhibited extremely low ${\hat{N}}_{e\left(\mathrm{adj}2\right)}/{\hat{N}}_{c\left(\mathrm{MR}\right)}$ ratios and the largest annual variation in ${\hat{N}}_{e\left(\mathrm{adj}2\right)}$ (58-fold and 35.4-fold respectively). These results suggest that sampling effort in these two streams may have been insufficient to properly capture the genetic diversity of the entire population and that individuals sampled were not representative of the population. Our study further validates CKMR as a method for estimating abundance in wild populations and it demonstrates how knowledge of the temporal variation in ${\hat{N}}_e$ can be used to identify potential sources of discrepancies between ${\hat{N}}_{c\left(\mathrm{MR}\right)}$ and ${\hat{N}}_{c\left(\text{CKMR}\right)}$ .