Simulation-Based Spatially Explicit Close-Kin Mark-Recapture

Abstract

Estimating the size of wild populations is a critical priority for ecologists and conservation biologists, but tools to do so are often labour intensive and expensive. A promising set of newer approaches are based on genetic data, which can be cheaper to obtain and less invasive than information from more direct observation. One of these approaches is close-kin mark-recapture (CKMR), a type of method that uses genetic data to identify kin pairs and estimates population size from these pairs. Although CKMR methods are promising, one limitation to using them more broadly is a lack of CKMR models that can deal with spatially structured populations and spatial heterogeneity in sampling. In this paper, we introduce a spatially explicit approach to CKMR that uses individual-based simulation in concert with a deep convolutional neural network to estimate population sizes. Using simulations, we show that our method, CKMRnn, is highly accurate, even in the face of spatial heterogeneity in sampling and spatial population structure, and demonstrate that it can account for potential confounders such as unknown population histories. Finally, to demonstrate the accuracy of our method in an empirical system, we apply CKMRnn to data from a Ugandan elephant population, and show that point estimates from our method recapitulate those from traditional estimators but that the confidence interval on our estimator is approximately 30% narrower.

FIGURE 1

A schematic of CKMRnn's convolutional neural network architecture. The input is a collection of maps of parent‐offspring and half‐sibling pairs and a map of sampling intensity, and the output is an estimate of population size. See the text for a precise description.

FIGURE 2

Empirical data for African elephants in Kibale National Park. (a) Locations of samples (points) within the park (outline). (b–d) Images provided to the neural network, showing (b) sampling intensity (pixel lightness is proportional to number of samples in that 1 km × 1 km pixel); (c) recaptures (lines connect original and recapture locations); and (d) parent‐offspring pairs (lines connect parent and offspring sampling locations).

FIGURE 3

Performance of CKMRnn when trained and tested on simulations with constant population size over time. (a) True vs predicted $N$ for three levels of spatial sampling bias. $y=x$ line included for reference. (b) Relative error for three levels of spatial sampling bias and three test sets: all simulations, simulations with $N<12000$ and simulations with $N\ge 12000$.

FIGURE 4

Performance of CKMRnn when trained on simulations with constant population size over time and tested on simulations with increasing, constant or decreasing population size. All results are for medium spatial sampling bias. (a) True vs predicted $N$ for population sizes increasing or decreasing by 1% per year. $y=x$ line included for reference. (b) Relative error for increasing, decreasing, or constant population size test sets.

FIGURE 5

Performance of CKMRnn when trained and tested on simulations with increasing, constant or decreasing population size. All results are for medium spatial sampling bias. (a) True vs predicted $N$ for population sizes increasing or decreasing by 1% per year or constant. $y=x$ line included for reference. (b) Relative error for increasing, decreasing, or constant population size test sets.

FIGURE 6

Performance of CKMRnn on elephant simulations. (a) True vs predicted $N$ for a held out test set of elephant simulations. $y=x$ line included for reference. (b) Relative error for a held out test set of elephant simulations.

FIGURE 7

Histogram of parametric bootstrap replicates for population size of African elephants in Kibale National Park. Vertical lines are the point estimate and bounds of the 95% confidence interval.