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 labor 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, a major limitation to using them more broadly is a lack of CKMR models that can deal with spatial heterogeneity both in population density and sample effort. We introduce a simulation-based approach to CKMR that uses spatially explicit individual-based simulation in concert with a deep convolutional neural network to estimate population sizes. Using extensive simulation, we show that our method, CKMRnn, is highly accurate, even in the face of spatial heterogeneity, 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 reduced by approximately 30%.

Figure 1:

CKMRnn’s convolutional neural network architecture.

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 1km × 1km pixel); (c) recaptures (lines connect original and recapture locations); and (d) parent-offspring pairs (lines connect parent and offspring sampling locations).

Figure 3:

Probability that a simulated female elephant is fertile in a given year, given her age and the number of years since she last reproduced.

Figure 4:

Performance of CKMRnn when trained and tested on simulations with constant population size over time.

Figure 5:

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.

Figure 6:

Performance of CKMRnn when trained and tested on simulations with increasing, constant, or decreasing population size. All results are for medium spatial sampling bias.

Figure 7:

Performance of CKMRnn on elephant simulations.

Figure 8:

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.