An Extended Empirical Saddlepoint Approximation for Intractable Likelihoods

The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a procedure that reduces the observed and simulated data to a set of summary statistics, and quantifies the discrepancy between them through a synthetic likelihood function. SL requires little tuning, but it relies on the approximate normality of the summary statistics. We relax this assumption by proposing a novel, more flexible, density estimator: the Extended Empirical Saddlepoint approximation. In addition to proving the consistency of SL, under either the new or the Gaussian density estimator, we illustrate the method using two examples. One of these is a complex individual-based forest model for which SL offers one of the few practical possibilities for statistical inference. The examples show that the new density estimator is able to capture large departures from normality, while being scalable to high dimensions, and this in turn leads to more accurate parameter estimates, relative to the Gaussian alternative. The new density estimator is implemented by the esaddle R package, which can be found on the Comprehensive R Archive Network (CRAN)

Variance propagation for density surface models

Data from the SCANS-II project were supported by the EU LIFE Nature programme (project LIFE04NAT/GB/000245) and governments of range states: Belgium, Denmark, France, Germany, Ireland, Netherlands, Norway, Poland, Portugal, Spain, Sweden, and UK. This work was funded by OPNAV N45 and the SURTASS LFA Settlement Agreement, and being managed by the US Navy’s Living Marine Resources program under Contract No. N39430-17-C-1982, US Navy, Chief of Naval Operations (Code N45), grant number N00244-10-1-0057 and the International Whaling Commission.Spatially explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density surface models (DSMs) are a two-stage approach for estimating spatially varying density from distance sampling data. First, detection probabilities—perhaps depending on covariates—are estimated based on details of individual encounters; next, local densities are estimated using a GAM, by fitting local encounter rates to location and/or spatially varying covariates while allowing for the estimated detectabilities. One criticism of DSMs has been that uncertainty from the two stages is not usually propagated correctly into the final variance estimates. We show how to reformulate a DSM so that the uncertainty in detection probability from the distance sampling stage (regardless of its complexity) is captured as an extra random effect in the GAM stage. In effect, we refit an approximation to the detection function model at the same time as fitting the spatial model. This allows straightforward computation of the overall variance via exactly the same software already needed to fit the GAM. A further extension allows for spatial variation in group size, which can be an important covariate for detectability as well as directly affecting abundance. We illustrate these models using point transect survey data of Island Scrub-Jays on Santa Cruz Island, CA, and harbour porpoise from the SCANS-II line transect survey of European waters. Supplementary materials accompanying this paper appear on-line.Publisher PDFPeer reviewe

Low levels of sibship encourage use of larvae in western Atlantic bluefin tuna abundance estimation by close-kin mark-recapture

Globally, tunas are among the most valuable fish stocks, but are also inherently difficult to monitorand assess. Samples of larvae of Western Atlantic bluefin tuna Thunnus thynnus (Linnaeus, 1758) fromstandardized annual surveys in the northern Gulf of Mexico provide a potential source of “offspring”for close‑kin mark‑recapture (CKMR) estimates of abundance. However, the spatial patchiness andhighly skewed numbers of larvae per tow suggest sampled larvae may come from a small number ofparents, compromising the precision of CKMR. We used high throughput genomic profiling to studysibship within and among larval tows from the 2016 standardized Gulf‑wide survey compared totargeted sampling carried out in 2017. Full‑ and half‑siblings were found within both years, with 12%of 156 samples in 2016 and 56% of 317 samples in 2017 having at least one sibling. There were alsotwo pairs of cross cohort half‑siblings. Targeted sampling increased the number of larvae collectedper sampling event but resulted in a higher proportion of siblings. The combined effective sample sizeacross both years was about 75% of the nominal size, indicating that Gulf of Mexico larval collectionscould be a suitable source of juveniles for CKMR in Western Atlantic bluefin tuna

Close-kin mark-recapture informs critically endangered terrestrial mammal status

Reliable information on population size is fundamental to the management of threatened species. For wild species, mark-recapture methods are a cornerstone of abundance estimation. Here, we show the first application of the close-kin mark-recapture (CKMR) method to a terrestrial species of high conservation value; the Christmas Island flying-fox (CIFF). The CIFF is the island's last remaining native terrestrial mammal and was recently listed as critically endangered. CKMR is a powerful tool for estimating the demographic parameters central to CIFF management and circumvents the complications arising from the species’ cryptic nature, mobility, and difficult-to-survey habitat. To this end, we used genetic data from 450 CIFFs captured between 2015 and 2019 to detect kin pairs. We implemented a novel CKMR model that estimates sex-specific abundance, trend, and mortality and accommodates observations from the kin-pair distribution of male reproductive skew and mate persistence. CKMR estimated CIFF total adult female abundance to be approximately 2050 individuals (95% CI (950, 4300)). We showed that on average only 23% of the adult male population contributed to annual reproduction and strong evidence for between-year mate fidelity, an observation not previously quantified for a Pteropus species in the wild. Critically, our population estimates provide the most robust understanding of the status of this critically endangered population, informing immediate and future conservation initiatives

A combined acoustic and trawl survey for efficiently estimating fish abundance

When fish are patchily distributed, unstratified trawl surveys give highly variable abundance estimates. If the patches are small and mobile, it is impractical to use pre-stratified or multi-stage adaptive designs to reduce variability. Based on recent trawl surveys for mackerel icefish Champsocephalus gunnari, we have modified the survey design and analysis to reduce estimation variance at minimal cost, using concomitant qualitative acoustic data. We have also developed new confidence interval procedures that should be accurate even for small samples. In computer simulations, the new method substantially outperformed a standard trawl survey