Nonequivalent lethal equivalents: Models and inbreeding metrics for unbiased estimation of inbreeding load

Inbreeding depression, the deterioration in mean trait value in progeny of related parents, is a fundamental quantity in genetics, evolutionary biology, animal and plant breeding, and conservation biology. The magnitude of inbreeding depression can be quantified by the inbreeding load, typically measured in numbers of lethal equivalents, a population genetic quantity that allows for comparisons between environments, populations or species. However, there is as yet no quantitative assessment of which combinations of statistical models and metrics of inbreeding can yield such estimates. Here, we review statistical models that have been used to estimate inbreeding load and use population genetic simulations to investigate how unbiased estimates can be obtained using genomic and pedigree-based metrics of inbreeding. We use simulated binary viability data (i.e., dead versus alive) as our example, but the concepts apply to any trait that exhibits inbreeding depression. We show that the increasingly popular generalized linear models with logit link do not provide comparable and unbiased population genetic measures of inbreeding load, independent of the metric of inbreeding used. Runs of homozygosity result in unbiased estimates of inbreeding load, whereas inbreeding measured from pedigrees results in slight overestimates. Due to widespread use of models that do not yield unbiased measures of the inbreeding load, some estimates in the literature cannot be compared meaningfully. We surveyed the literature for reliable estimates of the mean inbreeding load from wild vertebrate populations and found an average of 3.5 haploid lethal equivalents for survival to sexual maturity. To obtain comparable estimates, we encourage researchers to use generalized linear models with logarithmic links or maximum-likelihood estimation of the exponential equation, and inbreeding coefficients calculated from runs of homozygosity, provided an assembled reference genome of sufficient quality and enough genetic marker data are available.