A Bayesian method for the joint estimation of outcrossing rate and inbreeding depression

Abstract

The population outcrossing rate (t) and adult inbreeding coefficient (F) are key parameters in mating system evolution. The magnitude of inbreeding depression as expressed in the field can be estimated given t and F via the method of Ritland (1990). For a given total sample size, the optimal design for the joint estimation of t and F requires sampling large numbers of families (100-400) with fewer offspring (1-4) per family. Unfortunately, the standard inference procedure (MLTR) yields significantly biased estimates for t and F when family sizes are small and maternal genotypes are unknown (a common occurrence when sampling natural populations). Here, we present a Bayesian method implemented in the program BORICE (Bayesian Outcrossing Rate and Inbreeding Coefficient Estimation) that effectively estimates t and F when family sizes are small and maternal genotype information is lacking. BORICE should enable wider use of the Ritland approach for field-based estimates of inbreeding depression. As proof of concept, we estimate t and F in a natural population of Mimulus guttatus. In addition, we describe how individual maternal inbreeding histories inferred by BORICE may prove useful in studies of inbreeding and its consequences.

A genomic selection component analysis characterizes migration-selection balance

“…As in mating system estimation models (Ritland and Jain ; Koelling et al. ), the log‐likelihood (ln L) is a simple sum across families: where U i is the genomic data for the i'th dead individual, U j is the data for the j'th survivor, u jk is the data for the k'th offspring of that parent j (u jk is a series of datasets with k ranging from 1 to n j , the number of genotyped offspring in the family), and Prob[*] denotes a probability statement. Parents and offspring are considered jointly in the latter term, because with uncertain genotype calls, the relative likelihoods of the possible parental genotypes are at least potentially informed by the genotype data of progeny.…”

Shifts in outcrossing rates and changes to floral traits are associated with the evolution of herbicide resistance in the common morning glory

“…BORICE is reported to perform well when either family sizes are small or maternal genotypes are unavailable (Koelling et al . ). We used the following default parameters when estimating mating system parameters: 1 million iterations and 99 999 burn‐in steps, an outcrossing rate tuning parameter of 0.05, an allele frequency tuning parameter of 0.1 and an initial population outcrossing rate of 0.5.…”

“…We estimated mating system parameters using BORICE (Koelling et al . ), which is a Bayesian method to estimate the family‐level outcrossing rate (t) and maternal‐line inbreeding coefficients (F) (Koelling et al . ).…”

“…), which is a Bayesian method to estimate the family‐level outcrossing rate (t) and maternal‐line inbreeding coefficients (F) (Koelling et al . ). BORICE is reported to perform well when either family sizes are small or maternal genotypes are unavailable (Koelling et al .…”

“…We examined our ability to assign parentage using Cervus (Kalinowski et al 2007) and determined population-level estimates of genetic diversity and inbreeding using GenalEx (Peakall & Smouse 2012). We estimated mating system parameters using BORICE (Koelling et al 2012), which is a Bayesian method to estimate the family-level outcrossing rate (t) and maternal-line inbreeding coefficients (F) (Koelling et al 2012). BORICE is reported to perform well when either family sizes are small or maternal genotypes are unavailable (Koelling et al 2012).…”