Summary1. Heterozygosity-fitness correlations (HFCs) have been widely used to explore the impact of inbreeding on individual fitness. Initially, most studies used small panels of microsatellites, but more recently with the advent of next-generation sequencing, large SNP datasets are becoming increasingly available and these provide greater power and precision to quantify the impact of inbreeding on fitness. 2. Despite the popularity of HFC studies, effect sizes tend to be rather small. One reason for this may be low variation in inbreeding levels among individuals. Using genetic markers, it is possible to measure variance in inbreeding through the strength of correlation in heterozygosity across marker loci, termed identity disequilibrium (ID). 3. ID can be quantified using the measure g 2 , which is also a central parameter in HFC theory that can be used within a wider framework to estimate the direct impact of inbreeding on both marker heterozygosity and fitness. However, no software exists to calculate g 2 for large SNP datasets nor to implement this framework. 4. inbreedR is an R package that provides functions to calculate g 2 based on microsatellite and SNP markers with associated P-values and confidence intervals. Within the framework of HFC theory, inbreedR also estimates the impact of inbreeding on marker heterozygosity and fitness. Finally, inbreedR implements user-friendly simulations to explore the precision and magnitude of estimates based on different numbers of genetic markers. We hope this package will facilitate good practice in the analysis of HFCs and help to deepen our understanding of inbreeding effects in natural populations.

The multilocus Moran model with recombination is considered, which describes the evolution of the genetic composition of a population under recombination and resampling. We investigate a marginal ancestral recombination process, where each site is sampled only in one individual and we do not make any scaling assumptions in the first place. Following the ancestry of these loci backward in time yields a partition-valued Markov process, which experiences splitting and coalescence. In the diffusion limit, this process turns into a marginalised version of the multilocus ancestral recombination graph. With the help of an inclusion-exclusion principle and so-called recombinators we show that the type distribution corresponding to a given partition may be represented in a systematic way by a sampling function. The same is true of correlation functions (known as linkage disequilibria in genetics) of all orders. We prove that the partitioning process (backward in time) is dual to the Moran population process (forward in time), where the sampling function plays the role of the duality function. This sheds new light on the work of Bobrowski et al. (J Math Biol 61:455-473, 2010). The result also leads to a closed system of ordinary differential equations for the expectations of the sampling functions, which can be translated into expected type distributions and expected linkage disequilibria.

We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the genetic material of individuals in a population experiencing recombination. We aim at the law of the process over time. To this end, we investigate sets of realisations of this process that agree with respect to a specific order of events and represent each such set by a rooted (binary) tree. The probability of each tree is, in turn, obtained by Möbius inversion on a suitable poset of all rooted forests that can be obtained from the tree by edge deletion; we call this poset the pruning poset. Dependencies within the fragments make it difficult to obtain explicit expressions for the probabilities of the trees. We therefore construct an auxiliary process for every given tree, which is i.i.d. over time, and which allows to give a pathwise construction of realisations that match the tree.

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