SUMMARY: Optimal contribution selection (OCS) is a selective breeding method that manages the conversion of genetic variation into genetic gain to facilitate short-term competitiveness and long-term sustainability of breeding programmes. Traditional approaches to OCS and truncation selection (TS) rely on estimates of breeding values and do not explicitly account for uncertainty in these estimates. Here, we use concepts from robust optimization to formulate a robust optimal contribution selection problem (ROCS) and develop two solutions based on conic optimization and sequential quadratic programming. We implemented these methods in the robustocs Python package, which leverages the Gurobi and HiGHS solvers. Our results show favorable performance when solving the ROCS problem using sequential quadratic programming with the HiGHS solver. We show that classical TS and OCS arise as special cases of the robust selection formulations (RTS and ROCS). We demonstrate the package with a small example, comparing outcomes of TS, RTS, OCS, and ROCS. Compared to TS and OCS, RTS and ROCS find contributions that reduce the uncertainty of genetic gain and group coancestry at the expense of reduced genetic gain. AVAILABILITY AND IMPLEMENTATION: robustocs is implemented in Python and released, with documentation, on GitHub under the MIT license at https://github.com/Foggalong/RobustOCS.

SUMMARY: AlphaFamImpute is an imputation package for calling, phasing and imputing genome-wide genotypes in outbred full-sib families from single nucleotide polymorphism (SNP) array and genotype-by-sequencing (GBS) data. GBS data are increasingly being used to genotype individuals, especially when SNP arrays do not exist for a population of interest. Low-coverage GBS produces data with a large number of missing or incorrect naïve genotype calls, which can be improved by identifying shared haplotype segments between full-sib individuals. Here, we present AlphaFamImpute, an algorithm specifically designed to exploit the genetic structure of full-sib families. It performs imputation using a two-step approach. In the first step, it phases and imputes parental genotypes based on the segregation states of their offspring (i.e. which pair of parental haplotypes the offspring inherited). In the second step, it phases and imputes the offspring genotypes by detecting which haplotype segments the offspring inherited from their parents. With a series of simulations, we find that AlphaFamImpute obtains high-accuracy genotypes, even when the parents are not genotyped and individuals are sequenced at <1x coverage. AVAILABILITY AND IMPLEMENTATION: AlphaFamImpute is available as a Python package from the AlphaGenes website http://www.AlphaGenes.roslin.ed.ac.uk/AlphaFamImpute. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Summary: AlphaMate is a flexible program that optimizes selection, maintenance of genetic diversity and mate allocation in breeding programs. It can be used in animal and cross- and self-pollinating plant populations. These populations can be subject to selective breeding or conservation management. The problem is formulated as a multi-objective optimization of a valid mating plan that is solved with an evolutionary algorithm. A valid mating plan is defined by a combination of mating constraints (the number of matings, the maximal number of parents, the minimal/equal/maximal number of contributions per parent, or allowance for selfing) that are gender specific or generic. The optimization can maximize genetic gain, minimize group coancestry, minimize inbreeding of individual matings, or maximize genetic gain for a given increase in group coancestry or inbreeding. Users provide a list of candidate individuals with associated gender and selection criteria information (if applicable) and coancestry matrix. Selection criteria and coancestry matrix can be based on pedigree or genome-wide markers. Additional individual or mating specific information can be included to enrich optimization objectives. An example of rapid recurrent genomic selection in wheat demonstrates how AlphaMate can double the efficiency of converting genetic diversity into genetic gain compared to truncation selection. Another example demonstrates the use of genome editing to expand the gain-diversity frontier. Availability and implementation: Executable versions of AlphaMate for Windows, Mac and Linux platforms are available at http://www.AlphaGenes.roslin.ed.ac.uk/AlphaMate.

UNLABELLED: Multi-parent crosses of recombinant inbred lines exist in many species for fine-scale analysis of genome structure and marker-trait association. These populations encompass a wide range of crossing designs with varying potential. AlphaMPSim is a flexible simulation program that is efficiently designed for comparison of alternative designs for traits with varying genetic architectures and biallelic markers with densities up to full sequence. A large pool of founder haplotypes can be supplied by the user, or generated via integration with external coalescent simulation programs such as MaCS. From these, diverse founders for multi-parent designs can be generated automatically, and users can compare designs generated from diverse pedigrees. Full tracking of identity by descent status of alleles within the pedigree is undertaken, and output files are compatible with commonly available analysis packages in R. AVAILABILITY AND IMPLEMENTATION: Executable versions of AlphaMPSim for Mac and Linux and a user manual are available at http://www.roslin.ed.ac.uk/john-hickey/software-packages/.