The Breeder Genetic Algorithm (BGA) is based on the equation for the response to selection, R(t) = b(t)·I·σ(t), where R is the response, b(t) is the realized heritability, I is the selection intensity, and σ is the standard deviation of the fitness. Estimating the variance of the fitness is crucial for using this equation for prediction. In this paper, the problem of estimating the variance of the fitness for sexual recombination is discussed, along with several modifications of sexual recombination. The first method is gene pool recombination (GPR), which leads to marginal distribution algorithms. The paper also discusses more sophisticated methods for estimating the distribution of promising points. The paper begins with an introduction to the BGA and its basis in livestock breeding. It then discusses the analysis of uniform crossover for two loci. A simple example with two loci and proportionate selection is used to illustrate the difficulty of analyzing Mendelian sexual recombination. The paper presents a theorem showing that for proportionate selection and uniform crossover, the gene frequencies obey a specific difference equation. This equation is similar to those known for diploid chromosomes in population genetics, despite the different underlying genetic recombination. The paper also presents a theorem showing that the realized heritability for uniform crossover can be derived exactly. The paper concludes by discussing the problem of estimating distributions and outlining the conditional distribution algorithm, which is applied to optimization problems known to be difficult for genetic algorithms. The paper highlights the importance of estimating the variance of the fitness in the BGA and the challenges associated with sexual recombination.The Breeder Genetic Algorithm (BGA) is based on the equation for the response to selection, R(t) = b(t)·I·σ(t), where R is the response, b(t) is the realized heritability, I is the selection intensity, and σ is the standard deviation of the fitness. Estimating the variance of the fitness is crucial for using this equation for prediction. In this paper, the problem of estimating the variance of the fitness for sexual recombination is discussed, along with several modifications of sexual recombination. The first method is gene pool recombination (GPR), which leads to marginal distribution algorithms. The paper also discusses more sophisticated methods for estimating the distribution of promising points. The paper begins with an introduction to the BGA and its basis in livestock breeding. It then discusses the analysis of uniform crossover for two loci. A simple example with two loci and proportionate selection is used to illustrate the difficulty of analyzing Mendelian sexual recombination. The paper presents a theorem showing that for proportionate selection and uniform crossover, the gene frequencies obey a specific difference equation. This equation is similar to those known for diploid chromosomes in population genetics, despite the different underlying genetic recombination. The paper also presents a theorem showing that the realized heritability for uniform crossover can be derived exactly. The paper concludes by discussing the problem of estimating distributions and outlining the conditional distribution algorithm, which is applied to optimization problems known to be difficult for genetic algorithms. The paper highlights the importance of estimating the variance of the fitness in the BGA and the challenges associated with sexual recombination.