Genetic Algebras and Time Continuous Models

It is shown how linear genetic algebras, ordinarily applied in situations with discrete time, will also simplify certain systems of differential equations in time continuous models. These models describe the variation of genotype frequencies in infinite populations in different mating systems. The cases considered include matings between individuals randomly drawn from the population at each moment, a population which is continuously backcrossed to a second, constant population, and a population divided into two age groups, which take part in the matings with different intensities. For the first case the general theory is applied to an example with tetraploids having a mixture of chromatid and chromosome segregation.