A Coalgebraic Structure on Bisexual Populations

We introduce a coalgebra structure representing the backwards inheritance in genetic systems with finitely many male and female genetic types, and study its main algebraic properties. We endow these coalgebras with a 3-way array (matrix) realization, showing that when the comultiplication structure constants have probabilistic significance as inheritance probabilities, the associated 3-way arrays are stochastic. Besides of providing a graphical representation of these (known as bisexual) populations, we propose a bivariate Markov model to study their backwards evolution.