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.

中文翻译：

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双性恋人群的合子结构

我们介绍了一个代表着遗传系统中向后遗传的杂代结构，该遗传系统具有许多男性和女性遗传类型，并研究了其主要代数性质。我们为这些合并代数提供了3向数组（矩阵）的实现，表明当乘法结构常数作为继承概率具有概率意义时，关联的3向数组是随机的。除了提供这些（称为双性恋）种群的图形表示之外，我们还提出了一个双变量马尔可夫模型来研究其向后进化。