Mathematical modelling of complete recessive lethals: Adaptive dynamics across varying genetic and population structures

Abstract

The study of recessive lethal diseases in populations presents significant challenges, from estimating key parameters - such as the number of genes involved and the mutation rates driving genetic degeneration - to understanding the increased prevalence of autosomal recessive intellectual disorders (ARID) in the offspring of consanguineous unions. To address these challenges, we developed a mathematical model based on a diploid individual-based framework of adaptive dynamics. This model allowed us to make several important discoveries. <br /> First, we showed that the higher disease burden for ARID observed in consanguineous unions is a transient phenomenon associated with rapidly expanding population sizes. This finding highlights the need for widespread carrier screening, as the drop in prevalence in randomly mating populations is associated with an increased mutation burden. <br /> Second, we extended the drift-barrier hypothesis, which states that the ability of natural selection to refine traits is limited by genetic drift. We introduced a new parameter - the recessive gene count. We found that populations with a higher gene count face a similar barrier to that imposed by an increased mutation rate. In addition, our analysis provides a new perspective on Muller’s ratchet, a classic concept in population genetics that describes the irreversible accumulation of deleterious mutations in the absence of recombination. Our results show how mutations accumulate rapidly after a long period of stability, and how the population finds its way back to stability after the emergence of clusters of highly correlated genes. <br /> Finally, we have implemented a simulation framework based on Gillespie’s algorithm, which allows exact stochastic simulations of our model. This framework permits the study of the dynamics of complex interacting systems. The tool is flexible, scalable, and designed to facilitate further studies.