Natural selection and the distribution of chromosomal inversion lengths

Chromosomal inversions contribute substantially to genome evolution, yet the processes governing their evolutionary dynamics remain poorly understood. Theory suggests that a readily measurable property of inversions-their length-can potentially affect their evolutionary fates. Emerging data on the lengths of polymorphic and fixed inversions may therefore provide clues to the evolutionary processes promoting inversion establishment. However, formal predictions for the distribution of inversion lengths remain incomplete, making empirical patterns difficult to interpret. We model the relation between inversion length and establishment probability for four inversion types: (1) neutral, (2) underdominant, (3) directly beneficial, and (4) indirectly beneficial, with selection favouring the latter because they capture locally adapted alleles at migration-selection balance and suppress recombination between them. We also consider how deleterious mutations affect the lengths of established inversions. We show that length distributions of common polymorphic and fixed inversions systematically differ among inversion types. Small rearrangements contribute the most to genome evolution under neutral and underdominant scenarios of selection, with the lengths of neutral inversion substitutions increasing, and those of underdominant substitutions decreasing, with effective population size. Among directly beneficial inversions, small rearrangements are preferentially fixed, whereas intermediate-to-large inversions are maintained as balanced polymorphisms via associative overdominance. Finally, inversions established under the local adaptation scenario are predominantly intermediate-to-large. Such inversions remain polymorphic or approach fixation within the local populations where they are favoured. Our models clarify how inversion length distributions relate to processes of inversion establishment, providing a platform for testing how natural selection shapes the evolution of genome structure.