Southern-Summer School on Mathematical Biology

Evolutionary trade-offs are crucial to understanding dimorphism in a species. A common choice revolves around the distinction between natural and sexual selection: for a male, is it better to outcompete other males in the fight for resources or in their sexual prowess?

A clear example of this dilemma appears in the bulb mite Rhizoglyphus robini – an acarus often considered a pest in plantations around the world. Males of this species can be either brawny fighters or skinny scramblers. While fighters obviously come on top in the competition for resources, Van den Beuken et al. (2018) have found that scramblers can sire a higher number of offspring, balancing the scales and ensuring the morph's persistence.

Build a mathematical model that describes the showdown between scramblers and fighters in R.robini. Add whatever elements you deem essential to the population's dynamics.

• How does your model account for coexistence of scramblers and fighters in the population?

• What is the impact of resource scarcity on the ratio between scramblers and fighters?

This article here shows evidence of a third male morph: the mega-scrambler, a huge male that resembles a female. How would that morph change the scenarios you explored?

• Radwan J. and Klimas M. Male dimorphism in the bulb mite Rhizoglyphus robini: fighters survive better. Ethology Ecolgy & Evolution, 2001.

• Van den Beuken T. P. G., Duinmeijer C. C., Smallegange I. M. Costs of weaponry: unarmed males sire more offspring than armed males in a male-dimorphic mite. Journal of Evolutionary Biology, November 2018.