A few months ago my first paper was published in Genetics: Asumssen, Cartwright, and Spencer (2004) Genetics 167 (1): 499. Since it is now publically available, I am going to now explain parts of it to my readers.
Classic models of selection usually deal with constant selection. This is where the fitness of a genotype is independent of its frequency in the population. However, we know from natural studies that this is not always the case. One classic example of frequency-dependent fitness is the advantages that rare phenotypes can have in avoiding predators or acquiring mates. (I often think of the latter as the “foreign-exchange student” advantage.) Rare phenotypes may also be disadvantaged in herding/schooling species, as another example.
In the ACS paper, we analyzed a model of frequency-dependent selection that involved dominance. The condition of dominance simplified the model and allowed us to explicitly solve it. I won’t go in to much detail about the ACS model, unless y’all ask me to. However, I will discuss our results.
In the model, allele frequencies always change monotonically. They either always increase or always decrease to an equilibrium. No limit cycles or damped oscillations occur. In other words, allele frequency trajectories have simple behaviors. The structure of the mean fitness is also simple. As a function of the allele frequency, it has four simple shapes: always increasing, always decreasing, increasing to a maximum then decreasing, or decreasing to a minimum then increasing. However, when put together these two classic behaviors, produce atypical results.
Unlike with constant viability selection, this model has a polymorphic equilibrium that does not coincide with the maximum or minimum population fitness. This allows evolution to actually overshoot the optimum population fitness before settling down at a lower value. Evolution can also drive the population through a fitness valley, i.e. a minimum population fitness.
In total, an atypical behavior of the mean fitness of the population resulted from 35% of the parameter space. Furthermore, the population will end up with a mean fitness lower than when it started 20% of the time and will have an average decrease of 17%. If we are discussing viability selection, this means that 17% of the adults that used to survive to reproduction no longer do. This is a situation where simple competition between individuals hurts the population as a whole.