Frequency-dependent selection in the context of "Sir Edward Poulton"

In mathematics, the replicator equation is a type of dynamical system used in evolutionary game theory to model how the frequency of strategies in a population changes over time. It is a deterministic, monotone, non-linear, and non-innovative dynamic that captures the principle of natural selection in strategic interactions.

The replicator equation describes how strategies with higher-than-average fitness increase in frequency, while less successful strategies decline. Unlike other models of replication—such as the quasispecies model—the replicator equation allows the fitness of each type to depend dynamically on the distribution of population types, making the fitness function an endogenous component of the system. This allows it to model frequency-dependent selection, where the success of a strategy depends on its prevalence relative to others.

Müllerian mimicry is a type of biological mimicry in which two or more well-defended species, often foul-tasting and sharing common predators, converge in appearance to mimic each other's honest warning signals. This convergence of appearance achieves the following benefit to species that undergo it: predators need only experience a single unpleasant encounter with any member of a set of Müllerian mimics in order to thereafter avoid all creatures of similar appearance, whether or not it is the same species as the initial encounter. A ring of distinct species is thereby protected from their mutual predators by attempted predation upon any one of its members. The phenomenon is named after the German-Brazilian naturalist Fritz Müller, who proposed the concept in 1878, supporting his theory with a mathematical model of frequency-dependent selection, one of the first such models anywhere in biology.

Müllerian mimicry was first identified in tropical butterflies that shared colourful wing patterns, but it is found in many groups of insects such as bumblebees, as well as in other animals such as poison frogs and coral snakes. The mimicry need not be restricted to that detected by vision—many snakes share auditory warning signals. Similarly, the defences involved are not limited to toxicity—anything that tends to deter predators, such as foul taste, sharp spines, or defensive behaviour can make a species unprofitable enough to predators to allow Müllerian mimicry to develop.

Host–parasite coevolution is a special case of coevolution, where a host and a parasite continually adapt to each other. This can create an evolutionary arms race between them. A more benign possibility is of an evolutionary trade-off between transmission and virulence in the parasite, as if it kills its host too quickly, the parasite will not be able to reproduce either. Another theory, the Red Queen hypothesis, proposes that since both host and parasite have to keep on evolving to keep up with each other, and since sexual reproduction continually creates new combinations of genes, parasitism favours sexual reproduction in the host.

The genetic changes involved are changes in frequencies of alleles, variant forms of individual genes, within populations. These are determined by three main types of selection dynamics: negative frequency-dependent selection when a rare allele has a selective advantage; heterozygote advantage; and directional selection near an advantageous allele. A possible result is a geographic mosaic in a parasitised population, as both host and parasite adapt to environmental conditions that vary in space and time.

Müllerian mimicry is a type of biological mimicry in which two or more well-defended species, often foul-tasting and sharing common predators, converge in appearance to mimic each other's honest warning signals. This convergence of appearance achieves the following benefit to species that undergo it: predators need only experience a single unpleasant encounter with any member of a set of Müllerian mimics in order to thereafter avoid all creatures of similar appearance, whether or not it is the same species as the initial encounter. A ring of distinct species is thereby protected from their mutual predators by attempted predation upon any one of its members. The phenomenon is named after the German-Brazilian naturalist Fritz Müller, who proposed the concept in 1878, supporting his theory with a mathematical model of frequency-dependent selection, one of the first such models to be deployed in biology.

Müllerian mimicry was first identified in tropical butterflies that shared colourful wing patterns, but it is found in many groups of insects such as bumblebees, as well as in other animals such as poison frogs and coral snakes. The mimicry need not be restricted to that detected by vision—many snakes share auditory warning signals. Similarly, the defences involved are not limited to toxicity—anything that tends to deter predators, such as foul taste, sharp spines, or defensive behaviour can make a species unprofitable enough to predators to allow Müllerian mimicry to develop.