The fraction of offspring allocated to a particular habitat, under the evolutionary stable distribution, is proportional to the equilibrium density if that habitat were isolated ( 4, 5).
#Definition time sink free
Therefore, under an ideal free distribution, local population densities are equal to what they would be when all habitats were isolated. But when a habitat is the only one available and every individual is forced to allocate all its m children to that one habitat, at equilibrium density, the survival probability of offspring is also 1/ m. When the distribution of offspring is ideal free, the probability of a child to survive to an adult is the same in all habitats and therefore it is 1/ m in each and every habitat. When an individual has m children, the survival probability of each child, averaged over all habitats, is 1/ m. When the population is at equilibrium, every individual gives rise to exactly one adult individual in the next generation. This evolutionary stable state is known as the ideal free distribution ( 2, 3). Eventually, evolution thus leads to a distribution of offspring for which, when the whole population adopts it, all habitats are of equal quality and for which an individual cannot improve its reproductive success by using a different distribution. When the quality of habitats differ, any individual that allocates fewer offspring to the worst habitat and instead allocates them to the best habitat will have a higher than average reproductive success.
If population densities settle at an equilibrium value, the solution to this evolutionary problem is to distribute offspring such that the quality of all habitats becomes equal. If every individual allocated its offspring to the habitat that at that moment is the best, this habitat would soon degrade to be the worst. The problem becomes more complicated when the quality of the habitat depends on the local population density (the quality of a habitat is the probability that an individual born in that habitat gives rise to an adult). When the environment consists of habitats of different but constant quality, the evolutionarily optimal solution is, simply, to put all offspring in the best habitat. A genetically determined distribution of offspring is therefore under evolutionary control.
Individuals who distribute their offspring differently have different fitnesses. When habitat quality differs, the way in which individuals distribute their offspring over the different habitats affects the total number of surviving offspring produced. Sink habitats, by definition, are habitats in which populations cannot survive when they are isolated from other populations ( 1). It is believed that habitats can differ to the extent that some local populations act as sinks and only exist because of the spill over from other, source, populations. In ecological systems, some habitats are better than others.
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