The magnitude of egg swapping that occurs in their model is astonishing: if r < 0.5 (as in their Fig 1) then the dominant mode of reproduction is that a mother lays her own eggs into other nests and, in return, raises the eggs of other mothers. Eusociality arises via an extraordinary mutation that reduces the second "leaving" action while having no effect on the initial "migration" action.įor interpreting the model in terms of mothers laying eggs into other nests, LRQ assume that as soon as a mother lays an egg into another nest, she receives an egg into her own nest. In LRQ’s model, none of the migrant workers ever have a chance to take over the nest.įor the origin of eusociality, LRQ’s model assumes a presocial species in which a fraction of offspring migrate to new nests, but subsequently all offspring leave to start nests of their own, rendering the initial migration useless. In contrast, if an individual dies or leaves a colony to form its own nest, then the size of the colony decreases. Moreover, the migrant pool has the following strange property: as soon as a colony enters an individual into the migrant pool, that colony gets an individual back from the migrant pool. The model does not seem to describe a plausible biological scenario. In the second interpretation, if a solitary mother reproduces, then the following sequence of steps is executed: (i) with probability r (which is interpreted as "relatedness"), the new individual does not become a migrant but leaves and starts its own colony (ii) with probability 1 − r, the new individual becomes a migrant now one of two things can happen: (iii) with probability f s the individual is replaced by a solitary one that starts its own colony or (iv) with probability f e the individual is replaced by a eusocial one that goes back to the colony from which the migrant emerged there the individual can either (v) stay with probability q and thus increase the size of the colony headed by the solitary mother or (vi) with probability 1 − q, the now eusocial individual leaves and starts its own eusocial colony. LRQ’s first interpretation is incompatible with their own mathematical model, which does not contain any terms for queens taking over nests. Three interpretations of this mixing are offered: (i) queens take over other colonies (nest usurpation), (ii) workers migrate between colonies, or (iii) queens lay eggs into other nests. In their Model 1, LRQ introduce mixing of workers between nests. In attempting to uphold a discussion of inclusive fitness, LRQ perform three extensions of the eusociality model of NTW. Another recent finding is that inclusive fitness calculations, even when they are possible, can give the wrong result as to the direction of natural selection. The interpretation of regression coefficients as “benefit” and “cost” in this method is unjustified, and departs from the legitimate uses of regression in quantitative genetics. have demonstrated that this method (i) cannot make predictions and (ii) mistakes correlation for causation. What was the main discussion since NTW? Some theorists have argued that inclusive fitness can always be calculated using a method based on linear regression, but Allen et al. The success of eusociality depends on demographic and ecological parameters, while relatedness is the same for all species under primary consideration. (iii) Eusociality can arise by a simple mutation that causes some offspring to stay at their mother’s nest. (ii) There is a powerful mathematical theory of evolution, which can explain social behavior without using inclusive fitness. Consequently, whenever biologists use the term “inclusive fitness” to refer to an actual population, they are almost certainly in a situation in which that quantity does not exist. What are the main points of NTW? (i) Inclusive fitness, as defined by Hamilton and as used in all meaningful papers on the subject ever since, is a limited concept, which does not exist for the majority of evolutionary processes. Similarly, Liao, Rong, and Queller (LRQ) present a distorted view of NTW, introduce models for hypothetical phenomena that have no relevance for evolution of eusociality, and fail to analyze their own models with inclusive fitness theory. Attempts to rebut these findings have relied on dubious mathematics and verbal misrepresentations of the key results. Inclusive fitness, long regarded as an important concept in sociobiology, was shown by Nowak, Tarnita, and Wilson (NTW) to be of limited value for understanding the evolution of social behavior.
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