Weighted fitness theory: an approach to symbiotic communities

We see in our crystal ball that, in the near future, microbiology could have a new formulation for the theoretical conditions that explain the evolution of group selection in the symbiotic community. This formulation is a combination of the two main theories on evolutionary altruism: (i) Hamilton's (1963) theory of kin selection and (ii) the multilevel selection theory of Wilson and Wilson (2007). The first explained that the fitness (F) of any individual has an ei (0 < ei < 1) component that favours self-reproduction, and another (1 − ei) that altruistically favours the reproduction of the other members of the group. The second demonstrated the existence of different selective pressures that can operate at different levels in the biological hierarchy. Acting simultaneously, these pressures generate what is known as the genomic conflict (i.e. different genes affecting a given character can receive opposing selective pressures as the result of acting at different levels of that hierarchy). If multilevel selective pressures exist, then different levels of environmental resistance in an ecological niche also exist, both at group and individual levels. Thus, we can estimate the proportion of selective pressure due to competition at individual pi (0 < pi < 1) and group (1 − pi) levels. If we accept the previous models, an individual's inclusive fitness (F) will centre on the hierarchical level at which the selective pressure is highest. This is where the battle for life is most intense and the individual is most likely to die. Thus, if selective pressure is greater at group level, the life of the individual will be more dependent on the survival of the group. This increases the chances of more efficient groups being positively selected and these groups are precisely made up of the most altruistic subjects. Conversely, if selective pressure is greater at individual level, then selfish subjects have a greater chance of being the lucky winners. F ′ represents the relative contribution that each individual makes in terms of biological fitness to himself (ei), and his group (1 − ei), but also takes into account the relative selection pressure at each of these levels, pi and (1 − pi), respectively. Given that F' weights the degree of group cohesion with multilevel pressure at each hierarchical level, it is, in our opinion, the parameter that best represents what natural selection actually does or does not do to favour each individual. Thus, an individual with a greater F ′ will be the one that contributes more to the hierarchical level than his ecological niche demands. It is especially worth mentioning that since F' only takes into account the percentage of individual fitness, it can be applied to any kind of biological relationship regardless of the degree of kinship, including the interactions of symbiotic mutualism between species. Mathematically, the function F ′ is a hyperbolic paraboloid (Fig. 1). The hyperbolic paraboloid, the curve of weighted fitness function (F′). The curve is a three-dimensional saddle-shaped doubly ruled surface, i.e. through every one of its points two distinct lines lie on the surface. The point where the minimum value of the maxima coincides (S) is the saddle point. The X axis represents the individual selective pressure proportion (pi). The Y axis represents the individual fitness proportion (ei). Z axis is F′. The coordinates of the saddle point or minimax S are 0.5, 0.5, 0.5. The parabola from point A(0, 0, 1) to point B(1, 1, 1), whose vertex is S, represents the maximum values that ei takes for each given value of pi. That is, the BSA parabola represents the fitness ratio that will be positively selected for each level of selective pressure. When group pressure (pi < 0.5) rather than individual pressure predominates in the niche, only the individuals with ei < 0.5, that is, those with a higher F' or the most altruistic ones, will be positively selected. On the other hand, when individual pressure predominates (pi > 0.5), only those with ei > 0.5 (the selfish ones) will be selected. As 0 < pi < 1, so that FΔ > F′ and biological leverage can exist, selective pressure at individual level must be more intense than pressure at group level (pi > 0.5). If the prevailing selective pressure is the one of the group (pi < 0.5), this extra help (Δei) will decrease the F ′ of the individual. This apparent paradox makes sense only when selective pressure favors selfishness, then cooperation with other partners can be beneficial for the individual. And the greater the individual pressure with respect to group pressure (i.e. the closer pi is to 1), the greater the biological leverage, and also the greater the benefit the selfish individual obtains from being helped by the others. Conversely, if what prevails in the environment is competition between groups, then any deviation from group fitness towards individual fitness will penalize the group and all its members. The altruists (ei < 0.5) who work for the group will have to equip themselves with an increasing number of altruistic traits, because the egoistic features become deleterious for the group and would cause individuals to have a lower F'. As expected, to achieve > F ′ so that group biological leverage can exist, selective group pressure must prevail (pi < 0.5). This is exactly the case in eusocial animals and symbionts, in which altruistic traits only thrive for the benefit of the group (1 − ei) if they are combined with help for the group (−Δei), as these altruistic traits are the only ones that provide a larger F ′ for the individual. We found unequivocal cases of the two situations explained above in microorganisms. For example, bacteria of the Myxococcus (Travisano and Velicer, 2004) and Pseudomonas genera (Rainey and Rainey, 2003) usually live a solitary life until nutrients deplete. When this happens, groups of them die forming multicellular structures so others can survive and reproduce. These bacteria, like primitive eusocial animals, have an adaptive trigger that detects environmental changes and allows them to move from a free individual life, to a social one, or vice versa. However, if environmental conditions persist in one way or another, these peculiar species may reach the point of no return (Wilson, 1971) where rigid adaptations lacking phenotypic flexibility end up being selected. At this point, and under the predominant conditions, even when these adaptations impede going back, F′ increases. Genomic reduction in the primary endosymbionts of insects (Latorre and Manzano-Marín, 2016), with the creation of more complex entities (hologenomes), is a good example of rigid adaptation towards social/eusocial/group life. As we see, neither evolutionary altruism nor hierarchical speciation requires kinship or vigilance of selfish individuals. The only factor needed is the concurrence of future partners in an ecological niche in which group pressure predominates. To Manuel Soler and Jaume Terradas for their critical reading and valuable comments. To Olga Falgueras for her help in translating the text. This work was supported by grants from the Spanish Ministry of Science and Competitiveness (projects SAF 2012-31187, SAF2013-49788-EXP, SAF2015-65878-R), Carlos III Institute of Health (projects PIE14/00045 and AC15/00022), Generalitat Valenciana (project PrometeoII/2014/065) and FEDER to AM together with a grant from the Spanish Ministry of Science and Competitiveness (Project CGL2015-65387-C3-2-P) to JMC.

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