Is it possible to program aging (4)
Continuation. The beginning of the article is here.
Analytical models
Libertini (1988) suggested that aging is programmed, based on the idea that shortening life expectancy through aging reduces the life span of a generation. He argues that this would be an advantage for other favorable genes in the population, since the shorter the lifetime of a generation, the faster the spread of such genes. If gene C causes aging (and therefore is detrimental to its carrier), while simultaneously having a positive effect on other genetically related individuals, it may be subjected to positive selection in cases where a net advantage in selection has a positive effect. Libertini suggests that an individual whose death is a consequence of the action of gene C is replaced by a genetically related individual who is also a carrier, not only of this gene, but also of other favorable genes, the rate of spread of which increases. Thus, the aging gene C is a kind of allelic "companion", which is subjected to selection "at the same time", since it enhances the selective advantage of other genes that have a beneficial effect. Thus, Libertini's arguments are based on kin selection, in which a gene influences the fitness of not only its carrier, but also related individuals who also have this gene. For related selection, it is only necessary that related individuals live in close proximity to each other. Since this condition is very often fulfilled, Libertini gives a convincing argument for which he developed a recurrent equation describing how the frequency of occurrence of the aging gene C varies from generation to generation.
The equation depends on the breeding advantage S of the favorable gene, together with which the C gene is selected, the breeding disadvantage S0 of the shortening of the lifespan of the C gene, the degree of shortening of the Vc lifespan and the degree of kinship r of the carriers of the C gene with the individuals living in the neighborhood. Based on this equation, Libertini calculated curves demonstrating that genes that cause programmed aging can accumulate even at very low degrees of kinship (Figure 3, A).
Figure 3. Reproduction of Figure 8 from the Libertini publication (1988), demonstrating the spread of the aging-causing gene C for different degrees of kinship with neighboring individuals.
However, Libertini's analysis has a serious problem. The shortening of Vc lifespan caused by aging does not depend at all on the selection deficiency S0 associated with this phenotype. This means that Libertini is free to choose arbitrary values for these two parameters. This allows him to maximize the positive effects (helping carriers with by reducing life expectancy to Vc), while minimizing the negative effects (breeding disadvantage of early death) without any justification. When using more realistic values, the aging gene C disappears (Figure 3, C).
Continuation: Spatial models
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09.11.2016