When Does Selection Become Ineffective? Column in KomputerraOnline #47
When the fitness of an individual is influenced by the variation of many genes, and especially when the effect of some genes depends on the state of others, the rate of evolution under the Modern Synthesis model drops sharply.
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The Paradox of Accelerated Evolution When Does Natural Selection Become Ineffective? The Miracles of Sexual Reproduction
Article in ComputerraOnline #46 Article in ComputerraOnline #47 Article in ComputerraOnline #48
Well, judging by the responses to the previous column, many readers were not convinced by it. I am not referring to creationists and their ilk, who repeat like a mantra that "facts and logic refute evolution" while demonstrating unfamiliarity with the facts and an inability to use logic. It would be worth learning how to respond to such readers in a way that causes them to lose interest in repeating their artless arguments, but that is not the point here. One of the problems of comprehension manifested in the fact that some readers concluded that if I am saying elephants ought to evolve more slowly than foraminifera according to the Modern Evolutionary Synthesis (MES), then rapid evolution in elephants becomes something inexplicable or miraculous. Please, do not equate the MES with evolutionary biology as a whole! The MES, with its seventy-five-year history, is but one of the venerable theories, albeit a very authoritative one. Trust me: contemporary biology is one of the most dynamic sciences. A more serious problem is associated with the very concrete mode of thinking found among many readers. I offered a speculative example with three twins who were raised in different conditions, and this prompted commentators to discuss the life vicissitudes of these virtual people. But how would the fact that elephants can move from place to place affect their evolution? And how can the evolution of species account for what awaits them in the future?.. This preoccupation with particular anecdotal situations (things can go one way, or they can go another...) impedes analysis of how individual factors influence evolution. How can one make this connection more transparent? In any theory, the connection between initial premises and the conclusions derived from them is not accidental. Not everyone can intuitively grasp how a change in the viability of certain categories of individuals relates to their evolution. How can I make my reasoning more accessible to such readers? Build a model! Models, even simple ones, allow one to understand what consequences follow from the initial set of system properties that were taken into account during its construction. That is what I shall do. The strength of the MES — one of the reasons this theory remains afloat — is that it is highly formalised and relies on the mathematical apparatus of population genetics. Processes that proceed in accordance with its predictions are easy to model! How can one demonstrate that my model reflects the predictions that ought to be made according to the logic of the MES? A brief definition of the MES, from one of its opponents as in the previous column, will not suffice here. And what should be considered the canon of the MES? Since this theory had no single author, its creators never assembled the central tenets of their creation into a unified statement. The most formal description of the new theory was given by Nikolai Vladimirovich Timofeev-Ressovsky (1900–1981), who was working in Germany at the time. In 1939–1940 he distinguished the elementary structures, material, and factors of evolution. The first "skeleton" (set of postulates) of the MES was proposed with polemical intent by its fierce opponent, Alexander Alexandrovich Lyubishchev (1890–1972). Among proponents of the MES, it seems this was first accomplished by Nikolai Nikolaevich Vorontsov (1934–2000), one of Timofeev-Ressovsky's students. Vorontsov compiled a list of MES postulates in 1978–1980. However, both the development of biology and his own research (for example, on the role of chromosomal rearrangements in speciation) eventually convinced Vorontsov of the limitations of such a canon (and correspondingly of the limitations of the MES). Near the end of his life he described how his understanding of biology at the close of the preceding century diverged from the MES. I had the immodesty to post on my website a table comparing the MES postulates according to Vorontsov and his revisions to them made twenty years later. Do not forget that even the right-hand column of Vorontsov's table does not represent the end of the development of evolutionary biology... Thus, the formalised nature of the MES allows one to assert that the model I have constructed reflects the tenets of this theory. The model was built in Excel; if you wish, you can download it here; I hope, however, that everything will be clear from the column itself. In general, Excel offers remarkable possibilities for modelling, making it accessible to people without a mathematical or programming background. The model considers a population of freely interbreeding organisms. As is customary in the MES, phenotypes (and the fitness of organisms) are determined by their genes. Let us consider two genes, A and B, each represented by two alleles: A and a for gene A, and B and b for gene B. Thus, nine genotypes can exist in the population: AABB, AABb, AAbb, AaBB, AaBb, Aabb, aaBB, aaBb, aabb. Too simple? Even this minimum suffices for the combinatorics of genes to become non-trivially complex. So, let us specify the population size (we denote it K — carrying capacity — the maximum number of individuals that can inhabit the given conditions). We specify the initial proportions of genotypes (PAAbb; PAaBB, and so on). What next? According to the MES, the source of new traits is new genes arising as a result of mutations; let us not contest this for now. We specify in the model the rates at which transitions from one allele to another occur: Pa→A, PA→a, Pb→B, and PB→b. It remains to provide for the force that should change the ratio of alleles in a specific direction — selection. For each genotype we specify its fitness: FAAbb; FAaBB, and so forth. The model operates as follows. Based on the distribution of genotypes in the population, the composition of the gametes they will produce is calculated. For simplicity we consider hermaphroditic organisms that produce both eggs and spermatozoa (once in their lifetime). The probability of gametes of any genotype meeting one another is equal (this could be the case, for example, if gametes are released at random into the water, as many marine benthic animals do). When calculating gamete composition, the probability of mutations is taken into account. Combinations of gametes determine the genotypes of offspring. The chances of survival of offspring depend on their fitness. The model's operational cycle is complete. It remains to determine the composition of the next generation. Rounding the proportions of genotypes in the population to individual units is probabilistic in nature. For instance, the value 1.4 will round to 2 with probability 0.4, and to 1 with probability 0.6. It remains to repeat the described cycle many times (the model is built for 500 generations). We display on a graph the indicator most interesting from the MES perspective — the dynamics of the ratio of alternative alleles. I arranged the model's components on an Excel sheet so that both the graph and the input fields (the labels are listed above) fit on a single screen. Screenshots of this screen illustrate the ensuing exposition. Well then, let us begin. [IMG_1] The initial composition of the population consists entirely of aabb individuals. The fitness of all genotypes is equal; the composition of the population changes gradually as a result of mutations (slightly faster for gene A than gene B, owing to differing mutation rates). If only one allele per gene is represented in the initial population, mutations gradually increase the proportion of alternative alleles. But what will happen if the ratio of alleles is at equilibrium? [IMG_2] The initial allele ratio is equal and fluctuates under the influence of chance events (mutations and rounding during discretisation). Note the change of scale on the ordinate axis. In the absence of selection, allele frequencies begin to "drift" around the mean value. Incidentally, such random shifts can sometimes lead to the loss of one of the alleles. It is time to "switch on" selection. Let individuals possessing the "favourable" genotype have a 1 percent greater chance of survival than all others. Does it seem to you that such a small advantage cannot play a role in evolution?
The same conditions as in the previous case, only natural selection has been added. A one percent advantage for carriers of the dominant allele A is sufficient for the ratio of alleles for the first gene to change rapidly (the second is currently "excluded" from the game).
If an individual's fitness is determined by a single gene, a 1% advantage for carriers of the dominant gene is enough for a fairly rapid change in allele frequencies. And how will the recessiveness of the allele favored by selection affect the speed of evolution?
Selection for a recessive allele (from a state of equal frequencies of two alternatives) occurs even more effectively!
It accelerates (provided the initial allele frequencies are equal). Look: during the time considered in the model, the allele favored by selection has almost completely displaced its alternative! In reality, populations and species differ not by one, but by a multitude of genes. In our model, we can consider simultaneous selection for only two of them. How will the involvement of a second gene with another pair of alleles affect the speed of evolution? For gene B, we will also support the recessive allele (b) with selection.
We include the second gene in the "game"... and the efficiency of selection significantly decreases.
Observe how selection has slowed! The fitness of an individual's phenotype depends simultaneously on the alleles of two independent genes; the combinatorics of each impedes selection at the other gene. Our fairly simple model cannot demonstrate this, but if an individual's fitness is simultaneously influenced by 12 genes (with a choice between two alleles at each), selection becomes completely ineffective! This phenomenon is known as Haldane's dilemma, and was discovered by none other than one of the founders of the MES, J.B.S. Haldane (1892–1964). Incidentally, the Russian-language Wikipedia notes that creationists are fond of Haldane's dilemma. Let me remind you: this is an argument against the MES, not against evolution as such! As we have established, when allele frequencies are equal, selection in favour of the recessive allele proceeds more efficiently. Selection in favour of a rare allele is more effective if that allele is dominant. One circumstance touched upon in the previous column remains to be illustrated. We set in the model strong selection support for an initially rare dominant allele — 10%. Over 500 generations, selection of this intensity is sufficient for the rare allele to become predominant. [IMG_6] The increase in the proportion of the rare allele proceeds more efficiently in the case of dominance. But, as we discussed last time, genes in complex organisms interact. Let us consider two dominant alleles of different genes. When they meet together, they confer a substantial advantage — fully 20%. Separately, each confers a 1% disadvantage. Suppose there are very few such alleles in the population. Will selection be able to raise their proportion as effectively as in the previous example?
Example of gene interaction. Individually, rare dominant alleles of two different genes reduce fitness by 1 percent. However, individuals in whom these two alleles occur together gain a 20 percent advantage. Under these conditions, natural selection increases the proportion of such alleles extremely slowly.
Unfortunately. A small loss of individuals carrying only one of the complementary genes is enough for these genes to remain in the population in small numbers. Selection will support the lucky ones with a successful combination of genes, but most of their offspring will again receive these genes separately. Population evolution under such conditions is extremely slow. Why? When the phenotype unambiguously reflects the genotype, the survival of the fittest individuals effectively sorts genes. If the dependence of an individual's fitness on its genotype becomes complicated, the mechanism of evolution according to the STE begins to work inefficiently. That's enough for today. I hope you are convinced: in cases where the fitness of an individual is affected by the variability of many genes, and even more so if these genes exhibit complex interactions (rather than simple summation of their effects), the rate of allele frequency change slows down significantly. How to reconcile this with the fact that complex organisms, which exhibit various interactions of their genes, evolve faster than their simpler distant relatives? From the perspective of STE, this is unclear. However, the development of science has not stopped at STE...
← Dmytro Shabanov →
The Paradox of Accelerated Evolution When Does Selection Become Ineffective? The Wonders of Sexual Reproduction
Column in KompyuterraOnline #46 Column in KompyuterraOnline #47 Column in KompyuterraOnline #48