Adaptive Evolution and Population Size

MSC in Bioinformatics Module II – Core Bioinformatics

Marta Coronado Zamora NIU: 1244149 Adaptive evolution and population size The purpose of this exercise is to generate the fitness distribution of fixed mutations for a population of variable size and discuss the relation between adaptive evolution and population size. To achieve this goal we will assume a fitness distribution for new mutations arising in the population and will use the formulae for the probability of fixation and the rate of evolution that have been provided in the classroom to generate the results with the help of Microsoft Excel.

The following figure (FIG. 1) shows the distribution of fitness effects of new mutations arising in the population (Point 5). The graph has been generated with the proposed values.

Fig 1 Distribution of fitness effects of new mutations arising in the population.

We distinguish three types of mutations: mutations that are advantageous (s > 0), effectively neutral (s = 0) and deleterious (s < 0), and their proportions are different. Advantageous mutations, which increase fitness by allowing organisms to adapt to their environment, are rare; against, neutral mutations, which have no effect on fitness, are the most common, and finally, deleterious mutations, are widely distributed, with a small increase in the most deleterious (s = -0.5). Focusing in neutral mutations, it seems difficult that any mutation has no effect on fitness, but, there is a class that is effectively neutral, so the fate of which is determined by random genetic drift.

Now we will focus on calculate the fitness distribution of mutations fixed in populations with the following sizes:

 N = 500 and Ne = 50 (FIG. 2)  N = 10000 and Ne = 1000 (FIG. 3)  N = 500000 and Ne = 50000 (FIG. 4)  N = 10000000 and Ne = 1000000 (FIG. 5) in order to study the relation between adaptive evolution and population size.

All the steps, formulae, and graphs can be found in the Excel book, AdaptiveEvolution.xlsx.

1 MSC in Bioinformatics Module II – Core Bioinformatics

Fig 2 Distribution of fitness effects of new mutations arising in a population of size N = 500 and Ne = 50.

Fig 3 Distribution of fitness effects of new mutations arising in a population of size N = 10000 and Ne = 1000.

2 MSC in Bioinformatics Module II – Core Bioinformatics

Fig 4 Distribution of fitness effects of new mutations arising in a population of size N = 500000 and Ne = 50000.

Fig 5 Distribution of fitness effects of new mutations arising in a population of size N = 10000000 and Ne = 1000000.

From the graphs, we can infer several conclusions:

First, the proportion of neutral mutations depends on the effective population size. A smaller proportion of mutations will be effectively neutral in species with large effective population sizes, because in these populations genetic drift is a less powerful force compared to selection, so one might expect that species with large population sizes are better adapted. As we can see in Fig. 5, the large population size, the most proportion of advantageous mutations (s > 0) and the less neutral mutations (s = 0).

Furthermore, focusing on deleterious mutations, the more deleterious they are, the less likely to spread to high frequency and being fixed. But the efficiency of selection acting on mutations depends, again, on the population size: if the population is small, the selection will not be effective, so the fate of mutations is determined by random genetic drift. That is why in the first graphs, when the population size are little, we can observe an amount of slightly deleterious mutations fixed. But if the mutation is strongly deleterious (lower fitness, s = -0,5),

3 MSC in Bioinformatics Module II – Core Bioinformatics it cannot be fixed, may be they are eliminated immediately by natural selection - for example, if the mutation has a lethal effect or causes serious effects in the organism.

Last, we expected a few advantageous mutations with positive effects in fitness. In small populations, weakly selected beneficial mutations can be lost due to genetic drift, but as we said, selection will be more effective in large populations, so advantageous mutations are more likely to be fixed in these populations, as we can see in Fig. 5.

To conclude, say that the effective population size determines the rate of change in the composition of a population: it is crucial in determining the level of variability in a population, and the effectiveness of selection relative to genetic drift. As we have seen, a small population, will have lower fitness on average, because of fewer beneficial mutations rise, and detrimental mutations are more likely to reach high frequencies by genetic drift.

References EYRE-WALKER, A., and P. D. KEIGHTLEY (2007) The distribution of fitness effects of new mutations. Nat Rev Genet 8:610–618.

CHARLESWORTH, B. (2009). Fundamental concepts in genetics: Effective population size and patterns of molecular evolution and variation. Nat Rev Genet 10:195–205.

WHITLOCK M .C. and BÜRGER R. (2004). Fixation of new mutations in small populations. Evolutionary Conservation Biology, eds. Ferrière R., Dieckmann U. and Couvet D., pp.155–170. Cambridge University Press.