Figure 1
the issue of selection acting at different levels of organization has received a lot of attention both from biologists and philosophers. The issue can be confounding because we often can model evolution as though selection were acting at any of a number of levels. For example, kin selection can be modeled, with seemingly identical results, as selection acting on alleles, individuals, or family groups.
In general, if selection is acting at some level, A, we can model evolution as though it were acting at some other level, B, so long as we can calculate the frequency of units at level A in the next generation from the frequency of units at level B in the current generation. Any discussion of multi-level selection thus requires that we first clarify how units of selection are defined and how these reproduce.
Because we can sometimes model evolution as though selection were acting on any one of a number of levels, we need some other criteria to decide what the mechanistic level of selection is in a particular case.
I suggest that a useful test of whether selection is acting at some level is to ask the following question:
In order for selection to act, is it necessary and sufficient for there to be multiple (>1) units at that level and for there to be variation between these?
If the answer to this question is "yes", then we say that selection is acting at the level under consideration.
We can see how this test works by applying it to the case of kin selection. Consider a population composed of a single family of full siblings. Now imagine that some of these offspring carry an allele for altruism and others do not. In this case there are multiple individuals and variation in the trait (altruism) that influences fitness. Individuals are also related to one another and interact. Thus, if kin selection is a case of selection acting on individuals or alleles, it should happen here.
Since r = 0.5 for every pair of siblings in this scenario, Hamilton's rule predicts that altruism should increase in frequency if the benefit to the recipient of an altruistic act is greater than twice the cost of that act to the altruist. In fact, altruism will always decrease in this scenario, regardless of the costs and benefits.
To see why this is so, consider the figure below.
Figure 1
Here, the family contains three altruists (A) and two selfish individuals (S). I set the cost of an altruistic act (C) at 0.25 and the benefit (B) to the recipient at 1. Thus in this case B = 4C. Assuming that in the absence of any altruistic interactions each individual could produce 1 offspring, that each individual interacts with each of its siblings, and that the costs and benefits of altruism are additive, the altruists produce a total of 6 offspring while their selfish siblings produce 8. Thus, although the total number of altruists goes up, their frequency declines.
This decline in altruism, despite the benefit being greater than twice the cost, results because selfish individuals always do better than their altruistic siblings. Thus, having many individuals with variation between them is not sufficient for kin selection to act, so we conclude that it is not an instance of individual selection.
Now modify the scenario so that there are many family groups and variation in the frequency of altruists within these groups. An example of such a case is shown below:
Figure 2
Here, most groups have no altruists, so each individual produces one offspring. the family that contains altruists behaves in exactly the same manner as above, but now there is an increase in the frequency of altruists within the entire population. This increase occurs because the family with altruists has a much greater reproductive output than the other families.
Thus, the condition of having multiple family groups that vary in the frequency of altruists within them is sufficient for kin selection to occur. That variation between groups is necessary can be seen from the fact that if all the groups had the same frequency of altruists, the overall frequency would decrease regardless of the values of C and B.
Kin selection thus emerges as a result of selection on two different levels: selection between individuals within family groups (Figure 1) and selection between family groups (Figure 2). Hamilton's equation can be derived as the condition for the increase in the frequency of altruism in an infinite population in which most groups contain no altruists.
A number of authors have argued that the different ways of explaining the increase in altruism resulting from interactions between kin - as selection at the level of alleles, individuals, or groups - are all "equivelent" and simply represent different ways of looking at the world. The example presented here suggests that this is NOT true. If we think of kin selection as acting exclusively on alleles or individuals, than there is no clear explanation as to why altruism should not increase in frequency in a population composed of many identical family groups. Only by recgnizing the group selection component in the process can we see why this is so.
In order for selection at any level to lead to evolution there must be heritability of the trait being selected. Though many factors influence heritability, one that is particularly important for the consequences of multi-level selection is the process by which objects at a particular level reproduce.
Consider two levels (which I will call "individuals" and "groups", understanding that "individuals" may be alleles and "groups" genotypes, etc.) with selection acting at both levels. Selection at the higher level is most effective when there is little variation within groups and much variation between them. Some modes of group reproduction facilitate this condition more than others.
The figure below shows two different ways that groups could reproduce.
Figure 3
On the left, groups break up and contribute to a "migrant pool" from which individuals are drawn to form new groups. This is the case for mendelian reproduction, in which case the "individuals" are alleles and the "groups" genotypes. This mode of reproduction tends to produce much variation within groups and less between them, it thus reduces the efficacy of group selection.
On the right, each descendant group starts out as a sample drawn from an ancestral group, with no mixing. This is what we see in cases like speciation or the fragmentation of coral colonies. Here, the process of drawing a sample from the ancestral group tends to reduce the variation within the sample, and thus within the descendant groups. Variation between descendant groups, though, is greater than in the case on the left. This mode of group reproduction thus tends to increase the efficacy of group selection relative to selection between individuals.
The smaller the samples that form new groups, the less variation within each one and the greater variation between them. Thus, group selection is most efficient when new groups form as small samples from existing groups.
Species selection results from differential rates of speciation or extinction due to some characteristic of a species, such as allele frequency or geographic range. For purposes of this discussion, "species" are taken to be reproductively isolated populations that remain that way forever once they are isolated.
To see when species selection must be considered as an evolutionary mechanism, I will consider the case in which selection between individuals favors one allele at a locus while selection between species favors those that have a high frequency of the alternate allele.
Here is one way to visualize this process.
Figure 4
In the figure above, each horizontal line represents a species lineage and the shade of the line at a particular point in time represents the allele frequency at that time. Light lines have a high frequency of the allele favored by individual selection, dark lines have a high frequency of the alternate allele, favored by species selection.
Each lineage gets lighter over time, due to the effects of individual selection. Darker lineages, though, speciate at a higher rate and persist longer, representing species selection.
Modeling this sort of nested selection process is complicated (see the paper cited below) but the major results are straightforward. We only really need to consider those species that are fixed, or nearly so, for one or the other allele. This is because, even with rather weak selection on individuals, species with intermediate allele frequencies go to fixation before the next speciation event.
Define Ri as the rate at which species that are fixed for the allele favored by individual selection produce descendant species that are also fixed for that allele. Similarly define Rs as the rate at which species fixed for the allele favored by species selection produce descendant species that are so fixed. Note that this is not the same as the total speciation rate for such species, since some of the daughter species produced will have different allele frequencies due to mutation and individual selection. These do not contribute to Rs .
The condition under which species selection contributes to evolutionary dynamics - that is, the condition under which the allele favored by species selection is maintained in at least some species - is simply Rs > Ri .
Numerous factors combine to determine whether this condition is met. Increasing the time between speciation events reduces the efficacy of species selection by giving individual selection more time to work. Alternately, reducing the initial size of a newly isolated population increases the efficacy of species selection for reasons discussed in the previous section.
How these terms relate to the outcome of species selection is shown in the figure below:
Figure 5
Here, S, the strength of species selection, is the probability B that a species fixed for the allele favored by individual selection goes extinct before the next speciation event. The species phenotype is the frequency within a species of the allele favored by species selection. The histograms at the bottom show the equilibrium distribution of species phenotypes that result. Note that when Ri > Rs , all species are fixed for the allele favored by individual selection. Once Rs > Ri , some species start to appear that are fixed for the allele favored by species selection. The fact that the distributions have two distinct peaks results from the fact that species with intermediate allele frequencies are quickly fixed by individual selection.
Using the model that produced this figure, I have calculated that with mutation rates on the order of 10-6 per generation and individual selection coefficients on order .001 (weak but not negligible), species selection could influence evolutionary dynamics if speciation events occur around every 104 generations or more frequently. Evidence from the fossil record shows that this condition is probably met for some large mammals and ammonites.
For further discussion and elaboration of the mathematics of species selection, see:
Rice, S. H. 1995. A genetical theory of species selection. J.
theor. Biol. 177:237-245.
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