Having discussed relative fitness it is now time to turn to selection. The first important point is to think about the “breeders” equation:
here r is the response to selection, h2 is the heritability, and s is the selection differential. The important point is that evolution by natural selection (r) has two components, h2 and s. In other words, there is s, which is the ecological process of selection, and h2, which is a statement about genetics. This is an important detail. Selection is an ecological process with no statements made about the patterning process (read genetics) underlying the trait. I emphasize this because this has often been a source of confusion. Don’t feel bad if you were confused about this. No less than John Endler in his book “natural selection in the wild” made the mistake that it was only selection if it was acting on a heritable trait. If quantitative genetics isn’t enough for you there is a philosophical reason that selection is acting regardless of the heritable basis of a trait. That is that heritability is a continuous value going from 0 to 1, with 1 meaning that the offspring trait is exactly intermediate between the parents, and 0 meaning that there is no relationship between the parental values of the trait and the offspring value. If selection can only act on heritable traits the question becomes how low can the heritability be before it no longer counts as selection. Obviously regardless of what value you may choose it will be arbitrary. Much better to say that selection is simply an ecological process without regard to the transmission characteristics.
Endler’s mistake is worth commenting on. He cites the famous “necessary and sufficient” criteria for evolution by natural selection that were first put forward by Lewontin (Lewontin, R. C. 1970. Ann. Rev. Ecol. Syst. 1: 1-18). That is, Lewontin tells us that for evolution by natural selection to occur you need three conditions:
- There must be variation in among individuals in phenotype (phenotypic variation)
- Differences in phenotype must affect the fitness (covariance between fitness and phenotype)
- The phenotypes must be heritable (covariance between parents and offspring)
Lewontin was careful in two important regards. The one that is important for this essay is that he calls it evolution by natural selection. No less important, but not the subject of this essay, is that he refers to “heritability” generically, not in the formal sense that implies a well-defined genetic basis. (Oddly, however, he specifies that it is fitness, not phenotype, that is heritable. Seems incorrect to me.) Endler’s mistake was to call this natural selection. For natural selection criteria 1 and 2 are necessary and sufficient. For EVOLUTION by natural selection all three are required.
Making the distinction between selection and evolution by selection are important both for the conceptual and philosophical reasons outlined above, but also for a very practical reason. That is, typically the experiments we do to determine heritability are very different from the experiments we do to study selection. Studies of the genetic basis for a trait (I don’t call this heritability since heritability studies are a specific subset of methods for studying genetics) are typically done in the lab. Examples include parent offspring regressions in which a trait is measured in both the parents and in the offspring, and the regression of offspring on parents is used to determine the heritability, other quantitative genetic methods such as half sib breeding designs and QTL mapping, but also molecular methods in which specific genes are identified and their effect on the phenotype assessed. Also falling into this category, and deserving special mention because it tends to confuse people, are laboratory selection experiments. In selection experiments a known selection pressure is applied, so that is not in question. What is in question is the nature of the response to selection. Thus, somewhat counter-intuitively lab selection experiments are really about genetics and heritability. In contrast, studies of selection are typically done in the field. Selection is an ecological process, and studying it is really about measuring how an individual’s phenotype affects its fitness in nature. Thus, under most circumstances it makes little sense to study selection in anything other than intact ecological settings. I say under most circumstances because science is a broad field, and there are certainly exceptions to any general rule you can make. A good example of a laboratory study that was concerned with how selection works rather than the response to a known selection pressure is Wade’s experimental study of kin selection (1980, Evolution 34: 844-855). In this study he examined how changing he relatedness among members of a population changed the response to selection that was naturally occurring under the laboratory culture conditions. There are also several good documented examples of evolution by natural selection in natural populations (Endler’s book is excellent on this, so having attacked him on what was probably, in his mind, a minor point, let me now recommend the larger message of his book.).
Finally, in the Price equation, , it is tempting to include the second term, E(w,Δz), as part of selection, as I believe Okasha does. I have chosen to call this “environmental change”. Although E(w,Δz) has the relative fitness in it this does not imply that it is selection. The “practical” formula for this would be:
that is, it is the fitness weighted mean change in phenotype. The fitness weighting is corrects for the consequences of selection, but is not actually selection in this case. In the absence of selection , thus if there is no selection this reduces to the average change in phenotype as a result of an ecological event.
Let me end this discussion with a brief example of how selection is quantified. Selection, s, is simply the difference in the population mean of the trait before and after selection but before reproduction. That is:
where is the mean after selection, and is the mean before selection. For example, say you go out in a pond and measure all the turtles. There are 10, and they have the weights, in grams, of:
6, 7, 8, 9 10, 11, 11, 12, 12, and 14 grams, for a mean, , of 10 grams.
If little children come along and catch the smallest ones for pets (which is NOT good for the turtles), but leave the big ones (which bite), then the surviving ones might be
11, 11, 12, 12, and 14 grams, for a mean, , of 12 grams.
The point of this silly exercise is that s is a real number with a scale. In this case it is two grams. Selection in the form of taking the little ones away (as pets) increased the mean of the population by two grams.
Now we can bring back in the covariance approach (I just have to say, I used the Price equation for years before I knew it had a name . . . ). I am assigning a 0 fitness if they were captured, and a 1 fitness if they survived to reproduce. Then the mean fitness is 0.5, and the relative fitness is the absolute fitness divided by the mean fitness thus:
|Absolute Fitness||relative fitness||phenotype|
Using the covariances:
I hope that is not too sophomoric, but I find it helpful to actually spell out the math once in a while so that everybody is clear on what is happening. The bottom line is that, as Price told us, the selection differential is simply the covariance between a trait and relative fitness. Note, that this example fulfills Lewontin’s criteria. There is phenotypic variation, and that phenotypic variation covaries with fitness, thus we we have fulfilled the first two criteria, and selection is occurring. I made no statements about the heritability of body weight, thus, we do not know whether or not the phenotype is heritable (Lewontin’s third criterion), and we can make no statements about whether or not the selection will lead to evolution.
I am traveling to Montpellier France next week for the International Society for History Philosophy and Social Studies of Biology meeting (Giving a talk on community selection, and participating in a roundtable discussion on individuality). I am not sure whether or not there will be a post next week.