When I first learned about evolution I was taught that evolution was change in gene frequency. As I pointed out before this definition is inadequate, however, the gene frequency definition has the interesting property that evolution can be described in terms of deviations from the Hardy-Weinberg-Castle (HWC) equilibrium. For all its faults the HWC equilibrium gives us a familiar starting place for discussing the forces of evolution.
Consider a one-locus two-allele system with an A1 and an A2 allele. If the frequency of the A1 allele is p, and the frequency of the A2 allele is q (p + q = 1), then the HWC proportions are simply given by (p + q)2:
This result was independently “discovered” by Hardy, Weinberg, and Castle, which is why it bears their name. (Note I put discovered in quotes. Hardy, at least, was always a bit embarrassed that his name was attached to such an obvious result, and Castle’s graduate student, Sewall Wright, is reputed, although I can’t find a reference to this, to have referred to it as the “well known law of proportions”).
Importantly, the HWC equilibrium (as opposed to the proportions) is a phenomenon in which the HWC proportions are maintained for multiple generations, and gene frequencies and genotype frequencies do not change. This was the beauty of the “change in gene frequencies” definition of evolution. The HWC equilibrium forms a null hypothesis for that definition: If the HWC equilibrium holds then evolution is not occurring.
To move towards a phenotypic view of evolution we need to think about the informational function of genes. As I described in my last post, genes are a bit complex in that they have three different functions. They transmit information between generations, they interact with other genes and other heritable elements and the environment to create the phenotype, and they (or at least their sequence and position in the genome) are part of the phenotype. It is the transmission of information between generations aspect of genes that is of interest here.
Think of the birth of a new individual to be the creation of a new phenotype based on standard rules. In our simple one locus two allele genetic system the rules are that the offspring’s phenotype is determined by randomly selecting one allele from each parent. It is convenient to think of the phenotype of the offspring to be determined by a “transition equation” that converts the phenotypes of the parents into the phenotype of the offspring.
In our simple genetic system the simplest phenotype is the number of A1 alleles. Thus, an A1A1 individual has a phenotype of 2, an A1A2 a phenotype of 1, and an A2A2 a phenotype of 0. From this we can easily set up a table of the possible phenotypes that any pair of parents can produce:
Mother’s phenotype (and genotype)
|2 (A1A1)||1 (A1A2)||0 (A2A2)|
|2 (A1A1)||2 (A1A1)||1.5 (A1A1 & A1A2)||1 (A1A2)|
|1 (A1A2)||1.5 (A1A1 & A1A2)||1 (A1A1 & A1A2 &A2A2)||0.5 (A2A2& A1A2)|
|0 (A2A2)||1 (A1A2)||0.5 (A2A2& A1A2)||0 (A2A2)|
Thus, in this simple world the transition equation translating the phenotypes of the parents into the mean phenotype of the offspring is clear, and easily described as the mean of the two parents. Note that even here, however, there is a stochastic element. We can predict the mean phenotype for the offspring, but not its actual value. For example in a cross between two A1A2 individuals, the mean phenotype of the offspring is one, but it is impossible to exactly predict the phenotype of a specific offspring from the parental phenotypes.
In real systems with gene interaction, maternal effects, epigenetics, culture etc. the transition equations governing the formation of phenotypes are far more complicated, and almost certainly contain both discrete (genes) and continuous (culture) elements. Although it may be computationally difficult, there is no conceptual difficulty in adding additional factors to the “transition equation” from parental phenotypes to offspring phenotypes. In essence the transition equation of phenotypes in one generation to phenotypes in the next is simply the rules of inheritance for the factors that contribute to the patterning node described in the previous post.
Nothing is lost and much is gained viewing these Mendelian rules as “transition equations” that convert phenotypes one generation into phenotypes in the next generation. For example, one of the serious problems with the gene centric view of evolution is how to incorporate cultural inheritance. Culture is inherently a continuous phenomenon. You learn language primarily from your parents, but also from many others. I grew up in the Midwest, but my children grew up in Vermont. They swallow their t’s just like any red blooded Vermon’er does, and they did not learn that from me. Language is certainly heritable, but the rules are not discrete or simple like the Mendelian rules I outlined above. Incorporating continuous factors such as culture, and the complications of multiple cultural “parents” is a technical difficulty, but not a conceptual difficulty for the phenotypic view of evolution.
Note the strong contrast of this phenotypic view to the Dawkinsian genic view of evolution. In the phenotypic view of the world “genes” take on the subservient role of simply being mathematical constructs (transition equations) that have a physical reality in the form of DNA. In the genic view genes are central in evolution. In this view the genes are immortal “replicators” and create “vehicles” (phenotypes) that carry them forward to the next generation. You can’t make this stuff up. Here is the real quote: “The fundamental units of natural selection, the basic things that survive or fail to survive, that form lineages of identical copies with occasional random mutations, are called replicators. DNA molecules are replicators. They generally, . . ., gang together into large communal survival machines or ‘vehicles’. The vehicles that we know best are individual bodies like our own.” (Dawkins, The Selfish Gene). From a phenotypic perspective this quote is just silly.
I think Dawkin’s concept of the “meme” is particularly telling. As I pointed out culture is intrinsically continuous and no problem for the phenotypic view of evolution; however, for the genic view it is a huge problem. In Dawkin’s view the gene as an object is the center of evolution. Culturally inherited traits cannot be objects from the genic perspective unless they are atomized. The meme is an attempt to force this intrinsically continuous concept into the particulate framework that is essential for the genic view of evolution.
Historically I find this fascinating, since in the early 1900’s the Biometricians refused to accept the idea of particulate inheritance. Fisher came along and saved us by explaining how particles of infinitesimal effect could appear continuous. From that we became so enamored of genes and particulate inheritance that when our theory eventually was confronted with an aspect of inheritance that was continuous we find Dawkins being the mirror image of the biometricians and refusing to accept continuous inheritance.
If I may be a bit sarcastic for a moment (and I have always wanted to do this), to paraphrase Wolfgang Pauli, Dawkins isn’t right, he’s not even wrong. The only “replicator” I am aware of was invented by Xerox, and in the living world the only “vehicles” I am aware of are horses, but only when they are wearing saddles. (My colleagues point out that we need to include donkeys, camels and especially elephants – can’t forget elephants – in our definition of vehicles.)