Absolute Fitness in Theoretical Evolutionary Genetics

Joe Felsenstein, like other population geneticists, holds a special place in the Creation/Evolution controversy because his works are regarded highly by many creationists who are familiar with genetics. This is a thread for all of us (myself included) to try to learn and understand one of the key concepts in his book Theoretical Evolutionary Genetics, namely absolute fitness. He has generously made his book available on his website (a book of this calibre could sell for hundreds of dollars).

[I will state my best understanding of what is in the book. I welcome technical corrections.]

For me, population genetics seeks to quantify the evolution of genes in a population as they are distributed among genotypes. It seems to me various concepts and definitions such as “absolute fitness” were created in support of that goal. Sometimes there will be usage of the same terms such as “fitness” within population genetics which may intuitively mean something else outside of population genetics. As I was going through the book, I could see some of the motivation for defining things a certain way, but also how it might get misconstrued in contexts outside of population genetics.

The definition of most interest which I got from the book so far is that of absolute fitness (page 50 of the text):

$W_A=v_A f_A$

where

$W_A$ is absolute fitness for genotype A.

$v_A$ is the viability or probability that genotype A will become reproductively viable (i.e. alive and able to make offsring)

$f_A$ is the fertility for genotype A.

Evolution of the haploid asexual case is not too bad to conceptualize, but it becomes challenging to model the sexual diploid case.

With respect to unicellular micro organisms, I would assume we make $f_A=2$ since to me it seems the notion of a bacteria having several children is not appropriate. Hence $v_A$ would be the more important concept for unicellular creatures that reproduce by splitting themselves apart.

In contrast to absolute fitness, there is the additional concept of relative fitness of genotypes in a population, and that is meaningful regarding genotypes of the same species in a population. That was described also in the book.

But getting back to the notion of absolute fitness, it would seem then we can make statements about the mean absolute fitness of all the genotypes in the population. It would seem then we could say the mean absolute fitness of a population can increase or decrease.

I saw all the conditions for the Hardy-Weinberg Law to be valid and appreciate the motivation for making calculations tractable. I have to be careful when the infinite population size idealization is in play and when it is not.

Though relative fitness would seem rather meaningless in comparing individuals between species (like apples and oranges), can absolute fitness not be meaningful between species?

A rat might have 7 offspring per litter, and maybe 3 litters in a lifetime. That’s about 21 rats! Thus the mean absolute fitness of rats is higher than humans if we are talking raw numbers of

$W_A=v_A f_A$

But I understand that is probably taking the concept of absolute fitness in population genetics to a domain it was not intended.

Additionally, the viability factor would seem to be not an inherent quality of the genotype but the genotype and environment. Take the same genotype in one environment and the rats will multiply like crazy but in another they won’t.

Thus the absolute fitness is not completely determined genetically but must be related to the environment. Or is there an implicit assumption a population evolves to be more fit in stable environment or at least somehow there is a means of factoring out the effect of environmental effects (like introduction of new predators into the ecosystem). If that is the case, the notion of “absolute fitness” is highly dependent on context. Or again, this is starting to take the notion of absolute fitness in population genetics outside of its intended domain of usage?

Regarding the human population, if the average couple today makes less babies than their ancestors, then are modern humans are less absolutely fit on average? If environmental factors are affecting birth rates, then it would seem mean absolute fitness of a population is most meaningful in a stable environment, and it gets ambiguous when we try to make statements about a populations fitness in environments that are rapidly changing. Or is it correct to say “the environment can change the mean absolute fitness even without the introduction of new alleles or mutations”?

Thanks in advance for thoughtful responses.

NOTES:

1. Lewontin’s paper Santa Fe Winter 2003: Four Problems in Understanding the Evolutionary Process articulated problems in defining “fitness”. He appears to say “fitness” is merely restatement of reproductive statistics. This leads to some complications which I somewhat echo above.

2. Andreas Wagner points out the difficulty in using “fitness” to define complex systems as well as pointing out problems with the definition of “fitness” itself. So what is the accepted strategy for identifying and describing systems? Andreas Wagner in his book Robustness and Evolvability in Living Systems (Princeton Studies in Complexity) describes how in practice the fitness-based, Darwinist world view is supplanted in favor of a more effective methodology:

However, fitness is hard to define rigorously and even more difficult to measure….An examination of fitness and its robustness alone would thus not yield much insight into the opening questions. Instead, it is necessary to analyze, on all levels of organization, the systems that constitute an organism, and that sustain its life. I define such systems loosely as assemblies of parts that carry out well-defined biological functions.

Andreas Wagner

but Wagner’s definition of “system” sounds hauntingly similar to Michael Behe’s definition of Irreducible Complexity:

A single system composed of several well-matched, interacting parts that contribute to the basic function of the system