Theorems of Evolutionary Theory

I recently found a list of principles of evolutionary theory and I thought that it would be useful to organize this list according to their domain and level of generality. I like the term “theorems” for this, but perhaps I am mistaken in this usage.

The first section is for the highest level or “Universal Theorems”. These apply to all life. Below this are principles specific to animals. Below this level are others, structured as follows:

  • Animal kingdom
    • morphology (the structure of their bodies)
      • Mammalian morphology
    • biogeography (geographical distribution
  • Sexual dynamics
  • Social dynamics

Note that I have not placed sexual and social theorems under the animals, since they apply to plants and many other taxa as well. It is rather interesting how few and boring are the distinctively zoological theorems. The sexual and social theorems also apply to plants for example. However, I think that we can find some distinctively animal and even uniquely human principles in social dynamics, but sexual dynamics are surprisingly wide-ranging.

These principles are found by scrolling to the bottom of this page:

I will add to this list as I find or create more.


Universal Theorems


Biejernik’s Principle
(of microbial ecology): Everything is everywhere; the environment selects.

Bulmer effect: Genetic variance is reduced by selection, in proportion to the reduction of phenotypic variance of the parents relative to their entire generation.

Cope’s ‘law of the unspecialized’: The evolutionary novelties associated with new major taxa are more likely to originate from a generalized member of an ancestral taxon rather than a specialized member.

Fisher’s Fundamental Theorem: The rate of increase in fitness is equal to the additive genetic variance in fitness. This means that if there is a lot of variation in the population the value of S will be large.

Galton’s Regression Law: Individuals differing from the average character of the population produce offspring, which, on the average, differ to a lesser degree but in the same direction from the average as their parents.

Gause’s Rule (competitive exclusion principle): Two species cannot live the same way in the same place at the same time (ecologically identical species cannot coexist in the same habitat). This is only possible through evolution of niche differentiation (difference in beak size, root depths, etc.).

Haeckel’s ‘Biogenetic Law’: Proposed by Ernst Haeckel in 1874 as an attempt to explain the relationship between ontogeny and phylogeny. It claimed that ontogeny recapitulates phylogeny, i.e., an embryo repeats in its development the evolutionary history of its species as it passes through stages in which it resembles its remote ancestors (embryos, however, do not pas through the adult stages of their ancestors; ontogeny does not recapitulate phylogeny). Rather, ontogeny repeats some ontogeny – some embryonic features of ancestors are present in embryonic development (L. Wolpert: The Triumph of Embryo. Oxford University Press, 1991). Also discussed in detail with original pictures by Haeckel in D Bainbridge: Making Babies. Harvard University Press, 2001).

Hardy-Weinberg Law: In an infinitely large population, gene and genotype frequencies remain stable as long as there is no selection, mutation, or migration. In a panmictic population in infinite size, the genotype frequencies will remain constant in this population. For a biallelic locus where the allele frequencies are p and q:

p2 + 2pq + q2 = 1 (see Basic Population Genetics for more).

Heritability: the proportion of the total phenotypic variance that is attributable to genetic causes:

h2 = genetic variance / total phenotypic variance

Natural selection tends to reduce heritability because strong (directional or stabilizing) selection leads to reduced variation.

Protein clock hypothesis: The idea that amino acid replacements occur at a constant rate in a given protein family (ribosomal proteins, cytochromes, etc) and the degree of divergence between two species can be used to estimate the time elapsed since their divergence.

Red Queen theory: An organism’s biotic environment consistently evolves to the detriment of the organism. Sex and recombination result in progeny genetically different from the previous generations and thus less susceptible to the antagonistic advances made during the previous generations, particularly by their parasites.

Selection Coefficient (s): s = 1 – W where W is relative fitness. This coefficient represents the relative penalty incurred by selection to those genotypes that are less fit than others. When the genotype is the one most strongly favored by selection its s value is 0.

Selection Differential (S) and Response to Selection (R): Following a change in the environment, in the parental (first) generation, the mean value for the character among those individuals that survive to reproduce differs from the mean value for the whole population by a value of (S). In the second, offspring generation, the mean value for the character differs from that in the parental population by a value of R which is smaller than S. Thus, strong selection of this kind (directional) leads to reduced variability in the population.

Tangled Bank Theory: An alternative theory to the Red Queen theory of sex and reproduction. This one states that ‘sex and recombination’ function to diversify the progeny from each other to reduce competition among them (see a review by Burt & Bell (1987) on the Tangled Bank Theory).

Wright-Fisher model: The most widely used population genetics model for reproduction. It assumes a finite and constant size (N) and non-overlapping population and random mating. One of the results is that if a new allele appears in the population, its fixation probability is its frequency (1/2N). See a Lecture Note on Wright-Fisher Reproduction.”

Animal Kingdom



There is a gradient of increasing species diversity from high latitudes to the tropics (see New Scientist, 4 April 1998, p.32).


Allen’s Rule: Within species of warm-blooded animals (birds + mammals) those populations living in colder environments will tend to have shorter appendages than populations in warmer areas.

van Baer’s Rule: The general features of a large group of animals appear earlier in the embryo than the special features.

Cope’s Rule: Animals tend to get larger during the course of their phyletic evolution.

Mammalian Morphology

Bergmann’s Rule: Northern races of mammals and birds tend to be larger than Southern races of the same species.




Sexual Organisms

Bateman’s Principle: Males gain fitness by increasing their mating success whilst females maximise their fitness by investing in longevity because their reproductive effort is much higher.

Coefficient of Relatedness: r = n(0.5)L where n is the alternative routes between the related individuals along which a particular allele can be inherited; L is the number of meiosis or generation links

Fisher’s Theorem of the Sex Ratio: In a population where individuals mate at random, the rarity of either sex will automatically set up selection pressure favoring production of the rarer sex. Once the rare sex is favored, the sex ratio gradually moves back toward equality.

Haldane’s Hypothesis (on recombination and sex): Selection to lower recombination on the Y-chromosome causes a pleiotropic reduction in recombination rates on other chromosomes [hence, the recombination rate is lower in heterogametic sex such as males in humans, females in butterflies].

Lyon hypothesis: The proposition by Mary F Lyon that random inactivation of one X chromosome in the somatic cells of mammalian females is responsible for dosage compensation and mosaicism.

Muller’s Ratchet: The continual decrease in fitness due to accumulation of (usually deleterious) mutations without compensating mutations and recombination in an asexual lineage (HJ Muller, 1964). Recombination (sexual reproduction) is much more common than mutation, so it can take care of mutations as they arise. This is one of the reasons why sex is believed to have evolved.

Parental investment theory (Robert Trivers): The sex making the largest investment in lactation, nurturing and protecting offspring will be more discriminating in mating and that the sex that invests less in offspring will compete for access to the higher investing sex (Trivers RL. Parental investment and sexual selection. In Campbell BG (Ed) Sexual Selection and the Descent of Man, 1871-1971. Chicago:Aldine, 1972, pp. 136–179; ISBN 0-43-562157-2). See also Trivers-Willard Hypothesis.

Weismann’s hypothesis: Evolutionary function of sex is to provide variation for natural selection to act on (see (Burt, 2000) for a review of Weismann’s hypothesis).



Social Dynamics

Hamilton’s Altruism Theory: If selection favored the evolution of altruistic acts between parents and offspring, then similar behaviour might occur between other close relatives possessing the same altruistic genes, which were identical by descent. In other words, individual may behave altruistically not only to their own immediate offspring but to others such as siblings, grandchildren and cousins (as happens in the bee society).

Hamilton’s Rule (theory of kin selection): In an altruistic act, if the donor sustains cost C, and the receiver gains a benefit B as a result of the altruism, then an allele that promotes an altruistic act in the donor will spread in the population if B/C >1/r or rB-C>0 (where r is the relatedness coefficient).

Trivers-Willard Hypothesis: In species with a long period of parental investment after birth of young, one might expect biases in parental behaviour toward offspring of different sex, according to the parental condition; parents in better condition would be expected to show a bias toward male offspring (Trivers-Willard, 1973).





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