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The null evolutionary model

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In 1908, G. H. Hardy (a British mathematician) and Wilhelm Weinberg (a German doctor) independently formulated a hypothetical model, showing how under specific circumstances the genetic composition of a population will not change. This analysis of Mendel's First Law resolved a divergence of opinions (and outright misunderstandings), regarding its expected outcome. Dissolving this riddle - ultimately - led to the acceptance of evolution as a shift of an allele frequency in a population over time.

The "Hardy-Weinberg equilibrium" theorem states that evolution will not take place - if certain conditions obtain. It demonstrates how allele and genotype frequencies remain stable (in a state of equilibrium) - when undisturbed by intervening "forces of nature", and it paints a picture of an idealized, null-evolutionary scenario.

Mendel's First Law
1. A gene can exist in more than one form.

2. Individual organisms inherit two alleles for each trait.

3. When gametes are produced by meiosis, allele pairs separate leaving each cell with a single allele for each trait.

4. After combining when the two alleles of a pair are different, one is dominant and the other is recessive.

For one trait, an individual carries two, unblending versions of a gene. During meiosis (gamete formation), the two versions of the gene pair separate from each other to form gametes. When gametes unite at fertilization, they combine at random.

Dominant
an allele (X) which produces the same phenotype whether it is heterozygous or homozygous
Recessive
an allele (x) that is expressed only when homozygous; the recessive allele is not expressed in the heterozygote phenotype

Any population - which is in Hardy-Weinberg equilibrium, the ratio of homozygous dominant (XX) to heterozygous (Xx) to homozygous recessive (xx) is exactly 1:2:1.

Mendel's first law permits the following outcome: in a large (theoretically infinite in size) sexually reproducing population, allele and genotype frequencies will remain constant across generations - unless disrupted by evolutionary processes acting on them; that is, no evolution will occur - if the following conditions (1-7) hold.

Hardy-Weinberg equilibrium
1. All individuals have equal rates of survival success. Natural Selection does not occur.

2. No mutations (affecting the genes of individuals) occur which convert one allele to another.

3. No migration of individuals (gene flow) into or out of the population happens.

4. The population is sufficiently large (infinite) that no random events cause some individuals to pass on more of their genes than other individuals. Genetic drift does not occur.

5. All members of the population breed.

6. All individuals choose mates at random, i.e. "panmictic" mating is universal.

7. All individuals have equal rates of reproductive success. Sexual Selection does not occur.

Only if all of the above conditions are satisfied, then the relative frequencies of alleles and genotypes will not shift from generation to generation. Evolution will not take place. If any one of the above seven constraints is violated, then alleles shift and evolution occurs. In nature, such an equilibrium does not exist (case 4 above trivially does not hold).

The observable violation of Hardy-Weinberg equilibrium in natural populations set the scene for population genetics (the techniques of Fisher, Haldane and Wright) to emerge and dominate evolutionary biology, during the early Modern Synthesis. Evolution was unpacked through mathematical analyses of allele and genotype frequencies.

The Hardy-Weinberg model - on its most superficial level of interpretation - points-out that evolution is a fundamental feature on the part of organisms (and in populations). Only if - in a population, there were no Natural Selection, no mutation, no migration of organisms into (or out of) it, no unpredictable events such as floods, hurricanes, earthquakes, climate change, etc., no finite population size and no Sexual Selection prevailing, then no shift in that population's allele and genotype frequencies would appear.