While Natural Selection continuously increases fitness (relative contribution of a given phenotype to the next generation), degrading forces such as mutation, migration and changes in the environment tend to decrease fitness. Fisher quantified the rate at which fitness changes from one generation to the next in his Fundamental Theorem of Natural Selection, which states "The rate of increase in fitness of any given organism at any given time is equal to its genetic variance in fitness at that time." (Fisher, 1930). There has been much debate over what Fisher actually meant in this statement but it has been widely interpreted in two ways. First, in the absence of degrading forces, Natural Selection is thought to rapidly remove alleles conferring low fitness, while driving beneficial alleles to fixation. As a result, populations at equilibrium are predicted to have no genetic variation in fitness itself and therefore heritabilities (proportion of total phenotypic variation which is due to additive genetic variation) equal to zero. Second, traits more closely associated with fitness are thought to have smaller genetic variance than traits more indirectly related to fitness, which are also subject to the selective removal of detrimental alleles and fixation of beneficial ones but simply at a slower rate. Because of the difficulty of measuring fitness itself (particularly in natural populations), there have been few tests of the former prediction.

In two reviews of a total of 1245 published heritability estimates Roff and Mousseau (1987) and Mousseau and Roff (1987) found support for the prediction that life history traits would have lower heritabilities than morphological traits because of their relationship to fitness (h²_{Life history} < h²_Behavioural < h²_{Morphological}). Roff and Mousseau did not, however, suggest a mechanism for the observed trend of lower heritabilities in life history traits.

In contrast to the widely held belief that low heritabilities in life history traits were the result of the rapid erosion of their genetic variance by natural selection, Price and Schluter (1991) proposed that the low heritabilities of life history traits instead may be due to an increase in residual variation caused by the more complex nature of life history traits. In order to differentiate between the two hypotheses, Price and Schluter suggested examining genetic and residual variances separately rather than via the potentially ambiguous combination of the two terms within a single heritability estimate. Coefficients of variation [CV = 100 x (standard deviation/ mean)] allow for the partial standardization of variances, but they are still affected by the dimensionality of the traits measured (Roff, 1997), which can make comparisons between some traits (e.g. body size and fecundity) problematic (Burt, 2000).

Kruuk et al. (2000) used nearly 30 years of data on a population of red deer (Cervus elaphus) on the Isle of Rum in Scotland to examine the relationship between the heritability of a trait and its association with fitness within a single species. The long-term monitoring of this population allowed Kruuk et al. to quantify total fitness (total number of calves produced) and to determine the relationship of each of the other traits to total fitness using pair-wise correlations. Variance components (additive genetic variance and residual variance) and heritabilities were calculated for each trait using an 'animal model', which is similar to traditional parent-offspring regressions but incorporates information from the entire pedigree rather than just parent-offspring relationships. As expected, the heritability of fitness was not different from zero and traits more closely associated with fitness had lower heritabilities than traits more distantly related to fitness. Examination of coefficients of variation suggested that these low heritabilities were the result of larger residual variance and not lower additive genetic variance. While fitness itself had very little genetic variation in females there was substantial genetic variation for fitness in male red deer. While the possible misassignment of paternity represents a potential source of uncertainty and bias, this study represents a valuable advance in our understanding of quantitative variation in fitness and its components in natural systems. The future consideration of only linear morphological measures would avoid the problems associated with comparisons of CV's differing in dimensionality and would provide a more adequate test of Fisher's Fundamental Theorem of Natural Selection.
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Fisher, R.A. 1930. The Genetical Theory of Natural Selection, Clarendon Press. pp. 35.
Kruuk, L.E.B., Clutton-Brock, T.H., Slate, J., Pemberton, J.M, Brotherstone, S. & Guinness, F. 2000. Heritability of fitness in a wild mammal population. PNAS 97: 698-703. (http://www.pnas.org/cgi/content/full/97/2/698)
Mousseau, T.A. & Roff, D.A. 1987. Natural selection and the heritability of fitness components. Heredity 59: 181-197.
Price, T. & Schluter, D. 1991. On the heritability of life-history traits. Evolution 45: 853-861.
Roff, D.A. 1997. Evolutionary Quantitative Genetics, Chapman & Hall. pp. 121-123.
Roff, D.A. & Mousseau, T.A. 1987. Quantitative genetics and fitness: Lessons from Drosophila. Heredity 58: 103-118.