Genetic load

In population genetics, genetic load or genetic burden is a measure of the cost of lost alleles due to selection (selectional load) or mutation (mutational load). It is a value in the range $$0 < {L} < 1$$, where 0 represents no load. The concept was first formulated in 1937 by JBS Haldane, independently formulated, named and applied to humans in 1950 by H. J. Muller, and elaborated further by Haldane in 1957.

Definition
Genetic load is the reduction in selective value for a population compared to what the population would have if all individuals had the most favored genotype. It is normally stated in terms of fitness as the reduction in the mean fitness for a population compared to the maximum fitness.

Mathematics
Consider a single gene locus with the alleles $$ \mathbf{A} _1 \dots \mathbf{A} _n$$, which have the fitnesses $$w_1 \dots w_n$$ and the allele frequencies $$p_1 \dots p_n$$ respectively. Ignoring frequency-dependent selection, then genetic load ($$L$$) may be calculated as:


 * $$L = {{w_\max - \bar w}\over w_\max}~(1)$$

where $$w_\max$$ is the maximum value of the fitnesses $$w_1 \dots w_n$$ and $$\bar w$$ is mean fitness which is calculated as the mean of all the fitnesses weighted by their corresponding allele frequency:


 * $$\bar w = {\sum_{i=1}^n {p_i w_i}} ~(2)$$

where the $$i^\mathrm{th}$$ allele is $$\mathbf{A}_i$$ and has the fitness and frequency $$w_i$$ and $$p_i$$ respectively.

When the $$w_\max = 1$$, then (1) simplifies to


 * $$L = 1 - \bar w. ~(3)$$

Causes of genetic load
Load may be caused by selection and mutation.

Mutational load
Load caused by mutations is known as mutational load.

Selectional load
Selection occurs when the fitnesses of particular alleles are inequal, hence selection always exerts a load.

With directional selection, the allele frequencies will tend towards an equilibrium position with the fittest allele reaching a frequency in mutation-selection balance. As mutations are rare, this is effectively fixation. Consider two alleles $$\mathbf{A}_1$$ and $$\mathbf{A}_2$$. If $$w_1 > w_2$$, then at equilibrium, $$p_1 \approx 1$$ and $$p_2 \approx 0$$, hence $$\bar{w} \approx w_\max$$, and $$L \approx 0$$.

If the mean fitness is 0, the load is equal to 1, but the population goes extinct.

Segregational load
In contrast to directional selection, heterozygote advantage always exerts a load at equilibrium.

Creationist criticism
Some creationists (such as Henry M. Morris) have suggested that mutational load would increase over time and thus make populations inviable. However, they ignore the effect of selectional load acting to weed out (decrease frequency of) deleterious mutations.