Why People Still Talk About This Stuff

Most people who get into quantitative genetics stumble across R.A. Fisher's work by accident. They're reading about heritability estimates or breeding values and suddenly they're four hours deep into something written in 1930 that still underpins basically everything we do in modern selection theory. The Genetical Theory Of Natural Selection isn't a textbook you read cover to cover anymore. It's a reference document. You go back to it when your model isn't converging and you need to remember what assumptions you're actually making. Fisher brought together Mendelian inheritance and Darwinian selection at a time when the two fields were arguing with each other across the Atlantic. Biometricians thought variation was continuous and Mendelians thought it was discrete. Fisher showed they were looking at the same thing from different angles. That insight alone justified a career. He did more than that though.

The Genetical Theory Of Natural Selection and What It Actually Means

The core argument is that natural selection acts on the average excess of genes in a population, and that the rate of increase in fitness is equal to the additive genetic variance in fitness. This is the fundamental theorem. It sounds simple. It is not simple when you try to use it. I spent two weeks trying to fit a selection model to livestock data where the trait had low heritability and the population structure was messy. The textbook approach said to estimate breeding values using a standard BLUP procedure. What actually happened was that the relationship matrix was nearly singular because of recent bottlenecks in the herd. The model barely converged and the estimates were garbage. I ended up switching to a single-step GBLUP approach that folded the pedigree and the genomic data together before running the mixed model equations. That changed the estimation process from unreliable to usable in about a day. The fundamental theorem still applied. I just needed the right estimator to match the data structure. Additive genetic variance is the important part here. Fisher made a clear distinction between additive effects and dominance or epistatic effects. Selection only responds predictably to the additive component. Non-additive variance exists but it doesn't get passed on in a consistent way. That's why breeding programs focus on estimated breeding values rather than raw phenotypic performance. Your best-performing individual might have great genes but also a big chunk of favorable dominance deviation that won't show up in its offspring. The theorem also assumes that fitness is the only thing driving allele frequency changes. In practice, that's almost never true. There's drift, gene flow, mutation pressure, and often selection on correlated traits that pulls the population in a direction you didn't intend. When I was working on a plant breeding project, we selected for disease resistance and unintentionally dragged flowering time along with it because of pleiotropy. The selection response wasn't what we expected. That's a practical consequence of the theorem being about net fitness, not your target trait specifically.

Fisher's decomposition of variance is still the standard framework. Total phenotypic variance breaks down into additive genetic variance, dominance variance, epistatic variance, and environmental variance. Each component is estimated separately. The narrow-sense heritability is just Va over Vp. Breeders call it narrow-sense because it only counts the additive portion. Broad-sense heritability includes everything genetic. The difference matters enormously when you're trying to predict response to selection.

One thing beginners consistently get wrong is assuming that high heritability means the trait will respond quickly to selection. It means the response will be proportional to the selection differential, but if the genetic variance is small to begin with, the absolute change per generation can still be negligible. I've seen projects abandoned because the heritability was 0.6 but the genetic gain per year was less than measurement error. You need both a solid heritability estimate and enough standing genetic variation for the math to work out practically. The mathematical machinery Fisher developed is dense. He used approximations and normal distributions in ways that don't always hold up under scrutiny. Later work by Kempthorne and others formalized the quantitative genetics framework more rigorously. But Fisher's core insights survived the formalization. The concept of the average effect of a gene substitution is still how we think about allele action in polygenic traits. The regression approach he used to define breeding values is exactly what modern mixed models do, just with better computational tools. Here's a practical point that isn't in most textbooks. When you're estimating genetic parameters from real data, the confidence intervals on heritability estimates are often wider than people expect. A heritability of 0.4 might legitimately range from 0.2 to 0.6 depending on sample size and population structure. I learned this the hard way when a client demanded precise predictions based on a single study with 200 records. The predictions were wildly off because nobody accounted for the uncertainty in the variance component estimates. Running a Bayesian analysis with proper priors on the variance components would have given honest intervals instead of point estimates that implied false precision. Gene-environment interaction is another area where the basic theory falls short. The additive genetic variance you estimate in one environment might not be the same in another. If you're selecting for yield across multiple environments, you need to know whether the genotype-by-environment interaction variance is large enough to warrant separate breeding programs or whether a single set of breeding values transfers adequately. I worked with a maize program where the GxE variance was substantial for grain moisture at harvest but negligible for yield. They adjusted their testing protocol accordingly, which saved a lot of wasted field space. The theorem's assumption of constant fitness is particularly unrealistic. In nature, fitness depends on density, on the frequencies of other genotypes, and on environmental conditions that shift over time. Frequency-dependent selection is a well-known complication that Fisher acknowledged but didn't fully resolve. The mating system matters too. Inbreeding reduces additive variance by converting it into dominance variance, which changes the selection response trajectory in ways that aren't captured by the basic model. Mutation-selection balance is another practical consideration. For traits under strong purifying selection, the standing genetic variation is maintained by a balance between new mutations and removal by selection. The amount of variation you can expect is roughly the mutation rate divided by the selection coefficient. For traits under weak selection, drift dominates and the variance is harder to predict. This is relevant when you're working with traits that have very low heritability and wondering where the remaining genetic variation is coming from. Modern genomics has added layers of complexity that Fisher couldn't have anticipated. Genome-wide association studies and genomic prediction assume that marker effects are fixed and known, which is an approximation. The accuracy of genomic estimated breeding values depends heavily on the relationship between the training population and the selection candidates. If they're too distantly related, the prediction accuracy drops substantially regardless of how many markers you have. I've seen programs invest heavily in genotyping only to find that their prediction accuracy was barely above pedigree-based BLUP because of poor population structure management. Linkage disequilibrium between markers and quantitative trait loci is the mechanism that makes genomic prediction work at all. Fisher's theory treats genes individually. Genomic selection treats the genome as a collection of linked markers that collectively capture the breeding value. The connection between the two frameworks isn't straightforward but it's there. The genomic relationship matrix is essentially a molecular version of the pedigree relationship matrix that accounts for realized rather than expected relatedness. There's also the issue of cryptic relatedness. In human genetic studies especially, population stratification can create spurious associations that look like selection signals but are really just demographic artifacts. Correcting for this requires principal components or mixed model approaches that weren't available when Fisher was writing. The fundamental logic remains the same though. You're trying to separate genetic signal from noise, and the noise keeps changing shape. When the theory works well, it works beautifully. Dairy cattle breeding has been applying these principles for decades with measurable genetic gain every year. The response to selection is predictable and sustained because the genetic variance is well-maintained and the selection intensity is high. But that success requires careful management of effective population size and inbreeding. The same principles apply to any selected population. Ignore the long-term consequences and you'll see the response plateau or reverse as genetic diversity erodes. The Genetical Theory Of Natural Selection isn't a complete description of evolution. It doesn't handle neutral evolution, it doesn't account for soft selection well, and it struggles with complex epistatic architectures. But for anyone working with quantitative traits in agriculture, conservation, or evolutionary biology, it remains the foundational framework. The math is older than most of the people using it. The logic still holds.