Essay: The Correlation Between Relatives on the Supposition of Mendelian Inheritance

Background
The essay appeared at a time when Mendelian genetics and biometric studies of continuous traits were seen as conflicting schools. Biometricians emphasized statistical descriptions of variation and correlation among relatives, while Mendelians focused on particulate inheritance of discrete factors. Ronald A. Fisher provided a mathematical bridge by showing how Mendelian principles could produce the patterns observed in biometric data when many genes of small effect are involved.
Fisher set out to translate genetic mechanisms into expectations for variances and covariances of phenotypes among relatives. By doing so he addressed a fundamental conceptual problem: how to reconcile discrete heredity with smoothly varying traits such as height or yield, and how to extract genetic parameters from family correlation data.

Key ideas
Central to Fisher's argument is the decomposition of phenotypic variance into components attributable to transmissible genetic effects and to non-transmissible influences. He emphasized additive genetic effects as the principal component that determines resemblance between relatives, while recognizing dominance and non-genetic sources as contributors to the total variance. The additive component corresponds to the predictable part of inheritance that sums across loci and transmits from parent to offspring.
Fisher also stressed that continuous variation can arise naturally from the combined action of many Mendelian factors, each segregating according to simple rules. Through probabilistic aggregation of many small effects, the overall distribution of a trait can be approximately normal, matching biometric observations without abandoning Mendelian law.

Methods and derivations
The essay develops mathematical expressions for expected variances and covariances among relatives by modelling the segregation of genes and their contributions to trait values. Fisher used combinatorial and probabilistic arguments to show how allelic segregation produces sampling variance and how that variance partitions into components that influence correlations between specified kin classes. He derived formulas that relate observed correlations, such as between parent and offspring, between siblings, and between more distant relatives, to underlying genetic parameters.
Approximations employed include treating large numbers of independent loci and using linear combinations of their effects to justify normal approximations. The derivations yield explicit relations between coefficients of relatedness and the fraction of phenotypic variance attributable to additive genetic factors, enabling parameter estimation from empirical family data.

Results and implications
Fisher produced concrete expressions for the expected correlations among different categories of relatives in terms of additive genetic variance and other variance components. These results showed that a substantial portion of resemblance among kin can be accounted for by additive Mendelian factors and that observed biometric correlations provide a route to estimate the genetic contribution to a trait. He articulated how regression of offspring on parents and comparisons among siblings could be interpreted to obtain estimates of what later became known as heritability.
The essay decisively reconciled Mendelian genetics with biometric patterns and supplied a statistical framework for studying quantitative traits. By linking genetic theory to observable statistical quantities, Fisher opened the way for rigorous empirical estimation and for applying genetic theory to breeding, evolution, and human heredity.

Legacy
The 1918 analysis founded the modern field of quantitative genetics by introducing variance component thinking and by formalizing the concept of additive genetic variance as the driver of resemblance. Subsequent developments in population genetics, animal and plant breeding, and human quantitative genetics built on the formulas and intuition Fisher provided. The methods of variance partitioning, regression of relatives, and estimation of heritability trace directly to the ideas laid out in this essay, securing its status as a milestone that unified Mendelism and biometry.