- Environmental correlation describes the statistical association between environmental effects influencing two traits measured in the same individuals or experimental units. It indicates whether environmental factors that increase or decrease one trait tend to have similar or opposing effects on another trait. A positive environmental correlation means that environmental influences tend to affect both traits in the same direction, while a negative environmental correlation means that environmental effects tend to increase one trait while decreasing the other. Environmental correlation is an important concept in quantitative genetics because observed relationships between traits can arise from genetic effects, environmental effects, or both.
- Environmental correlation is closely related to phenotypic correlation, genetic correlation, and phenotypic covariance. A phenotypic correlation describes the association between observed trait values, whereas an environmental correlation focuses on the association between environmental components of those traits. Genetic correlation describes the association between genetic effects influencing traits. Separating these components helps researchers determine whether an observed relationship is likely to persist across environments or is primarily caused by environmental conditions.
- For two traits, environmental correlation can be expressed conceptually as the environmental covariance divided by the product of the environmental standard deviations:
- rE=CovE(X,Y)VE(X)VE(Y)r_E = \frac{Cov_E(X,Y)}{\sqrt{V_E(X)V_E(Y)}}
- where rEr_E is the environmental correlation, CovE(X,Y)Cov_E(X,Y) is the environmental covariance between traits X and Y, and VE(X)V_E(X) and VE(Y)V_E(Y) are their environmental variances. The correlation generally ranges from −1 to +1. A value close to +1 indicates strong positive association between environmental effects, a value close to −1 indicates strong negative association, and a value near zero indicates little linear association between the environmental components.
- The environmental component of a phenotype represents variation that is not attributed to the genetic effects included in a particular statistical model. Environmental influences can include nutrition, temperature, rainfall, soil conditions, management, housing, disease exposure, social conditions, developmental environment, measurement conditions, and other external factors. Depending on the experimental design, environmental variance may also include unexplained residual variation and other non-genetic sources.
- For example, suppose researchers measure body weight and growth rate in a group of animals. Individuals receiving better nutrition may both grow faster and reach greater body weights. The environmental effects associated with feed availability could therefore generate a positive environmental correlation between growth rate and body weight. The traits may also have a positive genetic correlation, but the environmental association is a separate component that should not automatically be interpreted as genetic.
- Environmental correlation can also be negative. For example, an environmental condition that increases reproductive investment may reduce resources available for growth. If individuals exposed to the condition show higher reproductive output but lower growth because of environmental resource allocation, the environmental effects on the two traits may be negatively correlated. Such relationships can contribute to observed phenotypic trade-offs without necessarily indicating a genetic trade-off.
- The relationship between environmental covariance and phenotypic covariance is particularly important. In a simplified two-trait quantitative-genetic framework, phenotypic covariance can be represented as containing genetic and environmental covariance: CovP(X,Y)=CovG(X,Y)+CovE(X,Y)Cov_P(X,Y) = Cov_G(X,Y) + Cov_E(X,Y)
- under appropriate assumptions and model definitions. This means that an observed association between traits may reflect shared genetic effects, shared environmental effects, or both. More complex models may include additional components, such as permanent environmental effects, maternal effects, dominance, epistasis, or genotype–environment interactions.
- Environmental correlation can therefore explain why phenotypic correlation and genetic correlation sometimes differ substantially. Suppose two traits have a strong positive phenotypic correlation because they are both strongly influenced by temperature. If their genetic effects are only weakly associated, their genetic correlation may be close to zero even though their observed phenotypes are strongly correlated. Conversely, environmental variation can sometimes obscure an underlying genetic relationship.
- This distinction is particularly important in animal breeding and plant breeding. Breeders are usually interested in inherited differences because selection changes allele frequencies and therefore affects future generations. If two traits have a strong phenotypic correlation caused mainly by environmental factors, selecting individuals based only on observed phenotypes may produce a different response than expected from the phenotypic association. Estimating genetic and environmental covariance separately can therefore improve predictions of breeding value and selection response.
- Environmental correlation also affects estimates of heritability. Heritability describes the proportion of phenotypic variation associated with genetic differences within a particular population and environment. If environmental effects are large, they can increase phenotypic variance and reduce the estimated heritability of a trait. Shared environmental influences can also create associations between traits that are not caused by genetic similarity. Understanding environmental covariance is therefore important when interpreting heritability and genetic relationships.
- The distinction between environmental correlation and permanent environmental effects is also important when traits are measured repeatedly. A persistent environmental condition experienced by an individual may influence several measurements across time. For example, long-term differences in housing, maternal environment, or early-life nutrition may affect multiple later traits. In such cases, statistical models may separate permanent environmental effects from temporary environmental effects and measurement error.
- Genotype–environment interaction (G×E) can further complicate environmental correlations. G×E occurs when different genotypes respond differently to environmental conditions. A particular environment may increase one trait strongly in some genotypes but only weakly in others. As a result, the environmental contribution to trait relationships may differ among populations, locations, seasons, or management systems.
- Environmental correlations can also vary across environments. A correlation observed under controlled laboratory conditions may differ from one observed in a field population. In agricultural studies, for example, the environmental association between yield and disease resistance may differ between dry and wet environments. Environmental conditions therefore need to be considered when interpreting correlations among complex traits.
- Researchers can investigate environmental effects using experimental designs that control or compare environmental conditions. Common-garden experiments place individuals with different genetic backgrounds in a shared environment, while reciprocal transplant experiments expose different genetic groups to multiple environments. These approaches can help separate genetic differences from environmental influences and can provide evidence about phenotypic plasticity and G×E.
- Statistical models are also important for estimating environmental covariance and correlation. Linear mixed models can partition phenotypic variation into different sources, including genetic effects, environmental effects, permanent individual effects, and residual variation. Restricted maximum likelihood (REML) is commonly used to estimate variance and covariance components in quantitative-genetic models. The exact interpretation of an environmental covariance depends on the model used and the components included.
- Environmental correlation can be especially important when individuals share the same environment. Family members, animals housed together, plants grown in the same plot, or people living in the same household may experience common environmental conditions. This shared environment can produce similarities in traits even when the traits are not strongly genetically correlated. If shared environmental effects are not modeled appropriately, researchers may incorrectly attribute environmental resemblance to genetic effects.
- This issue is closely related to covariance among relatives. Relatives tend to share genes, but they may also share environments. For example, siblings may have similar nutrition, household conditions, educational opportunities, or social environments. In animal breeding, littermates may share maternal and early-life environmental effects. Quantitative-genetic models therefore need to distinguish genetic covariance from environmental covariance whenever possible.
- Environmental correlation is also connected to phenotypic plasticity, which describes the ability of a genotype to produce different phenotypes under different environmental conditions. If two traits respond similarly to an environmental change, their environmental components may become positively correlated. If they respond in opposite directions, the environmental correlation may be negative. Plastic responses can therefore contribute substantially to observed trait relationships.
- Environmental covariance may arise from shared resources, developmental pathways, physiological constraints, management practices, or external conditions. For example, temperature can influence metabolic rate and activity, nutrition can influence growth and reproductive performance, and water availability can affect both plant biomass and flowering time. These relationships demonstrate that environmental correlation is not necessarily a single biological mechanism but rather a statistical description of coordinated environmental effects.
- Environmental correlation should not be confused with genetic correlation. Genetic correlation reflects how genetic effects influencing two traits vary together and is particularly important for predicting correlated evolutionary or breeding responses. Environmental correlation instead describes how environmental components of the traits vary together. A pair of traits can therefore have a positive genetic correlation and a negative environmental correlation, a negative genetic correlation and positive environmental correlation, or similar signs for both.
- The distinction is also important when interpreting selection response. The multivariate breeder’s equation is based on the additive genetic variance-covariance matrix, commonly called the G-matrix, rather than the environmental covariance matrix. Environmental correlation does not directly determine the inherited response to selection, although environmental effects can influence the accuracy with which individuals are evaluated and therefore affect practical selection decisions.
- Environmental correlation can influence the accuracy of phenotypic selection. If environmental conditions affect two traits in the same direction, individuals experiencing favorable conditions may appear superior for both traits even when their genetic merit differs less strongly. This is one reason why breeding programs increasingly use pedigree information, repeated records, environmental records, and genomic selection to improve prediction of genetic merit.
- In genomic and quantitative-genetic studies, environmental covariance may be modeled alongside genomic relationship matrices and genetic covariance structures. Genomic information helps estimate genetic relationships among individuals, while environmental information helps account for differences in conditions. Combining these sources can improve estimates of genomic estimated breeding values (GEBVs) and predictions of performance across environments.
- Environmental correlation is also relevant to human genetics. Individuals may share environments because they live in the same household, attend similar schools, experience similar socioeconomic conditions, or are exposed to similar environmental factors. Such shared exposures can produce correlations between traits or diseases without necessarily indicating a shared genetic cause. Separating environmental and genetic contributions is therefore important in family studies, epidemiology, and complex-trait research.
- In ecological and evolutionary studies, environmental correlations can help explain coordinated phenotypic responses to environmental change. Temperature, precipitation, food availability, habitat quality, and other ecological factors may simultaneously influence multiple traits. Understanding these relationships can help researchers distinguish environmentally induced changes from genetic adaptation and evaluate how populations may respond to changing environments.
- Environmental correlation can also change over time. Climate change, altered management practices, habitat modification, disease exposure, and changes in resource availability can modify environmental covariance among traits. Consequently, relationships observed in one period may not necessarily remain constant under future environmental conditions.
- As with other correlation measures, environmental correlation does not establish causation. A positive environmental correlation does not prove that one environmental factor causes both traits to change. Several environmental variables may be correlated with one another, and unmeasured conditions may contribute to the observed association. Experimental manipulation and appropriate statistical modeling are therefore needed when investigating causal mechanisms.
- The interpretation of environmental correlation is also population and context dependent. The same two traits may show different environmental correlations in different populations, seasons, management systems, developmental stages, or geographic regions. Environmental correlation should therefore be interpreted within the specific population, experimental design, and statistical model used to estimate it.
- Overall, environmental correlation describes how environmental influences affecting two traits vary together. It is an important component of the broader framework connecting phenotypic correlation, phenotypic covariance, genetic covariance, and genetic correlation. Understanding environmental correlation helps researchers determine whether observed relationships between traits are associated with shared genetic effects, shared environmental effects, or interactions between genes and environments.
- Environmental correlation is particularly valuable in quantitative genetics, breeding, ecology, and evolutionary biology because complex traits rarely vary independently of their environments. By separating environmental covariance from genetic covariance, researchers can better estimate heritability, predict breeding values, evaluate genetic correlations, understand G×E, and predict responses to selection. Together, environmental correlation, genetic correlation, and phenotypic correlation provide complementary perspectives on why traits vary together and how those relationships may change across environments and generations.
