Analysis of the reciprocal transplant assay

The direct and indirect responses to selection can be evaluated from a reciprocal transplant assay in which all evolved lines are grown on all substrates. This reciprocal transplant assay generates a matrix of scores for all combinations of selection environment and assay environment. If populations have become specifically adapted to the environment in which they were selected, scores along the leading diagonal of the matrix (in which the assay environment corresponds to the selection environment) will be consistently greater than scores in off‐diagonal cells. This will generate a statistical interaction between selection and assay environments that can be used to evaluate the occurrence of specific adaptation.

The results of the assay can then be used to answer two questions. The first is whether growth on a particular substrate is greater among lines that have been propagated on that substrate than among lines that have been propagated on other substrates. This expresses the improvement in a given assay environment that has been caused by natural selection in that environment, relative to any improvement that might be caused in that environment by selection in other environments. This is the sense in which “local adaptation” is usually understood (Kawecki and Ebert 2004). The second question is whether lines that have been propagated on a given substrate grow better on that substrate than on other substrates. This shows whether the improvement of a line in the environment of selection is consistently associated with its deterioration in other environments. This is often called the “cost of adaptation” (Levins 1968).

To evaluate the extent and the cost of adaptation, the overall response R(ijk) of the k‐th replicate line subjected to the j‐th selection treatment and grown in the i‐th assay conditions can be partitioned as follows:

where the subscript dots indicate averaging. The three components of the overall response are as follows.

The first term on the right‐hand side is the general response associated with a given assay environment, estimated as the difference between the average of all selection treatments in a given assay environment, R(i..), and the growth of the ancestor in that environment, A(i). This is attributable to common features of the selection environments.

The second term is the specific response to the selection treatment, estimated from the difference between the average of replicate lines subjected to this treatment, R(ij.), and the average of all selection treatments in this assay environment, R(i..). If i = j, this is the specific direct response, which expresses local adaptation, using replicate selection lines to test its significance. If i ≠ j, it is a specific indirect response in a given assay environment. The degree of local adaptation to the j‐th selection environment relative to the i‐th assay environment is evaluated by comparing R(jj.) with R(ji.), which corresponds to the “local versus foreign” comparison of Kawecki and Ebert (2004). The cost of adaptation in the i‐th assay environment is evaluated by comparing R(jj.) with R(ij.), which corresponds to the “home versus away” comparison of Kawecki and Ebert (2004).

The third term is the deviation of the growth of each line, R(ijk), from the average of lines subjected to a particular selection treatment and assayed in a particular environment, R(ij.). Functional interference is expressed by a negative correlation among replicate lines between the deviations for a given assay environment and those for the environment of selection, given that the direct response is positive (local adaptation has evolved) and varies among lines (potentially leading to different degrees of maladaptation).

This interpretation of a reciprocal transplant assay can be summarized like this: The specific direct response expresses the degree of local adaptation, while the specific indirect response expresses the cost of adaptation, whose source can be identified from the line‐based estimates.