Errors in genetic theory equations

This study addresses the consequences of eliminating terms such as x(2) and x(3) from genetic equations when the variable x is known to be small. This paper indicates logically that to assign such terms a value of 0.0 requires knowing the magnitude of the coefficients for each of these terms as well as the magnitude of all other terms in a given expression. Since most genetic expressions of interest involve several unknowns, the elimination of these terms appears difficult to justify in most situations. The effects of the elimination of a single term from an expression in a classical plant breeding paper were investigated as a simple exemplifying case. In the example, the simplified equation for change in population mean with selection sometimes greatly overestimated the response to selection and in some cases also altered conclusions as to best procedure. Though simplified equations are usually much more tractable and interpretable, the bias which is introduced into the research results and the potential for propagation of such biases in subsequent studies indicates that no term can be uncritically ignored in a genetic equation. The obvious alternatives are (1) do not simplify by eliminating terms, (2) perform a complete error analysis, or (3) restrict the range of values for variables so that terms can be justifiably eliminated in the error analysis.