The missing fraction problem as an episodes of selection problem

Abstract

In evolutionary quantitative genetics, the missing fraction problem refers to the case where phenotypes seen later in life are biased because a non-random subset of those phenotypes are missing from the population due to prior viability selection on correlated traits. As any such missing fraction will bias our estimates of selection, and therefore, responses to selection, it is one potential explanation for the paradox of stasis seen in wild populations. The two components required for the missing fraction problem to arise are: (1) viability selection; and (2) correlation between later-life traits and those important for early-life survival. Although it is plausible that these conditions are widespread in wild populations, this problem has received very little attention since it was first discussed (Grafen 1988; Hadfield 2008). It is impossible to know what phenotypes would have been expressed later in life by individuals who died during an earlier episode of viability selection, which has probably put researchers off. Here we show that we can break the problem down into episodes of selection and recover either (a) true estimates of phenotypic selection for later-life traits, or (b) adjusted estimates of the response to selection, depending on the data available. Implementation of complex statistics should uncover how prevalent the problem may be across many existing datasets (the latter approach). Whereas overall, we hope that viewing the missing fraction problem as an episodes of selection problem increases motivation, and provides justification, for a shift in focus to directly studying early-life viability selection. "...what a correlation with [lifetime reproductive success] or its components tells you depends on the causes of the natural variation in the character. It will not always be easy to discover those causes." -- Grafen (1988) "It is surprising that the problem of missing data has received so little attention given that viability selection is central to evolutionary biology." -- Hadfield (2008)