Resolving the paradox of stasis: addressing the missing fraction problem

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Quantitative genetics has been exceptionally successful at predicting evolution in simple scenarios, for example, the response to artificial selection on a specific traits, such as milk yield in cattle, or body size in mice. Evolutionary quantitative genetics seeks to apply the same principles in nature. This endeavor has so far had much more mixed success. It is clear that the basic ingredients for adaptive evolutionary change, i.e., genetic variation for and natural selection of a trait, both occur frequently in natural populations. However, the rapid contemporary evolutionary change that would be expected from an abundance of heritability and selection is rarely observed. This set of observations has been called the "paradox of stasis". A paradox is only an *apparently* illogical scenario: theoretical evolutionary quantitative genetics has been extremely successful at generating potential solutions to the paradox. In general, applying these more advanced theories is challenging, and there is consequently a great paucity of data on the solutions to the paradox, relative to the quantity of data on simple quantities such as heritability and selection. We propose to tackle one of the most theoretically important solutions, which is also one of the least studied empirically.The "missing fraction problem" occurs if viability selection alters the distribution of a trait before it is expressed. For example, if individuals that would otherwise produce large values of a trait are likely to die before producing the trait (because of viability selection at an earlier stage of the life cycle on a correlated trait) then this selection will not be picked up in a selection analysis that relates available phenotypes to fitness: importantly, selection estimated in this naïve analysis will be upwardly biased. There are a number of opportunities to get around this problem, for example, by jointly modeling the selection and genetics of focal traits, along with early life viability (i.e., treat survival as a trait), or traits that may influence early survival. We organize these opportunities into a hierarchy of four levels. All of these levels make greater demands on data than typical studies of the selection and genetics of traits in the wild. However, different levels of analysis could potentially be achieved in many study systems.In our study system, the Soay sheep population on St Kilda, we are able to apply all four levels of the hierarchy to a range of traits, with a special focus on body size and reproductive scheduling. We will conduct a coordinated series of studies on the extent of the missing fraction problem that will generate a comprehensive analysis of how much accounting for this key issue can change evolutionary inferences in the wild. Additionally, we also propose (1) theoretical work to address the potential severity of the missing fraction problem across different life histories, (2) methodological developments to help researchers (including initially ourselves!) apply some of the most advanced available statistical methods to the problem, and (3) a synthetic review, summarizing the available theory, methods and key results (which by the end of this project will come in large part from our own study). Our study will thus provide a comprehensive step forward for evolutionary quantitative genetics, and will enable the field in general to begin to properly tackle one of its biggest outstanding problems.