Quantifying Natural Selection on Multiple Timescales

Abstract

Quantifying the effect of selection on an evolving population allows us to better understand the mechanisms behind the process of evolution. We can calculate the change over time of a certain trait in a population, and determine the contribution of selection to this change. The Price equation is a mathematical equality that is a useful tool for this purpose. It provides an intuitive quantification of the change of a trait in a population over time due to selection: the covariance between the fitness of individuals in a population and their respective trait value. The resulting quantity, as well as its interpretation, is highly dependent on the chosen timescale. We will propose useful approaches, using the Price equation, to study the effect of timescales on the quantification of natural selection in an evolving biological system. The Price equation provides a suitable base to build on, as its generality allows for selection to be quantified on any chosen timescale. Applying the Price equation on a relatively short timescale is mostly uncomplicated: it requires the trait value of interest of all individuals in a population at one point in time, and the number of offspring they produced a short time later. Selection can then be quantified as the covariance between those two characteristics. The interpretation of the selection term for short timescales is also quite intuitive: the covariance represents the relation between a trait value and its associated fitness. However, for longer timescales the interpretation of the quantification of selection is less straight-forward as the relation is less direct. To remedy the problems we come across for longer timescales, we propose and contrast two main approaches: the Leap Approach, and the Incremental Approach. The former employs the Price equation once in one big leap, equal to the method for short timescales. This quantifies selection on the long term, meaning the benefit of the trait value as a long-term strategy. There are some caveats however, as this ‘leap’ jumps over possibly relevant information. We can rectify this by dividing the long time period into smaller intervals, which is the basis of the Incremental Approach. For every small time interval, the Price equation is applied separately and the results are added incrementally. This results in a quantification of selection over a long period without skipping over information. Another use of the Incremental Approach is to only quantify selection over every small time interval in which an event happens, which we will call Event-Based selection. Both the Incremental and the Leap Approach can be applied on a Sliding Window, to reduce arbitrary importance given to certain time points. Which approach to use depends on the research question, as the interpretation of the results of the different approaches provide qualitatively different insights into the evolutionary process in question.