On the Effect of Asymmetrical Trait Inheritance on Models of Trait Evolution

Abstract

Current phylogenetic comparative methods modeling quantitative trait evolution generally assume that, during speciation, phenotypes are inherited identically between the two daughter species. This, however, neglects the fact that species consist of a set of individuals, each bearing its own trait value. Indeed, because descendent populations after speciation are samples of a parent population, we can expect their mean phenotypes to randomly differ from one another potentially generating a "jump" of mean phenotypes due to asymmetrical trait inheritance at cladogenesis. Here, we aim to clarify the effect of asymmetrical trait inheritance at speciation on macroevolutionary analyses, focusing on model testing and parameter estimation using some of the most common models of quantitative trait evolution. We developed an individual-based simulation framework in which the evolution of phenotypes is determined by trait changes at the individual level accumulating across generations, and cladogenesis occurs then by separation of subsets of the individuals into new lineages. Through simulations, we assess the magnitude of phenotypic jumps at cladogenesis under different modes of trait inheritance at speciation. We show that even small jumps can strongly alter both the results of model selection and parameter estimations, potentially affecting the biological interpretation of the estimated mode of evolution of a trait. Our results call for caution when interpreting analyses of trait evolution, while highlighting the importance of testing a wide range of alternative models. In the light of our findings, we propose that future methodological advances in comparative methods should more explicitly model the intraspecific variability around species mean phenotypes and how it is inherited at speciation.

Figure 1.

Four different scenarios of trait inheritance at speciation. (Left panels) Evolutionary history of the mean phenotype before and after a speciation event. (Right panels) Geographical distribution of the individuals at the speciation event depicted in the left panel. Bubbles represent the spatial distribution of individuals splitting from a parent population into two species (grey and light blue). The size of the bubbles is proportional to each individual’s phenotype. In this example, individual phenotypes follow a geographical gradient with smaller trait values on the lower-left part of the geographic range and larger trait values on the upper-right part. Under random segregation, (a) speciation is not driven by the trait displayed here nor by geography and might result from a change in an uncorrelated trait, for example, polyploidization. The mean phenotypes of the two descendants are expected to be equal with some stochasticity (resulting in slightly different means). Speciation occurring by geographic isolation, for example allopatric (b) or peripatric (c) may result in asymmetrical trait inheritance even though the trait itself is not the cause of speciation. Finally, if the trait is itself driving the speciation we can expect a full segregation of phenotypes at speciation (d). In the present study, we analyzed cases A and D, which represent the extremes in terms of the size of cladogenetic jumps.

Figure 2.

Examples of phenotypic trajectories under the extreme scenarios: a) RSS flat, b) TSS flat, c) RSS normal, and d) TSS normal. Different colors represent different species. Some examples of cladogenetic jumps (for scenarios b and d) are pointed with black arrows. The bulk of the jumps are covered by the lineage lines, but a quantification of their sizes is shown in Fig. 3.

Figure 3.

Absolute jump sizes for every scenario. Boxplots represent the distribution of jump sizes for all speciation events across all simulations for a given scenario. Here, the size of a jump is the absolute difference between the starting values of the two daughter lineages right after a cladogenetic event. Scenarios following a flat and normal fitness landscapes are colored following the color pattern shown in Fig. 4.

Figure 4.

Model fit under all scenarios. Bars represent the percentage of simulations that were best fit by a given model. Parameters used for these simulations were drawn from uniform priors (Table 1, Variable). Mixed scenarios consist of 5, and 50% of TSS cladogenetic events along a single simulation run. BM = Brownian Motion; OU = Ornstein–Uhlenbeck; WN = White Noise. The second best fit is given in Supplementary Fig. B.4 available on Dryad.

Figure 5.

Parameter estimates of fitContinuous (R package geiger) and levolution (for jump rates; Duchen et al. 2017) of various model parameters. Green (purple) distributions represent the estimates of all TSS (RSS) simulations. evolutionary rate; parameter kappa; selective strength; jump rate; optimum. Median relative error (MRE) between RSS or TSS and their true values are depicted in Table 2.