A multivariate view of parallel evolution

Abstract

A growing number of empirical studies have quantified the degree to which evolution is geometrically parallel by estimating and interpreting pairwise angles between multiple replicate lineages’ evolutionary change vectors in multivariate trait space. Similar comparisons, of distance in trait space, are used to assess the degree of convergence. These approaches amount to element‐by‐element interpretation of distance matrices, typically testing for differences among replicate evolutionary vectors, compared to a null hypothesis of perfect parallelism. We suggest a complimentary set of approaches, co‐opted from evolutionary quantitative genetics, involving eigen analysis and comparison of among‐lineage covariance matrices. Such approaches allow one to identify multiple major axes of evolutionary change (e.g., alternative adaptive solutions), and also allow for the definition of biologically tenable null hypotheses, such as drift, against which empirical patterns can be tested. Reanalysis of a dataset of multivariate evolution across a replicated lake/stream gradient in threespine stickleback reveals that most of the variation in the direction of evolutionary change can be captured in just a few dimensions, indicating a greater extent of parallelism than previously appreciated. We suggest that applying such multivariate approaches may often be necessary to fully understand the extent and form of parallel and convergent evolution.

Phenotypic and genotypic parallel evolution in parapatric ecotypes ofSenecio

“…Within the S. lautus system, multivariate divergence between ecotypes and its association with the additive genetic variance underlying phenotypic traits suggests that Headland populations have strong phenotypic constraint arising from strong genetic correlations whereas Dune populations are freer to evolve across many axes of genetic variance (Walter et al, 2018a). This approach, now extended by De Lisle & Bolnick (2020) to also generate null hypotheses, promises to be a powerful approach to measure parallelism, but whether additive genetic variances can be measured in most systems remains a formidable challenge. Future work on null hypotheses should also strive to model the likelihood of phenotypic or genotypic parallelism while taking into account variance in factors such as gene flow, environmental heterogeneity, the recombination landscape, and the genetic architecture of adaptive traits (e.g., Thompson et al, 2019).…”

“…Although these traits might be highly correlated to other measured traits, especially for highly modular phenotypes (Murren, 2012), this needs to be first demonstrated experimentally before deciding which traits to measure and which traits to disregard. We must therefore be aware that the likelihood of detecting parallelism is highly dependent on the type and number of traits measured in a system (Stayton, 2008), suggesting that further work needs to enrich current theories of multi-trait evolution so we can develop better null hypotheses for parallel evolution while accounting for correlations between traits, including those that are highly pleiotropic (Yeaman, 2015;De Lisle & Bolnick, 2020).…”

Sensory-based quantification of male colour patterns in Trinidadian guppies reveals nonparallel phenotypic evolution across an ecological transition in multivariate trait space

“…Phenotypic analyses described above are ‘blind’ to the ancestral versus derived status of HP and LP population pairs with rivers. Therefore, we also adopted recent methods that use phenotypic change within lineages to quantify parallelism (De Lisle and Bolnick 2020). We assume that within each river, an HP and LP pair can be viewed as representing a ‘lineage’ in which the HP is ancestral.…”

“…HP-LP comparisons). We describe the approach briefly, using notion from De Lisle and Bolnick (2020) and referencing their equation numbers. First we calculated, the n trait row by m lineage column data matrix X , where each element of X represents Δ z n,m (the difference in mean standardized phenotype (z) between HP and LP populations for trait n in lineage m; Equation 3).…”

“…In contrast, a uniform distribution of eigen values (meaning low among-lineage correlations of change vectors), and/or a mixture of positive and negative lineage-specific loadings on the first eigen vector is expected under non-parallelism. As suggested by De Lisle and Bolnick (2020), for the case of fewer traits (here 4 or 8 depending on the version of C ) than lineages (here 9), we generated a null distribution of m eigenvalues by simulating 1000 random vectors representing evolutionary change under independence (among lineages) of multivariate phenotypic trajectories. While acknowledging that power to reject the null (no parallelism) may be low (De Lisle and Bolnick 2020), observed eigenvalues were then compared to the simulated distribution.…”