bioRxiv preprint doi: https://doi.org/10.1101/2020.01.26.920439; this version posted January 27, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 1 A Multivariate View of Parallel Evolution 2 3 Stephen P. De Lisle* 4 Daniel I. Bolnick 5 6 Department of Ecology & Evolutionary Biology 7 University of Connecticut 8 Storrs, CT 06269 9 10 * email: [email protected] 11 12 Running title: Parallelism revealed 13 14 Keywords: Convergent evolution, Gasterosteus aculeatus, microevolution, phenotypic vector 15 analysis, random matrix theory 16 17 18 19 20 21 22 23 1 bioRxiv preprint doi: https://doi.org/10.1101/2020.01.26.920439; this version posted January 27, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 24 Abstract 25 A growing number of empirical studies have quantified the degree to which evolution is 26 geometrically parallel, by estimating and interpreting pairwise angles between evolutionary 27 change vectors in multiple replicate lineages. Similar comparisons, of distance in trait space, are 28 used to assess the degree of convergence. These approaches amount to element-by-element 29 interpretation of distance matrices, and can fail to capture the true extent of multivariate 30 parallelism when evolution involves multiple traits sampled across multiple lineages. We 31 suggest an alternative set of approaches, co-opted from evolutionary quantitative genetics, 32 involving eigen analysis and comparison of among-lineage covariance matrices. Such 33 approaches not only allow the full extent of multivariate parallelism to be revealed and 34 interpreted, but also allow for the definition of biologically tenable null hypotheses against which 35 empirical patterns can be tested. Reanalysis of a dataset of multivariate evolution across a 36 replicated lake/stream gradient in threespine stickleback reveals that most of the variation in the 37 direction of evolutionary change can be captured in just a few dimensions, indicating a greater 38 extent of parallelism than previously appreciated. We suggest that applying such multivariate 39 approaches may often be necessary to fully understand the extent and form of parallel and 40 convergent evolution. 41 42 43 44 45 46 2 bioRxiv preprint doi: https://doi.org/10.1101/2020.01.26.920439; this version posted January 27, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 47 Introduction 48 How repeatable is the evolutionary process? Highpoints in the history of life include taxa that 49 have appeared to independently evolve similar adaptations in response to similar environmental 50 conditions. Such examples represent some of the most striking evidence for adaptive evolution, 51 suggesting not only that evolution can sometimes repeat itself, but that we can also identify the 52 broad environmental factors governing natural selection (Nosil et al. 2002, Langerhans and 53 DeWitt 2004, Losos 2011, Bolnick et al. 2018, Stuart 2019). Thus, this classical question cuts to 54 the core of ongoing debates over the role of chance and determinism in evolution at all 55 timescales. 56 The question of repeatability in evolution has been reframed in light of contemporary 57 approaches to studying evolution and natural selection in the wild. This new work has 58 distinguished the outcome of evolution, convergent (divergent), from the path of evolutionary 59 change, parallel (nonparallel) (Bolnick et al. 2018). Purpose-built statistical tests have been 60 invented to test hypotheses of parallelism and convergence at both the micro (Collyer and Adams 61 2007, Adams and Collyer 2009, Collyer et al. 2015) and macro scale (Mahler et al. 2013). This 62 work has led to some important advances in our empirical understanding of how repeatable 63 evolution can be (Oke et al. 2017, Stuart et al. 2017), yet has also highlighted some fundamental 64 challenges (Bolnick et al. 2018) of linking pattern and process in empirical tests of the 65 repeatability of evolution. 66 Here we emphasize an explicitly-multivariate set of approaches to the study of parallel 67 and convergent evolution. These multivariate approaches surmount three key difficulties: 1) 68 univariate analyses, often employed in studies of parallel and convergent evolution, can be 69 difficult to interpret when the data are multivariate, and can lead to 2) underestimation of the 3 bioRxiv preprint doi: https://doi.org/10.1101/2020.01.26.920439; this version posted January 27, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 70 importance of shared dimensions of evolutionary change, which have been difficult to identify 71 due to the challenge of 3) construction of a statistical null expectation that is also biologically 72 appropriate, against which empirical patterns can be pitted. We show how these challenges can 73 be resolved with some basics of linear algebra that permit analysis of entire matrices of similarity 74 of evolutionary change. We illustrate our points by revisiting a published dataset of parallel 75 evolution in a fish species, where a truly-multivariate approach reveals a far greater extent of 76 parallelism than can be concluded from univariate analysis. Our arguments largely ‘parallel’ 77 similar issues raised in a closely aligned subfield, evolutionary quantitative genetics, where it has 78 long been recognized (Lande and Arnold 1983, Phillips and Arnold 1989, Blows and Brooks 79 2003, Blows 2007a, b, Kirkpatrick 2009, Wyman et al. 2013) that understanding selection on and 80 expression of complex traits requires approaches that are explicitly multivariate. 81 Below, we first define parallelism and convergence as separate but related patterns. Next, 82 we outline a set of multivariate geometric techniques to explore the degree and form of 83 parallelism, applying these techniques to a reanalysis of a published dataset of parallelism in a 84 fish species. We then review approaches to assessing multivariate convergent/divergent 85 evolution, independent of parallelism, and highlight a specific published case study leveraging 86 such an approach. We discuss advantages and limitations of these multivariate techniques. 87 88 Defining parallelism and convergence as unique phenomenon 89 Parallel (nonparallel) and convergent (divergent) evolution can be seen as separated but related 90 patterns (Figure 1; see also Bolnick et al. 2018). This separation is potentially important because 91 it is the case that unique evolutionary processes could lead to patterns of evolutionary parallelism 92 without convergence, or vice-versa. But, parallelism and convergence also need not be viewed 4 bioRxiv preprint doi: https://doi.org/10.1101/2020.01.26.920439; this version posted January 27, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 93 as mutually exclusive phenomena. For example, conserved directional selection across lineages 94 could result in parallelism without convergence (Figure 1A). Alternatively, adaptation towards a 95 shared optimum by lineages with unique evolutionary histories, and thus unique ancestral 96 positions in trait space, could result in convergence without parallelism (Figure 1B). Yet, 97 parallel evolutionary processes can lead to divergence if, for example, one lineage evolves faster 98 along a shared trajectory. Thus, separating parallelism and convergence may often be necessary 99 to link evolutionary pattern and process. 100 101 Geometry of parallel evolution 102 An intuitive way to define parallelism is via analysis of evolutionary change vectors (Collyer and 103 Adams 2007, Adams and Collyer 2009), where the vector of multivariate evolutionary change 104 across an environmental gradient or time points a and b (e.g. and ancestral versus descendant 105 population), for a given lineage is ∆̺Ɣ̺Ŭ ̺Ŭ (1) 106 (Lande 1979) perhaps with traits standardized to make units comparable across traits. Note that, 107 beyond morphology, such a vector can be defined using breeding values, sequence variation 108 (Stuart et al. 2017), or gene expression profiles, and that environments can be defined using 109 external abiotic factors or any other feature of interest that defines subpopulations (e.g., sex; De 110 Lisle and Rowe 2017). ∆ is a vector of evolutionary change, or evolutionary response to 111 selection, and a growing number of studies have employed an approach (Collyer and Adams 112 2007, Oke et al. 2017, Stuart et al. 2017) where the angle between ∆ vectors is estimated for 113 each pairwise combination of lineages studied, as ͯͥ Έ Ɣ ͗ͣͧ ∆ͥ∆ͦ (2) 5 bioRxiv preprint doi: https://doi.org/10.1101/2020.01.26.920439; this version posted January 27, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 114 where each vector has been normalized to unit length. Statistical significance of the angle is 115 often assessed via permutation of the data, comparing the observed value to a null of perfect 116 parallelism across each pairwise combination of lineage replicates (Collyer and Adams 2007, 117 Adams and Collyer 2009).