Models of Continuous Trait Evolution

Transcription

1 Models of Continuous Trait Evolution By Ricardo Betancur (slides courtesy of Graham Slater, J. Arbour, L. Harmon & M. Alfaro)

2 How fast do animals evolve? C. Darwin G. Simpson J. Haldane

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6 How do we model continuous traits using PCMs?

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18 rate of character evolution

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41 In which case can we expect this value to be 0?

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43 Other Models for Phenotypic Evolution Brownian Motion (BM) Early Burst (EB/AC) or Late Burst (LB/DC) Ornstein-Uhlenbeck (OU) BM with a trend (Trend)

44 Why these? BM is assumed by almost all phylogenetic comparative methods EB (or AC) - greatest phenotypic divergence early; corresponds to the idea Simpsonian s adaptive radiation. LB (or DC) - greatest phenotypic divergence late OU may capture the importance of constraints on evolution BM with trend e.g., Cope s rule

45 Brownian motion (null) Single peak OU Early burst Body size Body size Body size Amount of variation in the whole clade Amount of variation within subclades Harmon et al. (2010) - Evolution

46 Other Models for Phenotypic Evolution Brownian Motion (BM) Early Burst (EB/AC) or Late Burst (LB/DC) Ornstein-Uhlenbeck (OU) BM with a trend (Trend)

47 Early Burst Model (EB or AC) Rate of evolution slows through time Highest rate at the root of the tree Three parameters: starting value (Θ), starting rate (σ 2 ), and rate change (r) i sij j

48 Early Burst Model (EB or AC) Rate of evolution slows through time Highest rate at the root of the tree Three parameters: starting value (Θ), starting rate (σ 2 ), and rate change (r) i sij j

49 Why EB? Allows rates across the tree to decline rapidly through time Consistent with Simpsonian ideas about adaptive radiation Clades entering new adaptive zone should diversity quickly Rates should slow as niches fill

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51 Early Burst Model (EB or AC) Body size Amount of variation in the whole clade Amount of variation within subclades Harmon et al. (2010) - Evolution

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53 How to fit competing models?

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60 EB OU

61 Example: Anolis lizards Lizards on Caribbean islands Phylogenetic and body size data for 73 species (out of ~140 total)

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63 Model Parameter estimates lnl Akaike weight BM EB OU

64 Model Parameter estimates lnl Akaike weight BM σ 2 = EB σ 2 = r = OU σ 2 = α =

65 Cichlids in Lake Tanganyika

66 Cichlids in Lake Tanganyika Model Parameter estimates lnl Akaike weight BM σ 2 = EB σ 2 = 0.02 r = OU σ 2 =... α =

67 Harmon et al. (2010) - Evolution

68 Late Burst Model (LB or DC) Rate of evolution increases through time Highest rate at the tips of the tree Three parameters: starting value (Θ), starting rate (σ 2 ), and rate change (r) i sij j

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70 Other Models for Phenotypic Evolution Brownian Motion (BM) Early Burst (EB/AC) or Late Burst (LB/DC) Ornstein-Uhlenbeck (OU) BM with a trend (Trend)

71 species evolving towards adaptive peaks that may impose limits on trait diversification

72 Ornstein-Uhlenbeck Model (OU) Evolution has a tendency to move towards some medial value Brownian motion with a spring Three parameters: starting value (Θ), rate (σ 2 ), and constraint parameter (α or rubber band) i sij j T = total tree depth

73 OU with single stationary peak Body size Amount of variation in the whole clade Amount of variation within subclades Harmon et al. (2010) - Evolution

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76 lineages evolving towards four different adaptive peaks (= adaptive optima)

77 What happens with intermediate forms? (denoted with arrow)

78 Intermediate forms lack adaptive fitness and are removed by natural selection

79 Intermediate forms lack adaptive fitness and are removed by natural selection

80 Why OU? places bounds on BM motion sometimes used to model different evolutionary optima Luke Mahler et al. (2014) - Science

81 Ornstein-Uhlenbeck (OU) dx(t) = α[θ - X(t)]dt + σdb(t)

82 Ornstein-Uhlenbeck (OU) dx(t) = α[θ - X(t)]dt + σdb(t) brownian motion

83 Ornstein-Uhlenbeck (OU) dx(t) = α[θ - X(t)]dt + σdb(t) change towards optimum brownian motion

84 Ornstein-Uhlenbeck (OU) dx(t) = α[θ - X(t)]dt + σdb(t) optimal value

85 Ornstein-Uhlenbeck (OU) dx(t) = α[θ - X(t)]dt + σdb(t) pull towards optimum

86 Ornstein-Uhlenbeck (OU) dx(t) = α[θ - X(t)]dt + σdb(t) strength of selection is proportional to distance of trait from optimal value

87 Ornstein-Uhlenbeck (OU) dx(t) = 0[Θ - X(t)]dt + σdb(t) when alpha is 0, OU becomes BM

88 Ornstein-Uhlenbeck (OU) dx(t) = α[θ - X(t)]dt + σdb(t)

89 OU evolution

90 The higher the optimal value Θ the greater the trait value

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94 Other Models for Phenotypic Evolution Brownian Motion (BM) Early Burst (EB/AC) or Late Burst (LB/DC) Ornstein-Uhlenbeck (OU) BM with a trend (Trend)

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98 Testing the Williston s Law in Fishes Williston s Law: reduction in the number of serial parts in skull bones Branchiostegal series data for 66 fossil and 440 extant species

99 Testing the Williston s Law in Fishes 240 fossils extant Pruned to 66 fossil extant

100 Testing the Williston s Law in Fishes

101 Disparity through time (DTT)

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103 Total disparity 1 Subclade disparity Brownian Motion Expectation Time 1 All taxa are in 1 subclade Subclade disparity All subclades have 1 species Time Slide courtesy of J. Arbour

104 1 Subclade disparity Subclade disparity Time 1 Time Slide courtesy of J. Arbour

105 1 Subclade disparity Morphological disparity index (MDI): Area between observed and average simulated curves Positive MDI: most disparity originated in recent divergence events Time 1 Subclade disparity Negative MDI: disparity originated in an early burst Time Slide courtesy of J. Arbour

106 Total disparity (ppc2) Disparity through time (DTT) in carangimorph fishes Betancur-R. et al. (2013) - Sys. Bio. Relative time

107 Model fitting also favors EB Betancur-R. et al. (2013) - Sys. Bio.

108 Phylogenetic Signal

109 Phylogenetic signal A "tendency for related species to resemble each other more than they resemble species drawn at random from the [phylogenetic] tree Blomberg & Garland (2002) J. Evo. Bio.

110 Phylogenetic signal 1. We expect phylogenetic signal under a wide range of evolutionary models. Brownian motion OU with small alpha Early burst

111 Phylogenetic signal 2. Phylogenetic signal is a pattern, not a process Phylogenetic signal simply describes a tendency (pattern) for evolutionarily related organisms to resemble each other, with no implication as to the mechanism that might cause such resemblance (process)

112 Phylogenetic Signal 3. Phylogenetic signal is NOT a constraint In fact, unconstrained models (like BM) create lots of phylogenetic signal, while constrained models (like OU) can result in very little phylogenetic signal

113 Measuring phylogenetic signal Blomberg s K statistic (comparison to BM) Pagel s lambda (branch length transformation)

114 Blomberg s K statistic (comparison to BM) K (a variance ratio) is rescaled by dividing by the Brownian motion expectation. A K < 1: relatives resemble each other less than expected under BM along the tree. A K > 1: close relatives are more similar than expected under BM.

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117 Other Pagel models

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