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Exploring the relationship between trait evolution and the generation of species diversity Magnuson-Ford, Karen 2011

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Exploring the Relationship Between Trait Evolution and the Generation of Species Diversity by Karen Magnuson-Ford B.Sc., Simon Fraser University, 2008 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in THE FACULTY OF GRADUATE STUDIES (Zoology) The University Of British Columbia (Vancouver) December 2011 c© Karen Magnuson-Ford, 2011 Abstract Macroevolutionary questions, such as “why do some lineages diversify faster than oth- ers?”, are often studied by investigating key traits related to species ecology and life- history. Many traits have been hypothesized to affect rates of diversification and often it is these traits that are used to address another macroevolutionary question: “do traits evolve gradually over time or in punctuated bursts during speciation?” Using phyloge- netic data and species present-day trait information, I present a novel approach to assess the mode of character change while accounting for state-dependent speciation and ex- tinction. The model, Binary-State Speciation and Extinction - node enhanced state shift (BiSSE-ness), estimates both the rate of change occurring along lineages and the probabil- ity of change occurring during speciation, while simultaneously estimating the speciation and extinction rates for each character state. Using simulations, I found BiSSE-ness is able to distinguish along-lineage and speciational change and precisely estimate the parame- ters associated with character change and diversification rates. I applied BiSSE-ness to an empirical primate data set examining five traits related to ecology, behaviour, and repro- duction. I provide evidence that changes in primate habitat type may be associated with speciation, whereas changes in social behaviour and mating system occur mainly along lineages. The BiSSE-ness model is flexible in that it may be used to address questions regarding species diversification, regardless of whether the trait changes in a manner that is proportional to time or to the number of speciation events. However, in cases where the trait is linked to the speciation process itself, such as niche-related traits, BiSSE-ness provides a suitable framework in which to simultaneously address questions regarding species diversification and character change. ii Preface The research described in Chapter 2 forms a manuscript that has been submitted for pub- lication to the journal American Naturalist. I played a lead role in developing the project design and model derivation with my supervisor, Dr. Sally Otto. I implemented the model, carried out all simulations and empirical data analyses, and completed the writ- ing of this chapter. Dr. Otto assisted with interpreting our results and provided helpful feedback on this chapter. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Evolution of Species and Their Traits . . . . . . . . . . . . . . . . . . . . 1 1.2 Current Phylogenetic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Thesis Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Linking the Investigations of Character Evolution and Species Diversification 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 BiSSE-ness Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Primate Diversification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5.1 Distinguishing Between Modes of Character Change . . . . . . . . . 25 iv 2.5.2 Using BiSSE-ness to Describe Character Change in Primates . . . . . 26 2.5.3 Investigating Trait-Dependent Diversification Using BiSSE-ness . . . 28 2.5.4 Applications of BiSSE-ness . . . . . . . . . . . . . . . . . . . . . . . . 30 3 General Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Appendix A: BiSSE and BiSSE-ness Models . . . . . . . . . . . . . . . . . . . . . . 43 Appendix B: BiSSE-ness Phylogenetic Tree Simulator . . . . . . . . . . . . . . . . 45 v List of Tables Table 2.1 Parameter sets for simulated trees . . . . . . . . . . . . . . . . . . . . . . . 11 Table 2.2 ML parameter estimates for the primate data set . . . . . . . . . . . . . . 23 vi List of Figures Figure 2.1 The amount and type of character change in simulated trees . . . . . . . 13 Figure 2.2 Parameter estimates associated with speciational character change . . . 14 Figure 2.3 Comparing ML parameter estimates between BiSSE-ness and BiSSE . . 15 Figure 2.4 Primate phylogeny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Figure 2.5 Akaike weights of the BiSSE and BiSSE-ness models . . . . . . . . . . . . 19 Figure 2.6 Differences in log likelihoods for the BiSSE and BiSSE-ness models . . . 21 Figure 2.7 Posterior distribution of the parameter estimates under BiSSE-ness . . . 24 vii Acknowledgments First and foremost I would like to thank my supervisor, Sally Otto, for her insightful com- ments and advice throughout my work at UBC over the past two years. From helping me to interpret my results and think about questions in new ways, to assisting me in making many R plots for the same old data points, thanks for your support and patience. Thank you to my committee members, Arne Mooers, and Rick Taylor, for your guidance in my establishment of this thesis topic as well as your thoughtful comments on the manuscript. A colossal thank you is in order to Rich Fitzjohn: thanks for all your help in guiding me through the Diversitree code, answering my long list of questions surrounding various statistical and modelling exercises, and among other things, the clever name for the model presented here, BiSSE-ness. I’m very proud to be a part of such a great lab group: thank you to Rich, Aleeza Gerstein, Kay Hodgins, Jill Jankowski, Liz Kleynhans, Nathan Kraft, Itay Mayrose, Leithen M’Gonigle, Jasmine Ono, Kate Ostevik, Alirio Rosales, Michael Scott, Thor Veen, and Shing Zhan, for all your helpful comments and questions at lab meetings and for your support throughout the whole thesis process. I’m very appreciative for the stimulating environment provided by the Zoology De- partment at UBC and those in the Beaty Biodiversity Research Centre. Thank you to Kai Chan and Lebby Balakshin for facilitating two internships for me through the BRITE pro- gram; these opportunities have greatly enriched my graduate school experience. Thanks, also, to Rich and Seth Rudman for being great officemates. I received many useful com- ments on the manuscript in its various stages: thanks to the UBC Delta-Tea group, Travis Ingram, and Emma Goldberg at the University of Illinois at Chicago for your input. A huge thank you to my friends and family, for your encouragement and support over the past two years. In particular, thanks a million to Patrick Gordon, for your constant motivation and reassurance, as well as your willingness to learn more about phylogenies than you ever wanted to know. viii Chapter 1 General Introduction 1.1 The Evolution of Species and Their Traits Much of the field of evolutionary biology centres around explaining the tremendous di- versity of living organisms. Exploring why this diversity is not uniformly spread across all groups of organisms is a key aspect in macroevolutionary studies. As speciation and extinction are processes involved in generating species diversity, examining how the rates of these processes change over time and across groups can inform us about the biological processes underpinning diversification. Many species’ traits are hypothesized to influence the rates of speciation and extinc- tion (see reviews in Coyne and Orr 2004; Jablonski 2008; Purvis 2008). These traits vary widely, relating to ecology (e.g. ecological specialization, pollination mode), reproduc- tion (e.g. mating system, sexual selection), and species-level attributes (e.g. range size; see references in Jablonski 2008). While these traits influence the rate of diversification through a variety of mechanisms, the traits themselves may also evolve and co-evolve with other traits, resulting in a complex evolutionary process, of which only the final out- come (present-day species and trait diversity) is observable in most cases. Trait evolution has received much attention from evolutionary biologists and paleon- tologists seeking to understand broad patterns of phenotypic diversity and how it inter- acts with the process of speciation. In the case of ecological speciation (Schluter 2001), evo- lution of ecological traits may initiate the speciation process directly (e.g., β-niche traits in rockfish, genus Sebastes; Ingram 2011). Alternatively, the rate of trait evolution may rapidly increase during or immediately following speciation in response to other changes 1 that occurred during speciation, regardless of the mode of speciation (Barraclough and Nee 2001). For example, if speciation results in each daughter lineage occupying different environments, local adaptation to these environments could promote relatively rapid trait evolution. Finally, traits may also evolve relatively independently of speciation, impacted more strongly by other processes such as the amount of time available for change or the rate of environmental or genetic change (Mooers et al. 1999). Analyzing character evo- lution has often focussed on distinguishing between character change that is associated with speciation (cladogenetic change) and character change that occurs along a lineage (anagenetic change). These studies have been fuelled by the influential discussions re- garding fossil support for the theory of punctuated equilibrium, whereby rapid change appears to be associated with speciation followed by periods of relative stasis in a trait (Eldredge and Gould 1972), in contrast to models of gradual evolution whereby changes accumulate gradually over time through natural selection (Mayr 1982). 1.2 Current Phylogenetic Methods Analyses studying the rates of diversification and how these rates are influenced by species’ traits have often been carried out independently of studies investigating character evolu- tion. While both paleontological and neontological data have been used to investigate these processes, I will briefly outline the methods that make use of the latter: that is, us- ing phylogenetic information and present-day species’ trait information. Underlying many of these methods is the notion that we may simply compare two clades of differing richness and identify a trait that correlates with the pattern of diver- sification. These methods include sister-clade analysis (Vamosi and Vamosi 2005; Par- adis 2011) and analyses that make use of independent clades (Bokma 2003). While sister clade analyses have been widely used, one key disadvantage is the fact that only the rel- ative balance between speciation and extinction is calculated, not the absolute rates of each (Ricklefs 2007). In general, calculating extinction rates from phylogenetic trees has proved challenging and are often assumed to be negligible (Purvis 2008; Rabosky 2010). Other assumptions such as rate homogeneity and random taxon sampling further limit these methods (Ricklefs 2007). Maddison (2006) demonstrated that the assumption that the shape of the tree is in- dependent of the trait of interest can generate misleading results. For example, if we examine a phylogeny and a single binary trait, where one state is rare, one might infer 2 that the rare state is associated with a lower diversification rate even though it may be that the rate of change from the rare state to the common state is simply higher than the reverse (Maddison 2006). One method that alleviates this confounding effect is the binary- state speciation and extinction model (BiSSE; Maddison et al. 2007), which simultaneously accounts for asymmetrical diversification rates and asymmetrical character state change. The BiSSE model is a likelihood-based approach and thus asks what is the most likely set of parameters given the shape of the phylogeny and the observed distribution of charac- ter states. While BiSSE designates two parameters to encompass trait evolution (the rate of change from state 0 to 1 and vice versa), it does not explicitly address the mode of trait evolution. Several models that make use of phylogenetic information and present day trait infor- mation have been developed to address the mode by which characters evolve over time (Simpson 1944; Bokma 2010; Monroe and Bokma 2010). For example, in the extreme case where the evolution of a trait occurs at a rate strictly proportional to time (anagenetic), we may expect that a species at the tip of a long branch on a time-scaled phylogeny would exhibit a high amount of trait divergence compared to species on shorter branches within the phylogeny (Monroe and Bokma 2010; Mooers et al. 1999). This concept is the basis for a number of methods that examine the evolution and co-evolution of discrete and contin- uous traits (Pagel 1994; Mooers et al. 1999; Bokma 2002). While these models have become increasingly more sophisticated, evaluating trait evolution using models of Brownian mo- tion, incorporating both speciation and extinction rates, and allowing for anagenetic and punctuated change simultaneously (Bokma 2002, 2008), these approaches assume that the shape of the phylogeny itself is independent from the trait under investigation. 1.3 Thesis Goals While there has been much progress in developing phylogenetic methods to investigate a variety of questions pertaining to trait-dependent species diversification and charac- ter evolution, these methods have remained separate analyses. As it is clear that the processes of trait-dependent diversification and trait evolution are inextricably linked in many cases, accounting for these processes simultaneously may allow us to separate out potentially confounding effects. Combining the investigations of these two topics into one evolutionary model is the main goal of my thesis. As the BiSSE model accounts for trait-dependent speciation and extinction while al- 3 lowing for trait change within a lineage (anagenetic change), it provides a suitable frame- work to incorporate parameters to account for trait change at speciation (cladogenetic change). In the following chapter I outline the mathematical formulation of a new model, BiSSE-ness (node enhanced state shift), which extends the original BiSSE model by ex- plicitly modelling changes in traits associated with speciation. Modelling simultaneous speciation and character change was mentioned as a useful extension by Maddison et al. (2007), but it has never been formally developed, and its performance has yet to be ex- plored. I present analyses using simulations in order to demonstrate some of the statis- tical properties of this model, such as statistical power and the precision with which the model parameters may be estimated. Finally, I also analyze an empirical data set of 233 primate species, including five traits related to their ecology, reproduction and behaviour. Using BiSSE and BiSSE-ness I investigate the mode of evolution in these five traits as well as trait-dependent diversification in primates. 4 Chapter 2 Linking the Investigations of Character Evolution and Species Diversification 2.1 Introduction The mode of character evolution, whether traits change gradually along a lineage or rapidly at speciation, is a topic that has received considerable attention from both evolu- tionary biologists and palaeontologists (see review in, Monroe and Bokma 2010). Darwin proposed that evolutionary change accumulates gradually via natural selection, resulting in the phenotypic differences we observe among species (Mayr 1982). However, since the publication of Eldredge and Gould’s theory of punctuated equilibria (1972), there has been increasing support for the concept that species’ phenotypes remain relatively static over time, interspersed with periods of rapid change coinciding with speciation. In cases of ecological speciation (Schluter 2001; Rundle and Nosil 2005), trait evolution may even drive the speciation process. For example, as niche-related traits evolve (e.g., ecological adaptation), this may result in niche divergence between two populations, thereby facili- tating speciation. Many studies have made use of the fossil record to demonstrate the tempo and mode of character change (Eldredge and Gould 1972; Cheetham 1986; Gould and Eldredge 1993; Benton and Pearson 2001), but the development of tools that use phylogenetic and species’ 5 present-day trait information have also furthered the investigation of this topic (Monroe and Bokma 2010). To illustrate how phylogenies contain information regarding the mode of character change, Avise and Ayala (1975) reasoned that if change occurs gradually, in proportion to the age of a lineage, then we may expect a correlation between genetic differentiation (or more generally, character differentiation) and the age of a lineage (i.e., branch length on a time-calibrated phylogeny). In this case, recently-diverged species would appear relatively similar (Bokma 2002). This type of change occurring along a lineage, also termed anagenetic change, has been detected using phylogenetic methods in a variety of cases, including unison calls in cranes (family Gruidae; Mooers et al. 1999) and body size and shape in salamanders (genus Plethodon; Kozak et al. 2006; Adams et al. 2009). In contrast, if character change tends to occur in punctuated bursts associated with speciation then we may expect a correlation between character differentiation and the number of speciation events, and thus, recently-diverged species may exhibit substantial differentiation (Avise and Ayala 1975; Mooers et al. 1999; Bokma 2002). Evidence for this type of ‘speciational’ or cladogenetic change was found in the evolution of body size in mammals (Mattila and Bokma 2008; Monroe and Bokma 2009) and birds (Bokma 2004), as well as pollen spur length in columbine flowers (genus Aquilegia; Whittall and Hodges 2007), and traits associated with the β-niche in rockfish (genus Sebastes; Ingram 2011). Initial phylogenetic methods posed several limitations such as the assumption that ex- tinction has not occurred and that the model of character change is either entirely gradual or speciational (Mooers et al. 1999; Paradis 2005). More recent methods allow for the esti- mation of both the speciation and extinction rates from the phylogeny as well as the rela- tive rates of anagenetic and cladogenetic change for continuous characters (Bokma 2008). When this method was used to investigate body size evolution in mammals, Mattila and Bokma (2008) found that a large portion of changes in body size were associated with spe- ciation. Because large mammals have greater speciation and extinction rates (Liow et al. 2008; a trend not accounted for by Mattila and Bokma 2008), further analyses showed an overall trend that old lineages of large-bodied mammal species tended to exhibit higher rates of body size evolution than their smaller-bodied counterparts (Monroe and Bokma 2009). However, relatively young mammal lineages did not exhibit differential rates of body size evolution (Monroe and Bokma 2009). This example provides an interesting yet complex case where the process of speciation may accelerate evolution of the trait of interest (or changes in the trait trigger speciation) while at the same time, the trait also 6 affects the overall rates of speciation and extinction. While the methods developed in Bokma (2008) may be used effectively to examine many aspects of continuous character evolution where diversification rates are trait-independent, we explore in this paper an alternative set of methods that may be used with binary traits that may be expected to influence the rates of speciation and/or extinction. Phylogenies have also been used extensively to address the relationship between species’ traits and rates of diversification (Barraclough et al. 1998; Paradis 2005; Jablonski 2008; Purvis 2008). Maddison (2006) pointed out the challenge of separating out the effects a trait has on speciation and extinction rates from differences in the rates of character change. For example, sister-clade analyses, which compare the size of two clades that are, by definition, of the same age and also differ in a trait of interest, have been used to draw an association between a particular state and a clade experiencing rapid or depressed diversification. However, it is possible that it is simply the rates of change between differ- ent character states that are asymmetric and the diversification rate is relatively constant (Maddison 2006). Subsequently, the Binary-State Speciation and Extinction model was de- veloped (BiSSE; Maddison et al. 2007), which estimates the speciation and extinction rates separately for each state of a binary character as well as the rate of change between states. This model has since been extended to accommodate incomplete phylogenetic and char- acter state information (Fitzjohn et al. 2009), continuous traits (QuaSSE; FitzJohn 2010), and spatial components of trait evolution (GeoSSE, Goldberg et al. 2011). As originally formulated, BiSSE accounts only for character change occurring along lineages. Here, we modify the BiSSE model to allow for cladogenetic change in addition to anagenetic change, thus enabling us to address the mode of character change while simultaneously accounting for the effect the character may have on rates of speciation and extinction. We outline the formulation of this new model, BiSSE-ness (node enhanced state shift), below. We then use simulation analyses to determine the ability of BiSSE-ness to dif- ferentiate between modes of character change. Finally, we apply our model to an em- pirical dataset of 233 primate species using a complete phylogeny. We use five binary traits: activity period (diurnal/nocturnal), habitat type (forest-savanna/forest), mating system (non-monogamous/monogamous), social behaviour (solitary/social), and terres- triality (arboreal/terrestrial), to investigate the degree to which changes in these traits occur along lineages or are concentrated at speciation. We also use the BiSSE-ness model to examine if any of these five traits are associated with differential speciation and/or extinction rates. 7 2.2 BiSSE-ness Model For a binary character (states 0 and 1), BiSSE computes the combined probability of both a phylogeny and the corresponding character states of each terminal taxa having evolved precisely as observed, with the ancestor of the lineage in question in either state 0 or 1 (Maddison et al. 2007; see eqn. (1) and (2) in Appendix A). Each state is associated with independent parameters for the rates of speciation (λ0,λ1), extinction (µ0,µ1) and a change in state (q01 for 0 → 1, and q10 for 1 → 0). In addition to calculating the probabilities of a lineage evolving as observed, BiSSE also calculates the probability that a lineage goes extinct before the present, given that it was in state 0 or 1 at time t before the present (eqn. (3) and (4) in Appendix A). BiSSE computes these diversification and extinction probabilities for each lineage and for each state, starting at the tips (present day) and working backwards in time. At each speciation event (i.e., node in the phylogeny), the probabilities calculated for each daughter clade are combined, yielding one probability pertaining to the larger clade. BiSSE makes the assumption that no change in state occurs simultaneously with speci- ation. Therefore, to calculate the probability (D) that at time tA, a lineage at node A is in state 0 and evolved as observed, BiSSE multiplies the rate of speciation in state 0, λ0, by the probability that both daughter lineages (N and M) are in state 0 and evolved as observed: DA0(tA) = λ0DN0(tA)DM0(tA) (2.1) (taken from eqn. (4a) in Maddison et al. 2007; similarly, eqn. (4b) describes the case for state 1, DA1(tA)). At the root, the diversification probabilities are combined to give an overall likelihood using the relative probabilities of observing the data, following Fitzjohn et al. (2009; Droot = D0 ∗ D0/[D0 + D1] + D1 ∗ D1/[D0 + D1]). To allow state change to occur simultaneously with a speciation event, we add four additional independent parameters to describe change at nodes, in addition to the six pa- rameters used in BiSSE. Two of these new parameters are the probabilities that there is a change in character state associated with the speciation process and thus one or both of the daughter lineages are in the state opposite to that of the parental lineage. These parameters, p0c and p1c, correspond to the cases when the parental lineage is in state 0 and 1, respectively, where c represents a change in character state. The remaining two parameters, p0a and p1a, refer to the probability that, given a change in character state 8 has occurred during speciation and the ancestral lineage is in state 0 and 1, respectively, this change is asymmetrical. That is, one daughter lineage retains the same state as the ancestral lineage and the other lineage changes to the opposite state. Alternatively, the probability that both daughter lineages change state is given by 1-p0a, when the ancestor was in state 0 and a change associated with speciation did occur. When both pc param- eters are 0, the pa parameters become irrelevant, and the 10-parameter BiSSE-ness model reduces to the 6-parameter BiSSE model. Accounting for all possible changes during the speciation process, we revised eqn. (2.1), the equation for node calculations, as follows: given the ancestor A is alive at time tA and in character state 0, we combine the probabili- ties of accounting for the phylogeny and extant character states for both daughter lineages (N and M): DA0(tA) = λ0DN0(tA)DM0(tA)(1− p0c) no change at speciation (2.2a) + 1 2 λ0 [DN1(tA)DM0(tA) + DN0(tA)DM1(tA)] p0cp0a one lineage changes (2.2b) + λ0DN1(tA)DM1(tA)p0c(1− p0a) both lineages change (2.2c) Interchanging the 1’s and 0’s, we obtain a corresponding equation, DA1(tA), for the prob- ability that the lineage was in state 1 just prior to node A. Even along branches of the tree where no nodes appear, speciation events may have occurred if one daughter lin- eage went extinct before the present, so we also updated the differential equations de- scribing diversification and extinction (eqn. (1) - (4) in Appendix A). BiSSE-ness may be used in a Likelihood or Bayesian framework. We focus on analyses using maximum likelihood (ML) but also present the results of the primate analyses as Bayesian posterior probabilities. BiSSE-ness and all subsequent analyses were written in and executed in R (R Development Core Team 2010), using the package Diversitree (v.0.6-1, available from http://www.zoology.ubc.ca/prog/diversitree/; see also Fitzjohn et al. 2009). BiSSE-ness will be incorporated into future versions of Diversitree. Recently, another method, ClaSSE (Goldberg and Igić 2011), has been independently developed to accommodate both anagenetic and cladogenetic trait changes while mod- elling trait-dependent diversification. This method is also based on BiSSE methodolo- 9 gies and is used to explore the evolution of self-incompatibility in the nightshade family (Solanaceae). 2.3 Simulations 2.3.1 Methods We simulated phylogenies with 500 taxa under a variety of different parameter sets using the BiSSE-ness model (Appendix B). We then used both the BiSSE and BiSSE-ness models to estimate the most likely parameter set for the simulated data. This allowed us to inves- tigate how accurately and precisely the BiSSE-ness model can recover the true parameter values as well as infer the true mode of character change. We conducted several sets of simulations in order to address two main questions. First, how often does character change need to occur with speciation in order to detect signifi- cant differences between BiSSE and BiSSE-ness? We explored this question by simulating trees under parameters that varied both in their values for the rate of anagenetic charac- ter change (q01 and q10) and the probability of cladogenetic change (p0c and p1c), setting these parameters equal between states (q01 = q10 and p0c = p1c; see Table 2.1, Set 1). It has been suggested that traits that change at a high rate may obscure any signal of change associated with speciation (Cheverud et al. 1985; Mooers et al. 1999), and therefore one advantage to our approach is that we may compare cases that had similar proportions of anagenetic and cladogenetic character change yet differed in the total number of character changes. Second, we investigated how accurately and precisely BiSSE-ness can estimate the parameters regarding speciational change. In particular, given that some amount of spe- ciational change occurs, how well can BiSSE-ness differentiate between symmetrical and asymmetrical state change at a speciation event? To address this, we simulated trees un- der various pa values combined with low, medium and high levels of speciational change (pc) and set all remaining parameters to constant values (Table 2.1, Set 2). We also ex- amine how BiSSE and BiSSE-ness compare in their ability to accurately estimate the rate parameters pertaining to speciation (λ), extinction (µ) and along-lineage character change (q). For the tree simulations, the initial character state at the root was determined using the equilibrium frequencies of state 0 and 1 as determined by the model (see eqn. (5) in Ap- 10 Table 2.1: Parameter sets under which we simulated trees using the BiSSE-ness model. Model Parameter Set 1 Set 2 speciation rate λ0 0.1 0.1 λ1 0.2 0.2 extinction rate µ0 = µ1 0.003 0.003 rate of character state change along lineages q01 = q10 0.005, 0.01, 0.05, 0.1 0.01 probability of character change at speciation p0c = p1c 0, 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1 0.005, 0.05, 0.5 probability of asymmetrical character change p0a = p1a 0.5 0.1, 0.3, 0.5, 0.7, 0.9 NOTE – We sought to address: how detectable is variation in the amount of speciational and along-lineage change (Set 1), and how sensitive is BiSSE-ness to asymmetrical vs. symmetrical change at speciation (Set 2). For each set, all combinations of parameters were simulated and replicated 10 times. pendix A). For each parameter set, 10 trees were simulated, each with 500 species. Each simulation proceeded until 501 species were generated and then pruned such that all ter- minal branch lengths were non-zero. In total, 55 unique parameter sets were used and 550 trees were simulated (Table 2.1, Set 1: 40 sets; Set 2: 15 sets). Although our parameter sets included trait-dependent diversification (λ1 > λ0), BiSSE-ness may also be used in cases where diversification is independent of the trait in question. In this case, BiSSE-ness may be considered the discrete analog to the methods developed by Bokma (2008) for contin- uous traits. Additionally, BiSSE-ness is fully compatible with BiSSE methods that account for incomplete taxon sampling, incomplete trait information, and unresolved clades (see Fitzjohn et al. 2009), although we do not test these issues here. The tree depths (distance from root to tip) of the simulated trees were approximately log-normal distributed, and averaged 36.44 ±7.64 (std. dev.) units of time. We conducted likelihood searches in a stepwise fashion to aid in reaching the max- imum likelihood point. The starting parameter values for the likelihood searches using BiSSE were determined from a heuristic search that makes use of the state-independent 11 birth-death model (starting.point.bisse function in the Diversitree R package). We then used the ML estimates of BiSSE and all p parameters set to zero as starting parameters for the BiSSE-ness likelihood search. In order to compensate for a potential bias in the BiSSE-ness estimates towards BiSSE parameter estimates due to these starting conditions, we also conducted a BiSSE-ness likelihood search where the starting values for the rates of character change along lineages (q01 and q10) were set to 0. The starting values for probabilities of cladogenetic change (p0c and p1c) were set to the values for q01 and q10 determined by starting.point.bisse and p0a and p1a were set to 0.5. Because the q param- eters are rate estimates based on the tree root to tip distance and the pc parameters are probabilities, the starting values for p0c and p1c are somewhat arbitrary, however, we do not expect this to impact the overall results of our analyses. We found the BiSSE-ness ML searches were largely insensitive to the two different starting points (corresponding to the reduced models where all state change occurs along lineages or at nodes) and converged on the same ML and parameter estimates. How- ever, when the data were simulated with high proportions of speciational change, we found that higher ML estimates were sometimes found using the starting point that as- sumed speciational change. All subsequent analyses were completed using output from the BiSSE-ness search that obtained the highest ML estimate. 2.3.2 Results We found that when character change had occurred both at speciation events and along lineages (273/400 simulations in Set 1 because often when pc < 0.001, no speciational change occurred), the BiSSE-ness model is able to infer this pattern with reasonably high power under the conditions simulated. When at least 10% of the total character change occurred at speciation (n = 181), BiSSE-ness provided a significantly better fit than BiSSE for 59% of these simulated datasets (p < 0.05). As proportionately more of the char- acter change occurred at speciation rather than along lineages, BiSSE-ness obtained in- creasingly higher likelihood values than BiSSE (fig. 2.1). In the cases where BiSSE-ness and BiSSE provided indistinguishable results, the proportion of character change that oc- curred at speciation averaged 17%, and the median proportion was just 7.5% (n = 166). BiSSE-ness was able to accurately estimate the probability of speciational character change (fig. 2.2). In contrast, the pa parameters, indicating the probability that only one daughter lineage exhibited character change, were estimated with considerably less pre- 12 1 2 5 10 20 50 100 200 500 1 2 5 10 20 50 10 0 20 0 50 0 number of cladogenetic changes nu m be r o f a na ge ne tic  c ha ng es q01, q10 0.005 0.01 0.05 0.1 Figure 2.1: The amount and type of character change for each of the simulated trees (including only cases where both anagenetic and cladogenetic change oc- curred). X and y- axes give the actual number of events that occurred during the simulation, excluding extinct lineages. Cases where BiSSE-ness significantly outperforms BiSSE are indicated in black (p < 0.05, likelihood ratio test, d.f. = 4). Curves show a constant total number of character changes. cision. This is likely due to a lack of statistical power because these parameters are con- ditional on the occurrence of speciation change. As λ1 is greater than λ0 in all our simu- lations, this provides more speciation events where the parental lineage is in state 1 and therefore more opportunities for character change corresponding to p1c rather than p0c. Consequently the pa parameters were estimated more accurately for state 1 (fig. 2.2). As the relative proportion of speciational change increased, both the pc and pa parameters were estimated with more precision. Both models were able to estimate the diversification parameters with a high degree of accuracy (fig. 2.3). As the probability of speciational character change increased, both models were less precise in recovering these parameters due to saturation of character state changes, although BiSSE tended to produce more variable estimates than BiSSE-ness. 13 0.0 0.2 0.4 0.6 0.8 1.0 pcs$true.pc S ta te  0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 sdfd M L P ar am et er  E st im at e S ta te  1 True P[Speciational Change] (pc) pas$true.pa 0.0 0.2 0.4 0.6 0.8 1.0 pas$true.paTrue P[Asymmetrical Speciational Change] (pa) Figure 2.2: Parameter estimates associated with speciational character change. BiSSE-ness accurately estimated the probability of speciational character change for simulated data with varying p0c and p1cvalues (p0c = p1c; p0a = p1a = 0.5; q01 = q10 = 0.01). BiSSE-ness also estimated well the degree of asymmetri- cal character change, p0a and p1a for simulated data with varying pa values (p0a = p1a; p0c = p1c = 0.05; q01 = q10 = 0.01). Lines indicate the 1:1 ratio; that is, if all the data fell on the lines, then BiSSE-ness would have perfectly recovered the actual parameter values under which the data was simulated. As the amount of speciational change increased, BiSSE-ness tended to underestimate the rate of along-lineage character change (essentially estimating no change), whereas BiSSE tended to overestimate this rate of change by several orders of magnitude. In the case where character change always occurred at speciation (p0c = p1c = 1), the character states become essentially randomized on the tree, and the high values of anagenetic change estimated by BiSSE may be seen as a worst case scenario. Overall, the simulations indicate that BiSSE-ness can infer the mode of character change with reasonable power given large phylogenetic trees. Interestingly, our results show that when the wrong model is used (e.g., speciational change is present but not detected un- der BiSSE), estimated rates of speciation and extinction are not strongly biased, although 14 estimates of trait change are (fig. 2.3). 0. 00 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 B iS S E  P ar am et er  E st im at e S ta te  0 Speciation Rate (λ) pc 0 0.005 0.05 0.5 1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0. 00 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 S ta te  1 BiSSE-ness Parameter Estimate 0. 00 0. 05 0. 10 0. 15 0. 20 0. 25 Extinction Rate (µ) 0.00 0.05 0.10 0.15 0.20 0.25 0. 00 0. 05 0. 10 0. 15 0. 20 0. 25 1e -1 5 1e -1 0 1e -0 5 1e +0 0 1e +0 5 Rate of Anagenetic Change (q) 1e-15 1e-10 1e-05 1e+00 1e+05 1e -1 5 1e -1 0 1e -0 5 1e +0 0 1e +0 5 Figure 2.3: Comparing ML parameter estimates between BiSSE-ness and BiSSE (a subset of Set 1; q01 = q10 = 0.01). Crosshair lines indicate the true parameter values under which the data was simulated. Allowing character change at spe- ciation events (pc > 0) had relatively little effect on estimates of speciation and extinction rates. To some extent, as the amount of speciational change increased, these rates were estimated less precisely under both BiSSE-ness (λ0 SD = 0.038 and 0.052 for pc = 0 and 1, respectively) and BiSSE (λ0 SD = 0.042 and 0.063 for pc = 0 and 1, respectively; similar patterns for λ1 and µ1). Note the use of a logarithmic scale for the rates of anagenetic character change. 2.4 Primate Diversification 2.4.1 Methods Primates provide us with an excellent opportunity to study trait evolution as they consist of a large, well-studied, monophyletic group. Primates have a well established phylogeny consisting of 233 species (Vos and Mooers 2006), and for a high proportion of these species, 15 many aspects of their biology and ecology are well studied. Niche shifts may play an important role in primate speciation as Malagasy primate diversity is associated with climatic niche divergence (Kamilar et al. 2010) and, more generally, mammal diversity is thought to be associated with ecological divergence (Bininda-Emonds et al. 2007; Fabre et al. 2009). If speciation is the result of a shift into novel niche space (Funk et al. 2006), then we expect that accounting for character change at speciation events may improve the fit to the data. We test this explicitly by examining five traits related to species’ behaviour, reproduction, and ecology and comparing output from both the BiSSE and BiSSE-ness models. The five binary traits represent different axes of primate niche space, taken directly from Redding et al. (2010: Appendix S2): activity period (diurnal/nocturnal, n = 233), habitat type (forest-savanna/forest, n = 215), mating system (non-monogamous/ monog- amous, n = 146), social behaviour (solitary/social, n = 205), and terrestriality (arbore- al/terrestrial, n = 197; fig. 2.4). There is evidence that shifts in activity period (from noc- turnal to diurnal and vice versa) have occurred several times over the course of primate evolution (Ankel-Simons and Rasmussen 2008). These shifts are thought to be associated with filling empty diurnal and nocturnal niches (Ankel-Simons and Rasmussen 2008). Changes in habitat type and terrestriality are also likely to have been the result of species adapting to novel niches (Conroy 1990). Less is known regarding how changes in mating system and social behaviour are related to niche structure in primates as these features cannot be explicitly analyzed in fossils, and there may be considerable variability in both traits even within species (Dixson 1998; Kappeler and van Schaik 2002), but both may be involved in the early steps of speciation as isolating mechanisms. We used a recent primate supertree (Vos and Mooers 2006) for our analyses. Be- cause this tree contains several polytomies (representing phylogenetic uncertainty), and we required a bifurcating tree, we followed FitzJohn (2010) in using a set of 10,001 fully- resolved trees that had been generated from the supertree using methods developed by Kuhn et al. (2011; fig. 2.4). In order to account for phylogenetic uncertainty, 20 phyloge- nies were randomly selected from the set of primate phylogenies for use in the maximum likelihood searches (note this set only reflects alternative resolutions of polytomies that exist in the primate supertree, not the full posterior distribution). In our experience with this data set, the level of uncertainty in parameter estimation is much greater than the variation observed among phylogenies, as indicated by the posterior distribution of pa- rameter estimates generated using Bayesian Markov chain Monte Carlo (MCMC) searches 16 ac tiv ity  pe rio d ha bit at typ e ma tin g s ys tem so cia l b eh av iou r ter res tria lity Trait activity period: habitat type: mating system: social behaviour: terrestriality: diurnal forest-savanna non-monogamous solitary arboreal nocturnal forest monogamous social terrestrial Strepsirhini Tarsiidae Platyrrhini Hominoidea Cercopithecoidea Figure 2.4: One of the twenty primate phylogenies used in our analyses that were randomly selected from the set of 10,001 resolved trees (n = 233). The five char- acter traits used in this study are also shown. (see below). Consequently, all results presented are mean values across the 20 trees and we present average p-values over trees, indicated as p (individual tree analyses available upon request). In addition, we found similar significance levels and parameter estimates using MCMC and ML searches, and we focus on the ML results for brevity. To investigate the importance of the mode of character change, we compared two ex- treme cases: character change occurs only along lineages (BiSSE), or only at speciation (BiSSE-ness with q parameters set equal to zero). As these are no longer nested models, we compared these models using Akaike Information Criterion (AIC) scores and Akaike weights (Burnham and Anderson 1998) rather than likelihood ratio tests. We found that 17 the degree of asymmetrical vs. symmetrical speciational change did not have a large im- pact on the overall ML estimate as there were negligible differences between the full, 10-parameter BiSSE-ness model and the 8-parameter BiSSE-ness model where specia- tional change is equally likely to occur symmetrically or asymmetrically (p0a = p1a = 0.5; p > 0.05 for all traits, d.f. = 2, likelihood ratio test). Consequently we explored a re- duced BiSSE-ness model (also with six parameters) where character change occurs only at speciation events and could equally affect one or both daughter lineages (p0a = p1a = 0.5, with q01 = q10 = 0). We expect that the 6-parameter BiSSE and BiSSE-ness models should be comparable representations of contrasting modes of character change. Over- all, we analyzed two models where character change can occur either along lineages or at speciation, and two models where character change can occur both along lineages and at speciation (the 10-parameter BiSSE-ness model and the 8-parameter BiSSE-ness model where p0a = p1a = 0.5). Accounting for the degree of anagenetic versus cladogenetic change in these traits, we also use BiSSE and BiSSE-ness to investigate whether these traits are associated with dif- ferences in speciation and extinction rates. Shifts in diversification rates within primate groups have been well studied, supported by both molecular and fossil evidence (Fabre et al. 2009), and several traits are thought to have influenced rates of primate diversifica- tion. Matthews et al. (2011) recently used BiSSE, finding that large-bodied primates are associated with higher rates of speciation. Primate species with large geographic ranges, ‘slow’ life history traits (such as small litter size and late sexual maturity), and island endemics are also thought to exhibit higher current extinction risks than other primates (Purvis et al. 2000). For the traits studied here, non-monogamous mating systems may facilitate sexual selection, a trait that is thought to be associated with increased speciation because sexual isolation may occur more readily (Coyne and Orr 2004). Diurnal activity has been associated with increased current extinction risk (Purvis et al. 2000), and social behaviour is thought to increase extinction risk as Allee effects may be more severe in social rather than solitary species (Courchamp et al. 1999). As with the simulation analyses, we conducted all BiSSE-ness ML searches with the primate data set using two opposing sets of starting parameters corresponding to the re- stricted models with character change occurring only along lineages or only at speciation. Again we found that the resulting maximum likelihood and parameter estimates typically converged on the same points (differences in likelihood estimates were within 0.00522% of the ML point 99% of the time and differences in parameter estimates were within 10% 18 of the ML point 71.1% of the time). All subsequent analyses use the search that yielded the highest ML estimate. 2.4.2 Results For activity period and habitat type, we found that when we compared models of equal complexity, cladogenetic change only (6-parameter BiSSE-ness) yielded better AIC scores than anagenetic change only (BiSSE; Akaike weights = 57.9% and 82.6%, respectively; fig. 2.5). The difference in AIC was minor (1.16) for activity period, but reasonably large (6.55) anagenetic + cladogenetic (10) anagenetic + cladogenetic (8) cladogenetic only (6) anagenetic only (6) A ka ik e W ei gh t 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 activity period habitat type mating system social behaviour terrestriality Model of Character Change (# parameters) BiSSE-ness BiSSE Figure 2.5: Comparing Akaike weights of the BiSSE and BiSSE-ness models, aver- aged over 20 trees, for each of the five traits. To compare between models of equal complexity (i.e., equal number of parameters), the 6-parameter BiSSE- ness model was restricted such q01 = q10 = 0 and p0a = p1a = 0.5. Increasing model complexity, we permitted character change both along lineages and at speciation (8 parameters) and allowed BiSSE-ness to estimate the proportion of speciational change that occurred in one or both lineages (10 parameters). for habitat type (Table 2.2). However, as we increased the number of free parameters in the BiSSE-ness model, the AIC scores became progressively worse. The 95% confidence set 19 based on Akaike weights for both traits include BiSSE and the restricted 6 and 8-parameter BiSSE-ness models. For mating system and social behaviour, we found that BiSSE typically outperformed BiSSE-ness, indicating that changes in these traits predominantly occur along lineages, changing at rates proportional to time (BiSSE) rather than number of speciation events. Comparing BiSSE with the next best fitting model, the 8-parameter BiSSE-ness model accounting for anagenetic and cladogenetic change, ∆AIC was 3.93 and 3.79 log likelihood units for mating system and social behaviour, respectively (Table 2.2). Together these two models comprise the 95% confidence set for both mating system and social behaviour, with the remaining BiSSE-ness models contributing less than 4% of the Akaike weights for both traits (fig. 2.5). We found the terrestriality data set could be explained almost equally well by models of both anagenetic and cladogenetic change (the full BiSSE-ness model) and pure anage- netic change (BiSSE; Aikaike weights = 33.9% and 31.8%, respectively; fig. 2.5). As the 95% confidence set includes all four models, we remain uncertain as to how changes in terrestriality have occurred in primates. In summary, comparing Akaike weights for these models of character change (fig. 2.5), we found that shifts in habitat type are likely to occur during speciation, whereas shifts in mating system and social behaviour are likely to occur primarily along lineages. We con- firmed these results using likelihood ratio tests, finding that for habitat type, the model that included cladogenetic change (8-parameter BiSSE-ness) performed significantly bet- ter than when just anagenetic change was included (BiSSE; p = 0.0363, d.f. = 2; fig. 2.6). Similarly, comparing the BiSSE-ness model that restricts change to occur only at speci- ation (6 parameters) with the model allowing both cladogenetic and anagenetic change (8-parameter BiSSE-ness), we found that allowing for along-lineage change provides a significantly better fit to the mating system and social behaviour data sets (p = 0.0197 and 0.0370, respectively, d.f. = 2). However, after correcting for multiple comparisons (Bon- ferroni α = 0.01 with five traits and sequential Bonferroni; Holm 1979), these results are just marginally significant. As in our simulation study, we generally obtained similar di- versification parameter estimates across all models and traits, especially for the speciation rates (see Table 2.2). We also examined differential rates of speciation and extinction against reduced mod- els in which the speciation and extinction rate parameters were constrained to be equal between character states. We completed these analyses for each of the four different mod- 20 0 1 2 3 4 D iff er en ce  in  L og  L ik el ih oo d activity period habitat type mating system social behaviour terrestriality Figure 2.6: Comparing differences between log likelihoods for the BiSSE model (6 parameters) and the BiSSE-ness model where character change at speciation occurs both symmetrically and asymmetrically in a 50:50 ratio (8 parameters). Differences in log likelihood values greater than 3.00 correspond to the signif- icance level p < 0.05 (dashed line; likelihood ratio test, d.f. = 2). Each point represents a different phylogenetic tree drawn from the set of trees (n = 20 for each trait). Allowing for cladogenetic change in habitat type results in a signif- icantly better fit than when change is limited to occur only along lineages (p = 0.0363). els of character change discussed above. Overall, the different models of character change did not have a substantial impact on the detection of differential rates of speciation or extinction. Thus, the p-values and rate estimates below pertain to the best model for each trait, as determined by the AIC score, and again, were averaged across the set of 20 trees. Because the 95% confidence set of character change models contained more than one model for each trait, the results given here should be interpreted with caution. Rate estimates for all four models and traits are given in Table 2.2. The MCMC posterior dis- tribution of rate estimates for all traits under the full, 10-parameter BiSSE-ness model are given in fig. 2.7. 21 We found that the models that account for differential speciation rates performed sig- nificantly better for three traits: activity period, mating system and terrestriality. We found that diurnal species tended to have speciation rates almost twice as high as noctur- nal species (mean λ = 0.20 and 0.12, respectively; Table 2.2), a difference that is marginally significant under the BiSSE-ness model of cladogenetic change (6 parameters, p= 0.0555). Our results suggest that primate species that are classified as polygynous, polyandrous, or polygynandrous tended to speciate at a rate almost two times higher than that of monog- amous species (mean λ = 0.23 and 0.12, respectivley, p = 0.0127 under the BiSSE model; Table 2.2). Finally, terrestrial species tended to have significantly higher speciation rates than arboreal species (mean λ = 0.32 and 0.16, respectively, p = 0.00244, Table 2.2). This pattern was highly significant under BiSSE-ness (10 parameters), however, it was just marginally significant under BiSSE, which had nearly equal Akaike weight (p = 0.0585). While habitat type and social behaviour were not significantly associated with differences in speciation rates, λ0 and λ1 were estimated consistently across the set of phylogenies and across models (see Table 2.2). After correcting for multiple comparisons (Holm 1979), our finding that terrestrial lineages have higher speciation rates than arboreal lineages remained significant. We did not observe any association between species’ traits and rates of extinction un- der the BiSSE and BiSSE-ness models. As a consequence, results for diversification rates (λ− µ) largely mirror those for the speciation rates. In general, extinction rate estimates were very similar across models (see Table 2.2). 22 Table 2.2: Parameter estimates generated through the maximum likelihood analyses. Trait Model ∆ LogLikelihood Speciation Extinction Anagenetic Change Cladogenetic Change λ0 λ1 µ0 µ1 q01 q10 p0c p1c p0a p1a Activity Period diurnal = 0, nocturnal = 1 BiSSE (6) -1.16 0.20 0.12 0.077 0.072 0.0010 0.0048 0 0 0 0 BiSSE-ness (6) * -0.58 0.20 0.12 0.084 0.076 0 0 0.0042 0.033 0.5 0.5 (8) -0.58 0.20 0.12 0.084 0.076 0 0 0.0042 0.033 0.5 0.5 (10) 0 0.20 0.12 0.081 0.071 0 0 0.0039 0.031 0 0 Habitat Type F/S = 0, F = 1 BiSSE (6) -3.72 0.24 0.19 9.0x10−4 0.12 0.30 0.0092 0 0 0 0 BiSSE-ness (6) * -0.45 0.22 0.19 0.14 0.10 0 0 0.63 0.046 0.5 0.5 (8) -0.38 0.15 0.19 0.042 0.11 0.16 0 0.24 0.046 0.5 0.5 (10) 0 0.18 0.19 0.18 0.10 0 0 0.58 0.041 1.0 0.45 Mating System NM = 0, M = 1 BiSSE (6) * -0.23 0.23 0.12 0.12 0.043 0.022 0.028 0 0 0 0 BiSSE-ness (6) -4.51 0.24 0.14 0.15 0.067 0 0 0.072 0.15 0.5 0.5 (8) -0.19 0.23 0.12 0.12 0.043 0.022 0.028 0.0016 7.1x10−5 0.5 0.5 (10) 0 0.24 0.12 0.12 0.040 0.018 0.029 0.012 0 1.0 0.60 Social Behaviour solitary = 0, social = 1 BiSSE (6) * -0.16 0.11 0.19 0.066 0.048 0.014 0 0 0 0 0 BiSSE-ness (6) -3.79 0.13 0.20 0.090 0.078 0 0 0.089 0.00064 0.5 0.5 (8) -0.05 0.11 0.19 0.066 0.049 0.014 0 0.0020 0 0.5 0.5 (10) 0 0.11 0.19 0.066 0.049 0.013 0 0.0036 0 0.74 0.12 Terrestriality arboreal = 0, terrestrial = 1 BiSSE (6) -4.06 0.17 0.26 0.11 0 0.0025 0.15 0 0 0 0 BiSSE-ness (6) -4.62 0.16 0.33 0.098 0 0 0 0.012 0.45 0.5 0.5 (8) -2.75 0.16 0.30 0.099 0 0.0023 0.067 0 0.26 0.5 0.5 (10) * 0 0.16 0.32 0.094 0 0.0015 0 0 0.50 0.75 0.99 NOTE – All estimates are averaged across all 20 trees. The number of parameters that are estimated is given in parentheses. The difference in log likelihoods between the full BiSSE-ness model and all sub-models is also given. ∆AIC can be calculated as the difference in log-likelihood minus twice the difference in number of parameters. F/S = forest-savanna, F = forest, NM = non-monogamous, M = monogamous. * indicates the model with the lowest AIC. 23 Index activity diurnal = 0 nocturnal = 1 P r o b a b i l i t y  D e n s i t y λ0 λ1 Speciation Rates Index µ0 µ1 Extinction Rates Index q01 q10 Rate of Anagenetic Change Index p0c p1c P(Cladogenetic Change) Index p0a p1a P(Asymmetrical Change) Index habitat type forest/savanna = 0 forest = 1 Index Index Index Index Index mating system non-monogamous = 0 monogamous = 1 Index Index Index Index Index social behaviour solitary = 0 social = 1 Index Index Index Index 0.0 0.1 0.2 0.3 0.4 0.5 Index Parameter Estimate terrestriality arboreal = 0 terrestrial = 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Index 0.00 0.05 0.10 0.15 0.20 Index 0.0 0.2 0.4 0.6 0.8 1.0 Index 0.0 0.2 0.4 0.6 0.8 1.0 Index Figure 2.7: Posterior distributions of the parameter estimates using the full, 10-parameter BiSSE-ness model for the five traits included in the primate diversification analysis. Each distribution is comprised of 20,000 steps: 2000 steps for each of the 20 trees where the first 1000 steps of each run were discarded as burnin. The bars beneath each plot correspond to the shaded areas, indicating the 95% credibility interval. 24 2.5 Discussion 2.5.1 Distinguishing Between Modes of Character Change Here we present a novel model, Binary-State Speciation and Extinction - node enhanced state shift (BiSSE-ness), that may be used to estimate of the degree of along-lineage and speciational change in a binary trait using phylogenetic and present-day species informa- tion. Our simulations demonstrate that when character change is concentrated at speci- ation, BiSSE-ness performs significantly better than the simpler model, BiSSE, which as- sumes only anagenetic change. We found that, as a higher proportion of character change occurred at speciation, the ability of BiSSE-ness to distinguish between modes of char- acter change increased except in cases where the total amount of character change was extremely high. At this point trait change was saturated and the signal of anagenetic versus cladogenetic change was essentially erased from the phylogenetic data. With regard to BiSSE-ness parameter estimation, we found that trait-dependent spe- ciation rates affected the precision with which the character change parameters were es- timated. In our simulations, more lineages originated in state 1 (due to λ1 > λ0), result- ing in more precise estimation of the probabilities regarding speciational change while in state 1 (p1c and p1a) and the rate of change along a lineage from state 1 to 0 (q10). In contrast, we found the diversification parameters (rates of speciation and extinction) were estimated similarly, regardless of whether or not the true mode of character change was modelled. When the total amount of character change increased, the speciation rate es- timates were less precise, particularly for BiSSE, because the frequent switching between states obscures any signal of state-dependent speciation. Because our simulations represent just a small portion of possible parameter combina- tions, several questions regarding the ability of BiSSE-ness to distinguish between various patterns of diversification must be addressed by future studies. For example, how well can the diversification rates be estimated if, for example, the rate of character change from state 0 to 1 is much higher than the rate of change from 1 to 0? Also, Maddison (2006) pointed out in the case of a recently-diverged clade, if a state is associated with an increased rate of speciation and character change occurs near the present, the extant species may be in the state opposite to that which spurred the speciation event. If only anagenetic change is assumed (i.e. BiSSE), then a likely explanation would be that the opposite state is associated with high speciation, since the likelihood of character change 25 occurring along a lineage is relatively small. This effect may be contributing to the vari- ation in the speciation rate estimates in our simulations (fig. 2.3). While BiSSE-ness may somewhat alleviate this problem by allowing speciational change, more explicit analyses examining this effect are required. Also, we point out that although we use a relatively low extinction rate in our simulations, it may be relevant to explore parameter combina- tions that include higher rates of extinction. We expect that a high rate of extinction may obscure the BiSSE-ness’ ability to detect differences between anagenetic and cladogenetic change as character changes occurring with speciation may be observed within a single lineage if the other lineage goes extinct. Another feature of our simulations is the relatively large number of terminal branches (i.e. 500 tips for each simulated tree). Although we do expect a decrease in statistical power when smaller trees are used (Maddison et al. 2007), we note that BiSSE-ness is fully compatible with the BiSSE methodologies that have developed to accommodate in- completely resolved phylogenies and incomplete taxon sampling and trait information (Fitzjohn et al. 2009). Therefore, a significant amount of power may be regained with these methods even when there are a limited portion of species. 2.5.2 Using BiSSE-ness to Describe Character Change in Primates When we applied the BiSSE and BiSSE-ness models to our primate data set, we found changes in habitat type (forested vs. forest-savanna regions) tended to occur with specia- tion. As habitat type represents a major component of primates’ ecological niche, changes in this trait during speciation supports the hypothesis of a role for ecological speciation in primates (Conroy 1990). Also consistent with our findings are the results of Curnoe et al. (2006), which provided evidence that primate speciation may be driven by prezygotic iso- lating mechanisms. There are relatively few primate species that inhabit savanna regions (14/215). These species are, however, distributed throughout the phylogeny relatively evenly and are often recently diverged from a forest-dwelling sister species (see fig. 2.4). This pattern of recently-diverged species occupying forest-savanna habitats is likely what is generating support for speciational change, because the chance of anagenetic change (or speciational change and subsequent extinction of one lineage) occurring along short branches near the present is relatively small. We found evidence that changes in primate social behaviour (social vs. solitary) and mating system (monogamous vs. non-monogamous) tend to occur gradually along a lin- 26 eage rather than concurrently with speciation. Social behaviour and mating system are both traits that largely describe the overall characteristic of a group and may exhibit con- siderable variation within species (Kappeler and van Schaik 2002). Therefore, changes in the degree of sociality and mating system may occur independently of speciation in response to other factors related to changes in ecology (e.g. resource defence) and/or demography (e.g. distribution of females; Kappeler and van Schaik 2002). For two traits, primate activity period and terrestriality, no single model of character change was highly preferred compared to the remaining models. It is possible that these data sets may be consistent with one of the models of character change we explored here, however, there is not enough statistical power in this case to demonstrate a strong sig- nal. Also, the evolution of activity period and terrestriality may be better described by processes other than the gradual and speciational change models presented here. Mooers et al. (1999) and Oakley et al. (2005) outlined several models of character change in ad- dition to the ones used here, each which differently weight aspects such as phylogenetic structure, genetic change, and patterns of character change. For example, the genetic model presented by Mooers et al. (1999) tests the association of character change with the number of genetic changes (inferred substitutions) that have occurred. Because there is evidence that the evolution of primates is not best represented by a strict molecular clock (Fabre et al. 2009), the genetic model may provide different results from the anagenetic model, which examines character change in proportion to time. Alternatively, the ‘free’ model allows character change to occur at a different rate for each lineage, allowing much more flexibility thereby providing insight as to how activity period and terrestriality have actually evolved (Mooers et al. 1999; Oakley et al. 2005). Overall, we find support for gradual diversification and punctuated evolution in pri- mates among the traits included here, although there remains considerable model uncer- tainty. Our analyses using neontological data and the BiSSE-ness model represents just one aspect of studying patterns of character evolution and, like all modelling exercises, can only assess the relative likelihoods of the hypotheses proposed to explain past events. The degree to which our models can inform us of historical processes is limited both by the size the dataset (i.e. statistical power), as well as the biases that are inherent in us- ing phylogenies to examine diversification. For example, even though larger phylogenies may generate more precise parameter estimates, they are a non-random sample of diver- sity (Ricklefs 2007). Rather than using our results to reconstruct the evolution of certain characters (as our MCMC results show there is considerable uncertainty in specific pa- 27 rameter estimates, fig. 2.7), we highlight the overall patterns of evolutionary change in the five primate traits investigated here. To confirm our results and gain a more complete understanding of primate diver- sification, we recommend further analyses including complete trait information for all species, conducted over a range of plausible phylogenies that incorporate the most recent molecular data (see e.g., Perelman et al. 2011). The primate fossil record is also extremely well-studied (Conroy 1990) and thus, coupling phylogenetic methods with paleontologi- cal information would be a valuable undertaking (Ricklefs 2007; Jablonski 2008). Another limitation with our BiSSE and BiSSE-ness methods is the assumption that diversification rates remain constant throughout time. As several studies have noted differences in diver- sification rates among primate clades (Curnoe et al. 2006; Fabre et al. 2009), future BiSSE and BiSSE-ness analyses that account for these shifts may be carried out (see, for example, FitzJohn 2010). 2.5.3 Investigating Trait-Dependent Diversification Using BiSSE-ness BiSSE-ness is distinct from other models investigating the mode of character change in that it explicitly accounts for trait-dependent speciation and extinction rates (Mooers et al. 1999; Bokma 2008). Because many of the characters that have been intensively studied with respect to the tempo and mode of character evolution, such as polyploidy in plants (Wood et al. 2009), and body size and range size in mammals (Mattila and Bokma 2008; Carotenuto et al. 2010), are also thought to influence the rates of speciation and extinction (Mayrose et al. 2011; Liow et al. 2008; Cardillo et al. 2003), we believe our methods that si- multaneously account for these effects will be widely applicable. While we have focussed in this paper on the contributions our model makes to studies regarding the tempo and mode of character change, BiSSE-ness also provides a more flexible framework for stud- ies investigating how traits are associated with differences in diversification rates. That is, BiSSE-ness may be used in place of BiSSE for studies that primarily investigate how a trait influences diversification rates (e.g., Fitzjohn et al. 2009; Wilson et al. 2011) with the advantage that it provides additional insight into the evolution of the trait, or at the very least, simply remains agnostic regarding the mode of character change. When we investigated if there was an association between the five primate traits and differential rates of primate diversification, we found this to be the case for two traits, mating system and terrestriality. Overall, non-monogamous lineages and terrestrial lin- 28 eages tended to be associated with increased rates of speciation as compared with monog- amous and arboreal lineages (p = 0.0127 and 0.00244, respectively). To the extent that non-monogamous mating systems increase sexual selection, our findings support the hy- pothesis that increased sexual selection is associated with higher speciation rates. While similar findings have been found in birds (Mitra et al. 1996; and for 1/3 sexual selection measures studied in Owens et al. 1999), lizards (Agamidae; Stuart-Fox and Owens 2003), and insects (Arnqvist et al. 2000), more recent studies investigating mammals, did not show this effect. Both Gage et al. (2002) and Isaac et al. (2005) used different measures of sexual selection: the degree of polyandry (measured using relative testes size) and sexual size dimorphism, respectively, which may contribute to the inconsistency between results (Isaac et al. 2005). In contrast to mating system, we are unaware of an obvious explanation for higher speciation rates in terrestrial lineages as compared to arboreal lineages. Driving this pat- tern may be the fact the most terrestrial primates belong to the species-rich Cercopitheci- dae family (Old World monkeys), a recent radiation that is thought to have relatively high speciation rates (Purvis 1995; Paradis 2005; Fabre et al. 2009). This group is also charac- terized by locomotion morphology that is not highly specialized to arboreal or terrestrial habitats and, at least for guenon monkeys (genus Cercopithecus), switches between these habitats may have occurred a number of times; (Gebo and Sargis 1994; Fabre et al. 2009). As with all phylogenetic comparative analyses, we note that while our analyses showed an association between non-monogamy and terrestriality and a higher speciation rate, this does not necessarily indicate that these traits cause an increase in speciation. Changes in the diversification rate may be the result of a secondary trait which is similarly distributed throughout the phylogeny, such as body size, for example (Paradis 2005). While the patterns we detected pertaining to trait-dependent diversification were not significant after accounting for multiple comparisons, we did find that these results re- mained largely consistent across different models of character change. Therefore, al- though previous analyses using BiSSE methodologies did not account for the mode of character change, we believe these studies remain convincing examinations of trait-dependent diversification. However, in cases where speciational change is likely to have occurred and BiSSE is used, we expect the parameter estimates pertaining to anagenetic character change will be biased towards larger values. 29 2.5.4 Applications of BiSSE-ness As the abundance of genetic data increases the number of large, well-resolved phylo- genies available and online data sharing facilitates global databases for life history and ecological data, we are well-equipped to address a vast range of macroevolutionary ques- tions using neontological data. The BiSSE-ness model provides a flexible framework with which we may simultaneously address questions regarding the mode of character evolu- tion and the effect of a trait on species diversification. Importantly, even in cases where processes such as trait-dependent diversification or speciational change are expected to be absent or negligible, BiSSE-ness may still be used, simply returning redundant param- eters or estimates close to zero. Alternatively, the user may also restrict the model as we have done in the primate analyses to test a particular hypothesis or in accordance with prior information (e.g. speciational change always occurs asymmetrically for state 1, that is, p1a is set to equal 1). Extending the BiSSE-ness model to accommodate multi-state and continuous trait data would be a worthwhile endeavour, increasing the number of traits that could be studied in this respect. For example, Monroe and Bokma (2009) explored the relationship between body size and the diversification of mammals by incorporating studies that separately investigated character evolution (Mattila and Bokma 2008) and diversification rates (Liow et al. 2008). Comparing their findings with a BiSSE-ness ap- proach would likely be informative in regard to both mammal diversification and to the limits of different phylogenetic methods. 30 Chapter 3 General Discussion While trait evolution and trait-dependent speciation and extinction have previously been investigated through independent analyses, BiSSE-ness now provides a suitable method for simultaneously carrying out these studies. For traits that play a central role in species’ life history, reproduction and/or ecological niche, integrating these questions into a single framework is necessary in order to separate out the various processes influencing the evolution of a taxon. Here, I show that BiSSE-ness can detect trait-dependent diversification as well as cladogenetic and anagenetic trait evolution. As the degree of cladogenetic change be- came more prevalent in comparison to anagenetic change in my simulations, the BiSSE- ness model provided an increasingly better fit to the data as compared to the simpler BiSSE model, which accounts only for anagenetic changes. In addition to observing a sig- nificant improvement in fit in many of the simulations, BiSSE-ness also improved the fit of the model to data on primate habitat type. Even when changes in a trait are likely to occur along a lineage, as was the case with primate mating system and social behaviour, BiSSE-ness may be used to explicitly compare modes of character change by contrasting the full model with a reduced version that restricts character change to occur along a lin- eage (equivalent to BiSSE). Using this kind of comparative approach revealed the amount of uncertainty associated with the mode of character change (fig. 2.5) as well as the fact that the BiSSE-ness estimates of the speciation and extinction rates were relatively robust to the mode of character change. Interestingly, the ability of the BiSSE-ness model to differentiate between modes of character evolution does not greatly affect its ability to detect trait-dependent diversifi- 31 cation. The simulation analyses show that even when the ‘wrong’ model of character change was used, the estimation of the speciation and extinction rates was not biased and differences between states were still detected. For example, when BiSSE-ness was used to estimate the diversification parameters for data that was simulated without cladogenetic change (BiSSE), the speciation and extinction rate estimates were very similar to those es- timated using the correct model, BiSSE (black points in fig. 2.3). In addition, I observed negligible differences in the confidence limits of these estimates between BiSSE and BiSSE- ness, indicating that despite the fact that BiSSE-ness has four additional parameters, there was not a significant loss of power. Also, the degree of trait-dependent speciation and extinction in primates remained similar across various models of evolution of five traits. Of the five primate traits investigated, just terrestriality exhibited significant differences in the speciation rates, where terrestrial lineages diversified at a higher rate than arbo- real lineages. Further simulation analyses that explore other combinations of parameter space and investigations of other empirical data sets may provide more insight into how BiSSE-ness can detect the interplay between diversification and character evolution. While the primate data set we used here provides an interesting first look at the abil- ities of BiSSE-ness and some aspects of primate diversity, it is certainly not a complete analysis of primate diversification and trait evolution. Fortunately, primates are an ex- tremely well-studied system and a more comprehensive investigation may be carried out as additional data becomes available (see e.g. PanTHERIA database; Jones et al. 2009). In addition to simply updating the number of traits used in the primate analysis or using a more comprehensive phylogeny, understanding primate diversification would also ben- efit from incorporating two additional data types. First, the inclusion of fossil data may shed significant light on the types and number of morphological transitions, as the fossil record is very well characterized in primates (Conroy 1990). More generally, fossil data is abundant for a vast number of organisms and while its use for evaluating patterns of char- acter evolution has been somewhat controversial (Stebbins and Ayala 1981), considering both neontological and paleontological data together is widely seen as an improvement over examining just one data type (Ricklefs 2007; Purvis 2008; Jablonski 2008). Integrating these approaches into one model framework may involve non-trivial challenges, such as the placement of fossil data into a molecular phylogeny (and the uncertainty surround- ing this placement) and the interpretation of transitional fossil forms. Also, as the fields of phylogenetics and paleontology currently remain relatively separate, simply forming collaborative studies between experts in each field may be an extremely valuable step 32 towards a more integrative approach. Second, allowing for the analysis of multi-state or continuous traits in a BiSSE-ness type framework would dramatically increase the number of traits that could be addressed. For primates, traits such as body size (Matthews et al. 2011), range size (Purvis et al. 2000; Harcourt et al. 2002; Gaston 2008), and ‘slow’ life history traits, such as slow growth rate, small litter size, and long gestation time (Purvis et al. 2000), are hypothesized to influ- ence their diversification. Using BiSSE-ness methods, one may examine the evolution of these traits and their interaction with the rate of species diversification, and compare these results with previous studies, thereby informing us about the robustness of different phy- logenetic methods to a variety of evolutionary processes. While extending BiSSE-ness to accommodate multi-state traits may simply involve additional parameters for each state, the process to incorporate continuous data would be considerably more complex. QuaSSE (FitzJohn 2010) currently models evolutionary changes in continuous traits using a dif- fusion process, thus requiring trait changes to occur gradually. To use BiSSE-ness with continuous traits, a model to describe the rapid character change that occurs with spe- ciation would need to be developed, such as a ”jump-diffusion” process. Including this process becomes particularly important for detecting cases of rapid evolutionary change even when the speciation event is no longer observed due to the extinction of one daugh- ter lineage. Geographic range size is one continuous trait that has received much attention in regard to both its effect on speciation and extinction rates (Jablonski 2008; Payne and Finnegan 2007; see also references therein) as well as its evolution during speciation events and the degree of range size heritability as a species level trait (Goldberg et al. 2005; Gaston 2008; Goldberg et al. 2011). While the rate of speciation is predicted to be highest for species with small to medium sized geographical ranges, the process of spe- ciation itself may result in changes to the geographical range, depending on the mode of speciation (Gaston and Chown 1999; Gaston 2008). Species with small geographic ranges are also predicted to have higher rates of extinction (Jablonski 2008; Purvis 2008). Not only are the interactions between these processes hard to disentangle, but they may also vary considerably between taxa (Gaston 2008). GeoSSE is a recently developed model (Goldberg et al. 2011) that was constructed using BiSSE methodologies, explicitly incor- porating spatial aspects of trait evolution and the effects of localized extinction and orig- ination processes on total species diversity. This method tackles the processes of range evolution as species experience local extinction and/or dispersal between two or more re- 33 gions specified in the model. GeoSSE is expected to be a useful tool for investigating traits that are associated with a geographical component, such as habitat type or host-parasite interactions (Goldberg et al. 2011), however, it does not directly consider the size of the geographical range as a trait itself. Considering the large number of studies examining geographical range size as a species level trait affecting speciation and extinction in and of itself (Gaston 2008; see also references therein), using an approach, such as BiSSE-ness, that examines range size as the focal trait may also be a valuable endeavour. Advancing our understanding of range size evolution and its interactions with the rate of species diversification also has conservation implications, as many species’ ranges are changing dramatically in response to human impacts. Often by definition, many small- ranged species are deemed to be at a higher risk of extinction (Mace et al. 2008) and iden- tifying traits that may predict species’ current extinction risk is a quickly growing area of study (Purvis 2008; McKinney 1997; Dulvy and Reynolds 2002). While geographic range size is just one trait that may be of particular interest for future studies using BiSSE-ness, the method developed here has broad applicability. For exam- ple, BiSSE-ness has already been used to examine the association between ploidy level and lineage diversification within angiosperm and seed-free vascular plant groups (May- rose et al. 2011). As shifts from diploidy to polyploidy are a well-studied mechanism of plant speciation (Coyne and Orr 2004; Wood et al. 2009), the use of BiSSE-ness, which can account for changes in ploidy at speciation, was a logical addition to their BiSSE analyses (Mayrose et al. 2011). This study revealed that while polyploidy is a relatively common trait, the diversification rate of these lineages was estimated to be significantly lower than their diploid congeners (Mayrose et al. 2011). The use of BiSSE-ness also allowed Mayrose and colleagues (2011) to estimate the approximate number of speciation events that were associated with the polyploidization of diploid lineages, finding this mechanism to be a significant contributor to the difference in speciation rates between diploid and polyploid lineages. The BiSSE-ness model may be used with a variety of traits and in conjunction with a wide range of other analyses investigating topics such as niche evolution, mechanisms of speciation, and the determination of lineages that will to contribute significantly to future biodiversity. As more data becomes available, we have an increasing ability to conduct more complete analyses as well as continuing the development these kinds of compara- tive methods. While I believe there is currently good support for the use of phylogenetic methods among those who have not necessarily been a part of their development (fa- 34 cilitated by the availability of these programs online as open-source software), it can be challenging for the user to know the appropriate implementation of such methods. I of- fer the recommendation that knowing the limitations of the method, such as BiSSE-ness in conjunction with a particular data set is an integral part of interpreting the parameter esti- mates output by the model. For example, experimenting with the data set by considering just a subset of the data or restricting the model parameters to represent different bio- logical scenarios may provide insight into the power BiSSE-ness has to detect differences between these cases, even when large data sets are used. 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Takebayashi, M. Barker, I. Mayrose, P. Greenspoon, and L. Rieseberg. 2009. The frequency of polyploid speciation in vascular plants. Proceedings of the National Academy of Sciences 106:13875. 42 Appendices Appendix A: BiSSE and BiSSE-ness Models Shown in bold text are the terms that were added to the original BiSSE model (Maddison et al. 2007) to account for speciational change in BiSSE-ness. The diversification probabil- ities for state 0 and 1, respectively, change over time according to: dDN0 dt = −(λ0 + µ0 + q01)DN0(t) + q01DN1(t) + 2λ0E0(t)DN0(t)(1− p0c) +2λ0 ( E0(t)DN1(t) 2 + E1(t)DN0(t) 2 ) p0cp0a +2λ0E1(t)DN1(t)p0c(1− p0a) (1) dDN1 dt = −(λ1 + µ1 + q10)DN1(t) + q10DN0(t) + 2λ1E1(t)DN1(t)(1− p1c) +2λ1 ( E1(t)DN0(t) 2 + E0(t)DN1(t) 2 ) p1cp1a +2λ0E0(t)DN0(t)p1c(1− p1a) (2) The probabilities of extinction in state 0 and 1, respectively, change over time according to: dE0 dt = µ0 − (µ0 + q01 + λ0)E0(t) + q01E1(t) + λ0E0(t)2(1− p0c) + λ0 ( E0(t)E1(t) 2 + E1(t)E0(t) 2 ) p0cp0a + λ0E1(t)2p0c(1− p0a) (3) 43 dE1 dt = µ1 − (µ1 + q10 + λ1)E1(t) + q10E0(t) + λ1E1(t)2(1− p1c) + λ1 ( E1(t)E0(t) 2 + E0(t)E1(t) 2 ) p1cp1a + λ1E0(t)2p1c(1− p1a) (4) These coupled ordinary differential equations were solved numerically in R using Diver- sitree (version 0.6-1; Fitzjohn et al. 2009), modified to allow speciation-associated trait changes. The equilibrium frequencies of state 0 and 1 can also be calculated using the BiSSE- ness model. This differs slightly from the BiSSE model (see eqn. (13) in Appendix 2 of Maddison et al. 2007), and in this study, it is used only to determine the root state of the simulated trees. We find the frequency of lineages in state 0, x= n0/(n0 + n1), is described by the differential equation: dx dT = gx(1− x) − x[q01+p0cλ0(2(1− p0a) + p0a)] + (1− x)[q10+p1cλ1(2(1− p1a) + p1a)] (5) where g = λ0 − µ0 − λ1 + µ1, the difference in diversification rates between states. Bold terms are those that were added to the original BiSSE model. 44 Appendix B: BiSSE-ness Phylogenetic Tree Simulator The following R code was adapted from the tree.bisse function in the Diversitree pack- age v.0.7-2 (Fitzjohn et al. 2009). This function simulates a phylogenetic tree under the BiSSE-ness model, incorporating parameters for both cladogenetic and anagenetic char- acter changes. The function argument ’pars’ corresponds to the input diversification rate and character evolution parameters, ‘max.taxa’ specifies the maximum number terminal branches (i.e. taxa), alternatively ‘max.t’ specifies the maximum amount of time the simu- lation should run for, ‘x0’ corresponds to the root state, and ‘single.lineage’ specifies if the simulation starts with one lineage as opposed to two. See also the R help file for ‘simulate’ in Diversitree. make.tree.bisse_scan<- function (pars, max.taxa = Inf, max.t = Inf, x0, single.lineage = TRUE) { p.pars<- matrix(c((1-sum(pars[7:8])), pars[7:8], (1-sum(pars[9:10])), pars[9:10]), 2, 3, byrow=TRUE) pars <- matrix(pars[1:6], 2, 3) extinct <- FALSE split <- FALSE parent <- 0 n.i <- c(0, 0) r.i <- rowSums(pars) len <- 0 t <- 0 hist <- list() if (single.lineage) { states <- x0 n.taxa <- lineages <- n.i[x0 + 1] <- 1 start <- 0 } else { stop("Nope.") 45 }while (n.taxa <= max.taxa && n.taxa > 0) { ## When does an event happen? r.n <- r.i * n.i r.tot <- sum(r.n) dt <- rexp(1, r.tot) t <- t + dt if (t > max.t) { dt <- dt - (t - max.t) len[lineages] <- len[lineages] + dt t <- max.t break } len[lineages] <- len[lineages] + dt ## Proceed. What state does an event happen to? state <- as.integer(runif(1) > r.n[1]/r.tot) state.i <- state + 1 ## Pick a lineage for that state: j <- sample(n.i[state.i], 1) lineage <- lineages[states[lineages] == state][j] ## Pick an event: 1= speciation, 2= extinction, 3= state change type <- sample(3, 1, FALSE, pars[state.i, ]) if (type == 1) { if (n.taxa == max.taxa) break new.i <- length(extinct) + 1:2 split[lineage] <- TRUE extinct[new.i] <- split[new.i] <- FALSE 46 if(p.pars[state.i,1]==1){ states[new.i] <- state n.i[state.i] <- n.i[state.i] + 1 } else{ ## The daughter states be inherited from the parent state? ## 1= complete inheritance (i.e. traditional bisse), ## 2= partial inheritance, ## 3= no inheritance. inherit.type<- sample(3, 1, FALSE, p.pars[state.i,]) states[new.i] <- switch(inherit.type, state * c(1,1), {new1<-sample(0:1, 1); c(new1, 1-new1)}, rep(1-state, 2)) if(inherit.type==1) n.i[state.i] <- n.i[state.i] + 1 if(inherit.type==2) n.i[(1-state)+1] <- n.i[(1-state)+1] + 1 if(inherit.type==3) { n.i[(1-state)+1] <- n.i[(1-state)+1] + 2 n.i[state.i] <- n.i[state.i] - 1 } } parent[new.i] <- lineage start[new.i] <- t len[new.i] <- 0 n.taxa <- n.taxa + 1 lineages <- which(!split & !extinct) } else if (type == 2) { extinct[lineage] <- TRUE lineages <- which(!split & !extinct) n.i[state.i] <- n.i[state.i] - 1 n.taxa <- n.taxa - 1 47 }else { n.i <- n.i + if (state == 0) c(-1, 1) else c(1, -1) states[lineage] <- 1 - state hist[[length(hist) + 1]] <- c(lineage, t, state, 1 - state) } } info <- data.frame(idx = seq_along(extinct), len = len, parent = parent, start = start, state = states, extinct = extinct, split = split) hist <- as.data.frame(do.call(rbind, hist)) if (nrow(hist) == 0) hist <- as.data.frame(matrix(NA, 0, 4)) names(hist) <- c("idx", "t", "from", "to") hist$x0 <- info$start[match(hist$idx, info$idx)] hist$tc <- hist$t - hist$x0 attr(info, "t") <- t attr(info, "hist") <- hist info } 48


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