Feature Diversity and Evolutionary Models of Character Change

Underpinning the theoretical arguments for maximizing the preservation of phylogenetic diversity is the assumption that it captures feature diversity (i.e. variance in measured ecological and morphological traits), and thus selecting the set of taxa to maximize phylogenetic diversity will also maximize feature diversity (Faith 1992; Crozier 1997). Many biological traits demonstrate significant phylogenetic signal (Blomberg et al. 2003) and therefore this assumption might be broadly valid. However, the relationship between phylogenetic diversity, which is measured in millions of years, and feature diversity is not straightforward, but assumes a linear divergence between species over time, for example, as might be modeled under a Brownian motion process, in which trait variance increases in proportion with time, but for which evidence is mixed. Frequently, traits demonstrate much weaker phylogenetic signal than assumed by a strict Brownian motion model (e.g. Kamilar and Cooper 2013). Although there are a large number of alternative models of

Fig. 3 Simulations showing accumulation of trait variance over time assuming a Brownian motion model of trait evolution a in which variance increases in proportion to time, versus a punctuated model of trait evolution b in which trait change occurs in bursts at speciation, and a pure-birth process of phylogenetic branching (see also Ingram 2011; Davies 2015)

evolutionary change, including the Ornstein-Uhlenbeck model which approximates stochastic evolution with stabilizing selection (Hansen 1997) and the early burst model that might characterize adaptive radiations (Harmon et al. 2010), we here (see Davies and Yessoufou 2013; Davies 2015) compare the potential loss of phylogenetic diversity under two models with very different assumptions: (1) a model of phylogenetic gradualism as represented by Brownian Motion (Fig. 3a), and (2) a punctuated model of evolution in which trait differences accumulate in bursts at speciation (Fig. 3b).

To date, the model of evolution has rarely been considered explicitly within the conservation phylogenetics literature (e.g. Owens and Bennett 2000). However, if traits evolve following a speciational model – as may be the case for body mass in mammals (Mattila and Bokma 2008) – where trait evolution occurs in bursts at speciation, each individual branch would capture similar feature diversity, and as such, the number of branches might be of equal, or greater conservation value than their summed lengths. Furthermore, because nonrandom extinction may target deeper branches in the tree-of-life (Mckinney 1997; Purvis et al. 2000a; Purvis 2008), we would predict a disproportionate loss of branches without necessarily a concomitant loss of total summed branch lengths (Fig. 2). Non-random extinction might therefore have a greater impact on number of branches lost than on the sum of their branch lengths – which has been the focus of most studies to date.

Using a dated phylogenetic tree for Primates, Carnivora and Artiodactyla, we (Davies and Yessoufou 2013) combined simulations and empirical extinction risk data from the IUCN Red List of threatened species (iucnredlist.org/) to explore the loss of phylogenetic diversity under two alternative evolutionary models. First, following standard practice, we calculated the expected loss of PD assuming a gradual model of evolution. Second, we also calculated the equivalent loss of diversity under a speciational model of evolution (in which all branches are assigned equal weights) following the approach of Witting and Loeschcke (1995). Extinction categories were first converted into extinction probabilities, p(ext), following Mooers et al. (2008) and assuming IUCN designations projected to 50 years. We then compared observed losses to expectations from the same distribution of p(ext), but randomly assigned to species at the tips of the phylogeny (100 replicates). Last, we explored the relationship between phylogenetic signal, estimated using Pagel's (1999) Lambda, and the loss of evolutionary history by evolving traits along the branches of simulated phylogenetic trees. Here, we assume a birth–death tree (b = 0.2, d = 0, size n = 240), in contrast to the unrealistic coalescent trees used by Nee and May (1997). Based on the simulated trait values, a constant fraction of species (the top 25 %, as this broadly matches the proportion of threatened mammal species in the IUCN Red List) were then assigned high risk of extinction (p(ext) = 0.75).

Our results reveal that under a speciational model of evolution, non-random extinction prunes more branches from the tree-of-life (see also Fig. 2), but that the loss of summed branch lengths (Faith's PD) does not depart significantly from random expectation (Davies and Yessoufou 2013). Although there is a weak trend for greater loss of phylogenetic diversity (PD) and number of branches lost with increasing phylogenetic signal in extinction risk, there is large variance in PD loss under random pruning such that observed losses typically overlap to a greater extent with the null distribution. In contrast, there is much less variance in the number of pruned branches such that random extinctions of equivalent intensity would prune similar number of branches. Therefore, observed number of branches loss more often falls outside the null distribution from randomizations (Fig. 4).

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