7.4.1 Data collection
Data on the presence or absence of chemical defence in 857 amphibian species were extracted from Arbuckle and Speed (in press; see Chapter 6). Briefly, this dataset was assembled from literature searches using a conservative approach
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in which data were only recorded for each species if it had been investigated and found to either possess or lack a chemical defence. If information was not available for that given species no data were recorded and, consequently, species included in this study are known to either possess or lack a chemical antipredator defence. Further details on the collation of this dataset are available in the original paper (Arbuckle and Speed, in press; see Chapter 6).
To assess extinction risk, we used IUCN Red List categories as a standard and widely-used proxy (Mace et al., 2008). We searched the IUCN Red List database (IUCN, 2014) for all 857 species in our chemical defence dataset and recorded the conservation status of all species for which the information was available. This resulted in a final dataset consisting of 809 species from across the amphibian tree of life for which we had data on both extinction risk and chemical defence. We coded extinction risk in two ways. Firstly as a binary trait (which we term 'threat') in which we considered Red List categories LC (least concern) and NT (near threatened) as 'non-threatened', and other categories (VU=vulnerable, EN=endangered,
CR=critically endangered, EW=extinct in the wild, EX=extinct) as 'threatened', in line with recommendations by the IUCN (2014). Secondly, we coded extinction risk as an ordinal trait (which we term 'status') representing increasing levels of threat as follows: 0=LC, 1=NT, 2=VU, 3=EN, 4=CR, 5=EW&EX.
To account for the non-independence of species as data points due to shared evolutionary history, we took a comparative approach using the time- calibrated phylogeny of Pyron and Weins (2013). This was pruned to include only the 809 species for which data were available for both chemical defence and conservation status, and the resulting tree was used for all subsequent analyses. The full dataset and R scripts used for analyses in this study is available at
http://dx.doi.org/10.6084/m9.figshare.1399172. All analyses were performed in R v3.1.3 (R Core Team, 2015), using ape (Paradis et al., 2004) for basic manipulation of the phylogeny and other packages as stated for particular methods.
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7.4.2 Phylogenetic regression models
We first tested whether threat was predicted by the presence of chemical defence using phylogenetic logistic regression with Ho and Ané’s (2014) method implemented in phylolm. We checked that phylogenetically informed analysis was justified over standard logistic regression in three ways, all of which provided support for this and so we report only the results from the phylogenetic logistic regressions. Firstly, we fit a standard (non-phylogenetic) logistic regression and compared these alternative models using AIC. We find a ∆AIC value of 61.8 in favour of the phylogenetic model (values greater than ~5 are often considered strong evidence to prefer one model over another). Secondly we examined the α parameter estimated in the phylogenetic model, which ranges between 0 and 1 with low values indicating greater phylogenetic signal. In this model α=0.016, again suggesting that the phylogenetic logistic regression was justified. Finally, we tested whether the residuals from the model exhibited significant phylogenetic signal (as expected if phylogenetic control is necessary) and found this to be true whether using Pagel’s λ (λ=0.653, P=3e-26) or Blomberg’s κ (κ=0.065, P=0.024), both estimated in phytools (Revell, 2012).
We then tested whether extinction risk was predicted by the presence of chemical defence using phylogenetic generalised estimating equations (GEEs; Paradis and Claude, 2002) with a Poisson error structure, also implemented in phylolm (Ho and Ané, 2014). GEEs are not likelihood-based and so cannot be compared with other models using information theoretical measures such as AIC, and nor do they fit an α parameter as with the phylogenetic logistic regression models. Nevertheless, we checked that the use of a phylogenetic model was justified here by evaluating the phylogenetic signal in the residuals as above. This was again found to be the case using both Pagel’s λ (λ=0.701, P=2.9e-38) and Blomberg’s κ (κ=0.071, P=0.009), and so we present the results from the GEE in this paper.
7.4.3 Evolutionary pathway models
The regression-based models in the previous section test whether chemical defence and extinction risk are linked, and do not assume that the traits evolve along a
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phylogeny (only that the residuals from the models are phylogenetically structured). This has a benefit as we acknowledge that our proxy of extinction risk, IUCN Red List status, is a human classification and so does not, in a strict sense, evolve.
Nevertheless, such models are limited in their ability to provide inference about cause-effect relationships, which can be evaluated for binary traits using
evolutionary pathway models (Pagel, 1994). Therefore, we attempt to use these to test more directly whether the hypothesis that chemical defence leads to an increase in extinction risk is supported, but we do so tentatively with the following three justifications for treating extinction risk as an evolving trait.
Firstly, a Pagel’s (1994) test for correlated evolution conducted in phytools, which uses pathway modelling, corroborate those from our phylogenetic regression (see Results) by finding evidence for correlated evolution between threat and chemical defence (P=0.003). This is despite the Pagel’s test assuming that both traits evolve and taking into account inferred ancestral transitions, suggesting that it is likely that assuming threat evolves is not strongly misleading.
Secondly, threat exhibits significant phylogenetic signal as measured by Fritz and Purvis’ (2010) D statistic for binary traits (D=0.495, P<0.0002), estimated in caper (Orme et al., 2013) based on 5000 permutations. Therefore, extinction risk as measured using IUCN Red List category as a proxy show similar properties to an evolving trait, in that it is more likely to be shared by more closely related species. Taken alongside the first point, this suggests that extinction risk behaves as an evolving trait for the purposes of comparative analyses.
Thirdly, IUCN Red List categories have been widely used as a proxy for extinction risk, which is itself a function of many attributes. Since many of these factors contributing to extinction risk are likely to be evolving traits of the species, extinction risk should be expected to evolve, in a sense, over the phylogeny via the evolution of related variables. Therefore, while Red List categories do not evolve, we consider it reasonable to expect that the underlying extinction risk (which it is intended to represent) should 'evolve' in the sense that it experiences transitions over the phylogeny, as modelled by evolutionary pathway analyses.
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Consequently, we tentatively treat threat as an evolving trait for the
purposes of the following analyses in order to investigate the hypothesis behind this paper in more detail. To do this, we first determined whether transition rates best fit an equal rates (ER), symmetrical rates (SYM) or ‘all rates different’ (ARD) model, and used the best of these (ARD according to AIC values) in subsequent pathway models. We then constructed two models and compared their fit using a likelihood ratio test. The first was a full (8-parameter) model assuming correlated evolution between threat and chemical defence without imposing constraints on the evolution. The second was a constrained (7-parameter) model incorporating a single constraint which assumes that chemical defence is gained first which then leads to the lineage becoming threatened, as per Pagel (1994). Comparison of these models allows direct evaluation of the evidence for a pattern of defence-driven extinction risk as opposed to a non-directed correlation or extinction risk-driven defence.