The genus Acropora (commonly known as staghorn corals) is an ideal model group for studies of extinction risk because 50% of Acropora species are predicted to face an elevated risk of extinction this century under IUCN categories and criteria [23]. Species in this genus display complex spatio‑temporal patterns and an extensive literature exists on their global ranges [46,47,48,49]. Many species of Acropora are described as rare, occurring in small, restricted, isolated and/or disjunct populations [47,49,50]. In general, species of Acropora are extremely susceptible to coral bleaching [51], changes in water quality, disease [52,53] and predation (e.g., the corallivorous starfish Acanthaster planci; and the gastropods Coralliophila abbreviata and Drupella spp.).

Acropora is the largest extant genus of reef-building corals. The genus Acropora was formally known as Madrepora (Linnaeus 1758) before the name Acropora was introduced by Oken in 1815 and reintroduced by Verrill in 1901. In 1999, the first full monograph of the genus was published since Brook (1893) [47]. Under this system, 114 species were described. Although another 250+ species of Acropora have been described—some are represented by fossil material only, and others are nomina nuda, meaning they are not officially validated (i.e., some of the species described in [49]); and many others were placed into synonymy after extensive examination of type material [47]. However, 14 of the new Acropora species described in [49] have recently been validated [54,55]. In addition, 6 new species have been described since the 1999) revision [54,56,57,58,59].

Currently, the morphological phylogeny portrays the rudis group to be the oldest living lineage and the echinata group to be the youngest [47]. However some fundamental differences are apparent with the published molecular phylogenies. For example, mitochondrial DNA suggests the Atlantic species—A. cervicornis and A. palmata are the basal lineage [60,61] rather than members of the rudis group, A. longicyathus occurs in a near basal position in the molecular phylogeny [60] despite belonging to the ‘most recently evolved’ echinata group [47]. Most Acropora phylogenies have included only common and widespread species, however the inclusion of rare species in a new phylogeny [62], suggest that not all rare species are recently evolved and hence, there is substantial risk that novel phylogenetic information will be lost if rare and threatened species are driven to extinction by the end of this century as predicted [23].

For this study, the threatened status of 173 coral species was downloaded from the IUCN Red List ([63], see Table 1 and Table 2). For this assessment, nearly all extinction risk assessments were made with the IUCN criterion that uses measures of population reduction over time [23]. Most reef building corals do not have sufficient long-term species-specific monitoring data to calculate actual population trends; thus, to complete the global coral threatened species assessments, a less quantitative (surrogate) approach was adopted to assess the status of coral species. Specifically, the vast majority of coral species were assessed under a criterion in which population reductions are estimated from the “decline in habitat quality.” They were based therefore on a conservative interpretation of the most current global and regional estimates of coral reef status in 17 regions across the world [64]. For each species, a weighted average was calculated by multiplying the area of reef within the species distribution by the percent of total coral cover loss or the combined percent of total coral cover loss and critically declining reef [64]. Overall, estimates of habitat loss (in conjunction with life history traits and susceptibility) are used as a surrogate for population reduction, assuming the generation time of corals is 10 years [23]. Therefore, rates of population decline for each species have their basis in the rate of habitat loss within its range adjusted by an assessment of the species-specific response to habitat loss (i.e., more-resilient species have slower rates of decline).

In the next sections, our calculations using estimated extinction probabilities will follow the “pessimistic case” [65] to convert these categories to estimated extinction probabilities (Table 1).

Various markers are available to assess phylogenetic relationships within the Acropora, including ribosomal DNA (rDNA) and ITS (internal transcribed spacer) sequences [66,67,68]. However, rDNA performs suboptimally when testing evolutionary relationships in the Acropora because it is a fast evolving genus [69], and extremely high rDNA diversity can predate species divergence [70]. Single‑copy nuclear markers have also been used in Acropora phylogenetics (e.g., Mini-C [70,71], Cnox2 [72]; Calmodulin [73]); and an extensive published datasets exists for the Pax-C 46/47 nuclear intron [60,62]. However extensive intra-individual polymorphisms are observed when this marker is cloned (i.e., when different alleles are sequenced from a single PCR product from a single individual, the different alleles can occur in divergent clades), and such genetic heterogeneity greatly complicates the interpretation of extinction risk.

For the purposes of this study we utilize a single-copy mitochondrial marker, the putative mitochondrial control region rns-cox3, for which an extensive amount of data is publicly available (via Genbank, see Table 2). Being maternally inherited, there is one haploid per genome unlike repetitive markers (such as rDNA) that occur in multiple copies. Further, single-copy mitochondrial introns are expected to accumulate mutations relatively rapidly providing many potentially phylogenetically informative characters; lineage sorting is expected to occur relatively rapidly which further benefits the interpretation of evolutionary relationships [74].

Mitochondrial rns-cox3 data with sufficient coverage was available for 65 species and these were downloaded from Genbank [75] (See Table 2 for species names and source details). A total of 640 positions were included in the final dataset and 1st + 2nd + 3rd coding positions + non-coding positions were included. All positions with less than 95% site coverage were eliminated. That is, fewer than 5% alignment gaps, missing data, and ambiguous bases were allowed at any position. For the purposes of this study, evolutionary analyses were conducted in MEGA5 [76].

The evolutionary history was inferred by using the Maximum Likelihood method based on the Kimura 2-parameter model [83] plus a discrete Gamma distribution was used to model evolutionary rate differences among sites (5 categories (+G, parameter = 0.9062)). The tree with the highest log likelihood (−2,744.0067) chosen by Bayesian Information Criterion is shown. The bootstap support values are shown next to the branches based on 1,000 replicates. The tree is drawn to scale, and branch lengths were measured as the number of substitutions per site. Isopora cuneata is included as the outgroup.

In our brief review, we cited examples where species threats or extinctions were dispersed on the phylogenetic tree, so that consequent loss of PD was relatively small, for the given level of species loss. Based on our estimated phylogeny for the Acropora corals (Figure 2), we can conclude that we have a similar case of phylogenetically dispersed threats. However, the Acropora phylogeny suggests the need to move beyond the standard summary of PD loss over whole trees. For Acropora, a finer phylogenetic scale is of interest, because some parts of the tree show clumped threats. In one part of the tree (Figure 3), the three Acropora species found in the Caribbean form a monophyletic group, and two fall into the critically endangered category, while the third is not yet assessed (Figure 2).

How do we best measure the potential impact on PD, including the loss of deeper branches, given the clumped impacts in this part of the tree? Here, we will consider indices that convert the IUCN threat categories (Table 1) to extinction probabilities. Higher threat categories are assigned higher probabilities of extinction [65,84]. Mooers et al. [65] discussed several possible transformations of category to extinction probability, and analyzed the sensitivity of conservation priorities to choice of transformation. Here, we will conservatively adopt the “pessimistic” transformation to extinction probabilities [65] (Table 1).

One existing priority-setting approach based on extinction probabilities is the EDGE program (“evolutionarily distinct and globally endangered”) [84]. EDGE takes phylogeny into account in its calculations of priority scores for threatened species. A given species gains a credit, or partial contribution, from a given ancestral branch equal to 1/n, where n is the number of descendants of that branch. The total of these credits over all ancestral branches is then multiplied by the estimated extinction probability for the species for a final score. Species with higher scores receive higher conservation priority—they have ancestral branches with relatively few other descendants, and have highly threatened status.

The EDGE programme has promoted the practical use of phylogeny in conservation priority setting. However, it has been noted [85] that the method could be improved by incorporating existing PD‑based methods that incorporate probabilities (“expected PD”), as described by [86]. A key advantage over conventional EDGE calculations is that complementarity among species is accounted for effectively.

Here, the complementarity value of a given species reflects the degree to which related species do not already ensure the persistence of shared branches. A phylogenetically distinctive species that is only moderately threatened nevertheless may be given high conservation priority because it has high complementarity—there are no closely related secure species to ensure the persistence of its ancestral branches. The importance of complementarity in “expected PD” calculations has been illustrated for forest songbirds in the genus Myadestes [85] where the “Expected PD calculations would justify a relatively high conservation priority for Myadestes obscures, reflecting not only its increased extinction risk but also its elevated importance, given the expected loss of sister species, in representing the unique PD of this genus”.

We will illustrate this approach by examining two parts of the phylogeny of Figure 2, re-drawn in Figure 4. Suppose two species that are currently near-threatened, A. nasuta and A. pichoni, are competing for conservation priority. In each case, we will focus on the protecting the left-most branch shown in Figure 4 (the more ancestral branches to these are assumed secure, Figure 2). If we apply standard EDGE methods, A. pichoni would gain a large credit for its left-most ancestral branch (1/3, given the 3 descendants of that branch). A. nasuta has smaller credit for its left-most branch (1/4, given 4 descendants). The EDGE score then would be produced by multiplying these credit values by the estimated probability of extinction of the species. Here, near-threatened species, A. nasuta and A. pichoni, have the same probability, and A. pichoni gains EDGE priority, because it has greater credit for its ancestral branch (Figure 4).

In contrast, expected PD calculations take into account the degree of threat to fellow descendants of any ancestral branch. For A nasuta, two of these species are vulnerable, with probabilities of extinction of 0.8 (Figure 2). The total probability of loss of the deep branch is 0.10. For A. pichoni, the sister species are quite secure, including one species of least concern (Figure 2 and Figure 4). The total probability of loss of the deep branch in this case is a much smaller value of 0.03. Therefore priority for A. nasuta would result in much greater gain in the expected persistence of phylogenetic diversity. In contrast, A. pichoni has relatively secure sister species, and so its ancestral PD is already well protected. It can be assigned lower priority. This example illustrates how the EDGE methods provide weaker priority setting when the objective is to maximize persistence of phylogenetic diversity.

With these lessons in mind, we now consider the Caribbean species (Figure 3). Two of the species, A. cervicornis and A. palmata, are critically endangered, and the third species, A. prolifera, is “not assessed”. For purposes of this example, we will consider a future scenario in which A. palmata is also designated critically endangered. The probability of loss of any terminal branch for critically endangered species is 0.99, based on the “pessimistic case” [65] for the conversion of the IUCN categories to extinction probabilities (Table 1). The probability of loss of the longer deep branch of length 35 (Figure 3) can be estimated as 0.99 × 0.99 × 0.99 = 0.97, assuming independent probabilities of extinction. This is the standard assumption for EDGE and expected PD methods. However, we note that the co-distribution of these 3 species in the heavily affected Caribbean region may mean that the probability of loss of the deeper branch is even higher.

In this example, we can use expected PD calculations to derive an expected PD loss. This is the sum of each branch length times its corresponding probability of loss. The total expected PD loss is 82.29 branch length units = 32(0.99) + 17(0.98) + 35(0.97). We can see that the contribution of the deeper branch (0.97 times length of 34 = 33.0) to this expected PD loss is a high proportion of the total expected loss of 82.29. This calculation provides one simple index of the expected PD loss for phylogenetically-clumped impacts in a portion of a phylogenetic tree.

A more informative index in practice would reflect the changes in expected PD loss that could be achieved under a particular candidate conservation action, for a given species or set of species. We extend the basic formulae [85,87], following the approach of [86,88], where the expected-PD change value for a set of species, S, is given by:

ExpectedPD(0) is the expected PD value, with extinction probabilities from current IUCN categories), and expectedPD(1) is the value when the probabilities are converted to a smaller value as a result of a conservation action. We will calculate an expected PD change value for the set of three Caribbean species (Figure 3). Here, expectedPD(0) is the expected PD calculation for this part of the tree, with extinction probabilities from current IUCN categories of 0.99 for each species. The expectedPD(1) is the value when the probabilities are converted to a smaller value—e.g., an extinction probability for the “near-threatened category (0.4). Because the change value reflects a change in expected PD as a consequence of changes in extinction probability for just these species, we do not have to calculate the expected PD for the entire tree.

This index reflects more than just the consequence of individual-species PD losses and can be applied to provide a score for conservation action for a region, as illustrated here for the Caribbean Acropora. When we assume that conservation action can change the extinction probabilities to those for the near-threatened category (0.4; Table 1), we have:

The improvement in expected PD, of 64.67 branch length units, is large compared to the original expected PD loss of 82.29. This improvement occurs even with an outcome where the species are still near-threatened.

It has been argued that the focus of expected-PD assessments on finding good outcomes “on average” may not be the best way to avoid possible “worst-case” losses of PD [85] and that alternative risk aversion approaches for “phylogenetic risk analysis” are needed. Faith [85] presented a hypothetical example where the conservation option that best increased expected PD nevertheless implied a high probability of high PD loss, compared to other conservation options. An alternative conservation option would better avoid worst-case losses of PD, with only a small decrease in expected PD. We will explore this problem for a real phylogeny, again focusing on one portion of the larger corals tree (Figure 5).

Suppose we have some conservation budget that allows for either of two actions. A. batunai could be protected to the extent that its current probability of extinction of 0.8 could be reduced to a probability of extinction of 0.6. A. abrotonoides alternatively could be protected to the extent that its probability of extinction of 0.2 could be reduced to a probability of extinction of 0.0 (Figure 5). In order to maximize expected PD, we calculate the current expected PD and the change in expected PD for each alternative conservation action. Then we choose the conservation option with the greatest gain. The change in expected PD is the sum of all branch lengths, each multiplied by the change in the probability of extinction of the given branch. The conservation option focused on A. batunai would imply a change in expected PD of 22.6 (113 × 0.2; Figure 2). The alternative option focused on A. abrotonoides would imply a greater increase in expected PD (change value) of 24.1 (0.2 × 66 + 0.2 × 0.2 × 154 + .032 × 150 = 13.2 + 6.2 + 4.7; Figure 5). Maximizing expected PD therefore points to the option focused on A. abrotonoides. This choice, however, leaves open the high probability (0.8) that the relatively long branch leading to A. batunai will be lost. On average, the choice of A. abrotonoides may be a good one; however, choosing the best average outcome in this case is not sufficiently risk averse regarding the worst case loss of the relatively long branch of length 113 (Figure 5). If the A. abrotonoides conservation option is not selected, the probability of a PD loss as high as 113 is only 0.04. However, the possibility that maximizing an expected diversity outcome may not be sufficiently risk averse regarding possible worst case losses may be an important issue for conservation of corals PD; there are many cases where a threatened species is similar to A. batunai in being the sole descendent of a moderately long branch.

No procedure for phylogenetic risk analysis was provided by [85]. However, expected PD calculations are flexible enough to be used to address this problem. While there seems to be no one formula that would provide a simple protocol for phylogenetic risk analyses, the best general guideline is to proceed as follows: nominate classes of “worst case” PD loss outcomes, and then assess the current probability of occurrence of these larger PD losses. Conservation options then can be assessed according to implied changes in these probabilities of worst-case losses, using the normal calculations for expected PD.

Our review of studies of climate change impacts on PD pointed to a notable case where PD loss was relatively small, but there were dramatic projected changes in the geographic distribution of PD [38]. This study suggested that “the tree of life faces a trend towards homogenization across the continent” but these changes were not quantified. Measures of PD homogenization (or the opposite: PD spatial heterogeneity) would be useful for tracking changes over time and for making comparisons among taxonomic groups and among regions.

The term “biotic homogenization” refers to the increase in the biotic similarity of different localities in a region, and is now recognized as a major issue in biodiversity science (for review, see [89]). Typically, the focus is on the species level, but these indices suggest analogous measures of PD homogenization. Olden et al. [89] describe several species-level calculations: “taxonomic homogenization is calculated using species presence or absence data to examine the degree of similarity in community composition, and can be quantified using any one of a suite of similarity indices, diversity indices, cluster analyses or ordination approaches.”

Olden et al. [89] noted that most homogeneity analyses use the Jaccard measure to calculate dissimilarity among localities. The Jaccard measure has a much-used phylogenetic counterpart based on PD [90]. The dissimilarity of two places/communities in this case reflects the count of the number of branches found (represented) in one place but not the other (see also [91]). This phylogenetic dissimilarity provides a simple PD-based spatial heterogeneity measure. Consider two localities or ecosystems, i and j. Let DPD(i,j) be the PD dissimilarity. We define the PD heterogeneity of the region, HPD1, as the average value of DPD(i,j) over all i and j.

This measure may be useful for understanding changes in the PD distribution of corals as a result of possible climate change impacts. The geographic distribution of corals has been described based on 141 different eco-regions or ecosystems [92]. These can define “localities” for PD spatial heterogeneity assessments. Would loss of endangered coral species increase or decrease the global PD spatial heterogeneity? The three critically endangered species (Figure 2 and Figure 3) are only found in the Caribbean ecosystem types. This implies that a total branch length of 35 + 32 + 17 = 84 currently contributes to the PD dissimilarity of a Caribbean ecosystem to other global ecosystems. If the three Caribbean species were lost, the PD dissimilarity of a Caribbean ecosystem to other global ecosystems would appear to be smaller, contributing to a smaller HPD1. However, this extreme case where all Acropora are lost from the region has further implications. Those three species are the only Acropora species in the Caribbean. Consequently, not only those relatively short branches counted above but also the branch uniting all Acropora (Figure 2) is lost from the Caribbean ecosystem types. This loss of the deeper branch increases the PD dissimilarity of a Caribbean ecosystem to other global ecosystems, which have retained one or more Acropora species. Thus, the HPD1 measure would indicate an increase in spatial heterogeneity in this extreme case. In general, HDP1 could indicate lower heterogeneity for initial losses of species and branches and then greater heterogeneity as some ecosystems lose deeper branches while other ecosystems retain them.

A possible limitation of HPD1 is that species and branches that are rare—for corals, found in few ecosystems—contribute to relatively few dissimilarities, among all i and j, and so will not have much influence on the overall value. Loss of rare PD therefore typically will not be reflected as a large change in HPD1.

We suggest an alternative phylogenetic spatial heterogeneity measure that is more sensitive to changes in rare species, including the loss of rare PD. We follow other workers (e.g., [93] in creating a phylogenetic version of a general measure of diversity and evenness, developed by Hill [94]:

We follow the notation in Chao et al. [93], where ^qD is the effective number of species, S is the number of species, and p_i is the proportional abundance of the ith species. The parameter q can be varied in order to give more or less weight to the most abundant features, defining a range of “Hill numbers”. When the ^qD index value is large, the “effective number of species” is large, and we have greater heterogeneity.

Chao et al. [93] extended this fundamental measure of diversity and evenness to PD:

L_i is the length of branch i from the phylogenetic tree, and a_i is the total abundance of all species descended from branch I (T is the total of all a_i). When q is 0, the measure is equivalent to PD. Chao et al. [93] offered no general phylogenetic model as a rationale for this measure. However, the basic rationale for PD—branch lengths as counting features (Section 2)—provides a simple justification for this PD-based “Hill numbers” framework. It can be interpreted as equivalent to applying the standard species-level Hills measure, but with features (as indicated by PD) substituted for species.

For Chao et al., the abundance of a branch is the summed abundance over descendant species. Here, we generalize this measure to cover the case where “abundance” reflects geographic abundance—that is, some measure of geographic range or rarity. We will consider number of localities (or ecosystems in the case of corals) containing a given branch as the abundance measure for that branch. This differs from the Chao et al. formulation in that the abundance for a branch is not the sum but the union over the abundance of descendants. We then define: Our notation is the same as above, except that we use r_i to refer to the use of a range-type count as our abundance measure. When HPD2 is large, the effective amount of PD is large, and we have greater heterogeneity. We will explore the application of the measure for q equal to 1. The Hill number is undefined for q = 1, but, following [93,94], it is defined by a limit as q approaches 1, yielding: We now will apply this measure to the Caribbean species, using counts of the number of ecosystems containing a branch/species as the basis for abundance of that branch/species (Figure 6). For this example, we do not have information on the numbers of ecosystems for all other species and branches from the overall tree (Figure 2). However, we can illustrate properties of the method by considering an additional branch of length 32 that is found in a large number of ecosystems.

We begin by considering a case where the number of ecosystems for A cervicornis has dropped from 8 (Figure 6) to just 2 (scenario A in Table 3). The value of HPD2 is calculated as follows:

Now we compare this value of HPD2 to the value obtained for scenarios B and C (Table 3). In scenario B, A cervicornis becomes even rarer (present in only 1 ecosystem). HPD2 goes down, reflecting lower spatial PD heterogeneity. In contrast, in scenario C, the common species, at the end of a branch also of length 32, is now absent from one of its 50 ecosystems. HPD2 goes up, reflecting higher spatial PD heterogeneity. Thus, these simple scenarios suggest that HPD2 provides a measure of phylogenetic spatial heterogeneity that is sensitive to reductions in abundance of rare species/branches. This captures an important aspect of geographic homogenization from climate change impacts, and may provide a basis for the monitoring of PD change that complements the conventional monitoring of PD losses.