Complementarity: A Key PD Attribute

Interpretation of PD as counting-up features extends the fundamental species-level measure of “complementarity” to the features level. A taxon complements others in representing additional evolutionary history (Faith 1994a, b), as depicted in the branches of the estimated phylogeny. The degree of complementarity reflects the relative number of additional features contributed by that species. For example, given some subset of species that are well-protected, and two species in that taxonomic group that are endangered, the priority for conservation investment may depend on the relative gains in feature diversity (the complementarity values) expected for each species.

Given the importance of complementarity, particularly when dealing with complex conservation issues, it is worth comparing PD with some published phylogenetic calculations. Calculating PD naturally requires that phylogenetic overlap among taxa be taken into account, so that branches – and corresponding features – are not multi-counted. Often, when PD is not applied correctly, the result is a misleading multiple-counting of features. For example, Perez-Losada et al. (2002) incorrectly calculated PD values for sets of freshwater crab species. They simply added up the PD values for individual taxa to produce the overall score for the set of taxa. Consequently, their measure, in multi-counting branches, did not correspond to a valid calculation of PD. Similarly, a study by Vamosi and Wilson (2008), using the term “EH” to refer to evolutionary history, stated that “the combined EH of all the angiosperm orders and families was estimated at 35,244 million years by summing the ages of the separate clades over the angiosperm phylogeny.” Their “combined EH” measure, in multi-counting branches, did not correspond to an estimate of PD. PD calculations would have better captured their intention to assess loss of traits/features.

Calculations Using Phylogenetic Distinctiveness Fail to Integrate Complementarity

More complex calculations have used measures of phylogenetic or taxonomic “distinctiveness”. These values, calculated for individual taxa, are then to be combined to score sets of taxa or areas. The problem for all popular variants of this approach – whether the terminal taxa (or tips for the tree) are individuals, populations, or places, is that the scores for the taxa do not add up to the proper scores for sets of taxa.

In an early example of such an approach (López-Osorio and Miranda-Esquivel 2010), an area received a score equal simply to the sum of individual scores of member species. López-Osorio and Miranda-Esquivel (2010) used 50 phylogenies covering multiple taxonomic groups in the Amazon, and integrated this phylogenetic information into conservation priority setting in order to “establish conservation priorities for Amazonia's areas of endemism on the basis of measures of evolutionary distinctiveness”. “Taxonomic rarity” was to be indicated by species that are members of a small number of groups on the cladogram. López-Osorio and Miranda-Esquivel (2010) used an approach suggested by Posadas et al. (2001), which extends the W Index of Vane-Wright et al. (1991). The W index assigns to each species a value that is inversely related to the count of the number of groups on the phylogenetic tree for which the species is a member. Thus, a species that is taxonomically (phylogenetically) distinctive will have a high W value reflecting its relatively few close relatives. The key index derived from W is the We index (each W value is divided by the number of areas with that species, yielding We). An area receives a score, equal to the sum of the We values of its species. This is to indicate a degree of endemism that integrates phylogeny.

Faith et al. (2004) compared those measures to the phylogenetic diversity measure, PD, and its associated calculations. Faith et al. argued that the We indices for areas differ from PD in not considering the degree of phylogenetic overlap/nonoverlap among species (phylogenetic complementarity), and so may fail to effectively represent evolutionary history in priority sets of species or areas. A simple example of the problem is illustrated in Fig. 1. The We method cannot distinguish between the scenarios, yet the PD-endemism value differs for the two.

A family of relatively new measures, while based on PD, also does not fully account for complementarity. ED (“evolutionary distinctiveness”; Isaac et al. 2007; see also Collen et al. 2011) divides up the total PD among all species on the given phylogeny. This provides a fixed score for each species, reflecting its contribution to the total evolutionary history (PD). A species receives a partial credit for each ancestral branch. Thus, ED appears to capture the idea of complementarity among species. However, a key limitation is apparent when species ED scores are combined to provide scores for areas or for sets of priority species. Here, the ED approach does not take phylogenetic complementarity among the species into account. For example, consider the phylogenetic tree in Fig. 2. Based on summed ED scores, we cannot distinguish between an area with four closely related species and an area with four distantly related species; yet the scenario on the right corresponds to higher PD.

Such limitations may be critical in assessing diversity within communities or assemblages. In this context, phylogenetic diversity may be predictive of functionality or productivity (Cadotte et al. 2009). Dalerum (2013) set out to investigate the possible correspondence between phylogenetic diversity and functional diversity for assemblages of large carnivores. While Dalerum referred to “phylogenetic diversity” and to “PD”, in fact, their study used ED, not PD. Dalerum calculated ED for each species and then “estimated the ED of each assembly as the sum of the ED of contributing species.” As the simple example of Fig. 2 shows, this summed ED score will not correspond to the total PD. Unfortunately, the Dalerum study therefore provides little useful evidence for the claimed relationship between phylogenetic and functional diversity in assemblages of large terrestrial carnivores.

These same issues arise for regional or global studies. An interesting study by Daru et al. (2013) on mangroves “identified biogeographic regions that are relatively species-poor but rich in evolutionary history.” While the study presented results referring to loss of “mangrove phylogenetic diversity”, in fact, the measure used was based on ED calculations. Daru et al. argued for the significance of the finding that “areas with a high proportion of species experiencing global declines correspond to areas of unique evolutionary history” arguing that “the loss of currently threatened species might still have a disproportionate impact on mangrove

Fig. 2 Two drawings of a hypothetical phylogenetic tree. For this simple tree, the ED value is the same for every species. Given the unit length branches, it is 1 + ½ + ¼ + 1/8 + 1/16 = 1.94. Dark branches in each case indicate the PD represented by the species in an area. On the left, the area has four closely related species and on the right, the area has four distantly related species – and higher total PD. The PD on the left is 9 units, compared to a much higher PD of 15 on the right

phylogenetic diversity regionally”. This conclusion was based on apparent “overlap between regions in which species are undergoing declines and regions rich in evolutionarily distinct species.” Unfortunately, their use of a sum of species' ED values as the regional indicator of phylogenetic diversity loss provides only weak evidence. To see this I again consider Fig. 1. For both trees, the sum of the ED values for the four species found in area B is the same. Thus, ED cannot distinguish between the large PD loss when the species are phylogenetically clumped, and the smaller PD loss when the species are phylogenetically dispersed (as in Fig. 1, left). Again, the PD loss corresponding to an area loss is not well-indicated by total ED, because phylogenetic complementarity is ignored.

A contrasting study is that of Abellán et al. (2013), who found that most of the highly evolutionarily distinct and vulnerable taxa were not covered by any national parks. Critically, while distinctiveness was noted, their proposed solution was based on priorities for areas providing increased PD. They concluded that “when additional conservation areas were selected maximizing the number of unrepresented species, the variation in PD could be very high, and as a consequence, depending on the group and the number of areas added, they could preserve much less evolutionary history than when they were specifically selected to maximize PD.”

The weakness of summed ED scores resembles the limitations of the LópezOsorio and Miranda-Esquivel method. This kind of problem seems to link to a longstanding idea that we simply might add up scores for individual taxa, perhaps with some distinctiveness “weighting”. For example, Gotelli and Chao (2013), in the Encyclopedia of Biodiversity, claim that we can calculate “PD” by appropriately weighting the species and then applying conventional species indices such as richness: “The concept of traditional diversity can therefore be extended to consider differences among species.... Differences among species can be based directly on their evolutionary histories, either in the form of taxonomic classification (referred to as taxonomic diversity) or phylogeny (referred to as phylogenetic diversity (PD)) … weighting each species by a measure of its …phylogeny.”

The relationship between ED and PD has been investigated previously for calculations that use probabilities of extinction. An EDGE score (Isaac et al. 2007) simply multiplies extinction probability by EDevolutionary distinctiveness (a score that gives each species some partial credit for ancestral branches). Naturally, that arbitrary partial credit and multiplication is not a particularly good way to determine changing expectations about the diversity that persists as the status of species changes. Faith (2008) showed how the arbitrary partial credit and multiplication in EDGE-type methods does not take phylogenetic complementarity into account, and so will not do a good job in determining conservation priorities delivering high expected PD. Faith also suggested that such priorities can be set by directly looking at expected PD gains and losses. May-Collado and Agnarsson (2011) and Kuntner et al. (2011) also concluded that the PD methods are better in achieving the goal of phylogeny-based conservation than EDGE.

These results are relevant to an interesting study by Safi et al. (2013), who set out to “identify regions of the world where priority species are concentrated, much like the original definition of the biodiversity hotspot.” They identified those regions/ countries having the “highest accumulation of top mammal species ranked in terms of their EDGE score” and argued that “Conservation resources would therefore be best allocated among the countries in these regions to protect mammal species with the highest EDGE scores.”

Unfortunately, this may be a weak guideline for the efficient use of limited conservation resources. Their study recalls the issues raised by the use of ED methods in the Daru et al. study, where a given ED score could correspond either to phylogenetically clumped species and a large PD loss (as in Fig. 1, left), or phylogenetically dispersed species and smaller PD loss (Fig. 1, right). Once again, the potential PD loss arising from a given area loss is not well-indicated by a summation of ED (or EDGE values), because phylogenetic complementarity is ignored.

Recent extensions of the ED methods provide some important modifications to take into account species' range extent and abundance; however, these interesting innovations may suffer similar problems to those described above. Cadotte et al. (2010) introduced one important extension by taking into account numbers of individuals of a given species in a community or ecosystem. The rationale, analogous to that of conventional ED, is that individuals differ in their representation of evolutionary history or phylogenetic diversity, and can receive partial “credit” for a given ancestral branch. Given that PD has been linked to ecosystem functioning (e.g. Cadotte et al. 2008, 2009), the loss of some individuals (e.g. those from species with few individuals and uniquely representing some long branches) should set off alarm bells if we want to maintain ecosystem functions. Cadotte et al. argue that their measure “can be used by managers to identify individuals, and by extension species, whose loss corresponds to the greatest loss of evolutionary information. If, as has been proposed, evolutionary history captures functional diversity necessary for ecosystem processes and services (e.g. see Cadotte et al. 2008), minimizing this loss of evolutionary diversity might maximize the preservation of ecosystem function.”

Their basic measure, AEDi, follows the partitioning logic of ED; here, it records the share of all branches credited to any individual of species i. A problem is that, when AEDi values are summed over individuals, complementarity once again is ignored. This implies that the score for a set of individuals (say, those lost under a nominated management regime) cannot be a reliable indicator of potential PD loss – yet it is PD that matters, given its link to functions. We can see the problem by adapting the example of Fig. 1, imagining that the terminal branches represent individuals. The AED scores for the set of four individuals on the left (marked with B) is the same as that on the right; yet, the loss of PD feature diversity and perhaps functional diversity is much greater in the scenario on the left. Consequently, there seems to be no justification for Cadotte et al.'s claim that AED can be “used by managers to identify individuals, whose loss corresponds to the greatest loss of evolutionary information. … minimizing this loss of evolutionary diversity might maximize the preservation of ecosystem function.” For a single individual, AEDi may be a useful index, but if a management strategy potentially impacts numerous individuals, AED will not provide a good comparative index of PD loss.

A measure similar to AED is the “biogeographically weighted evolutionary distinctiveness” metric (BED or BEDT; Cadotte and Davies 2010). BED extends ED by also partitioning the credit among (for example) the grid cells occupied by each species in a region. In this way, range extent information for species is incorporated along with phylogenetic distinctiveness. For species i, BEDi is a weighted sum of the ancestral branch lengths. Each length is weighted by the inverse of the sum, over all descendent species of the branch, of the number of cells occupied by the descendent species (if each descendent species is found in just one cell, then BEDi is the ED of species i). The BEDT score for a cell is the sum of the BEDi scores for all species i found in the cell. Thus, restricted range species that also uniquely represent deep branches will count a lot in the overall scores for grid cells or other areas.

As an example, in Fig. 3, suppose that we can only protect one area. Which is best? For the Area (1) in Fig. 3a, the BEDT score is BEDa + BEDb + BEDc + BEDd. The BEDi for each of these four member species (a, b, c, d) is the same, and is equal to m/1 + L/5. Here, the length L is divided by 5 because a, b, c, d, and x each are found in one area; thus, the sum of the number of cells occupied is 5. The BEDT score equals 4 times (m/1 + L/5), or 4 m + 4(L/5).

For the Area (2) in Fig. 3b, the BEDi for each of the four member species again is the same, and equal to m/1 + L/5. The length L again is divided by 5 because A and the four sister species each are found in one area. The BEDT score for Area (2) is BEDA + BEDB + BEDC + BEDD, or 4 m + 4(L/5). BEDT therefore makes no distinction between the two areas. In contrast, the PD offered by Area (2) is much greater. Thus, BED fails to detect a huge gain in raw PD (and in restricted range PD)

Fig. 3 Portions of hypothetical phylogenetic trees occurring in two areas. (a) Area (1) uniquely has species a, b, c, d which are on small branches of length m, and are at the end of a long branch of length L. Species x is not found in Area (1), but uniquely occurs in some other area. (b) Area (2) uniquely has species A, B, C, D, which are on small branches of length m, and are at ends of different long branches of length L. For each member species, four other sister species on small branches of length m all uniquely occur in some other area

that could be achieved through protection of the area in Fig. 3b. BED (and the related method of Tucker et al. 2012), is not effective for setting conservation priorities that reflect both phylogenetic diversity and range-restrictedness. I conclude that there is little justification for Cadotte et al.'s conclusion that “Metrics such as BEDT, which combines evolutionary diversity and rarity into a single measure of diversity, may allow a more holistic approach to conservation prioritization.”

I noted above that PD gives priority to Area 2 in Fig. 3b, because it offers almost 4 times as much PD. However, this basic PD calculation does not take range rarity into account. Weighted PD-endemism or “PE” (the sum of branches represented in an area, each inverse-weighted by its range, expressed as number of cells; Rosauer et al. 2009) also gives priority to Area 2, because it scores Area 1 with a PE score of 4 m + L/2, and Area 2 with a higher PE score of 4 m + 4(L/2).

PE has an interesting property analogous to ED, in that a given cell receives proportional credit for a branch (analogous to the basic ED score where a species gets proportional credit for branches). PE performs well in the example above; however, it shares a weakness of ED, when combined with probabilities and summed-up to provide overall scores. To see this, I consider a recent study of the phylogeny of Malagasy lemuriformes (Gudde et al. 2013). This study set out to identify places with a concentration of threatened phylogenetic distinctive and rare species. Here, the PE measure was combined with probabilities of extinction. Their “imperilled phylogenetic endemism” (IPE) index is the sum over all branches of branch length times its probability of extinction (product of extinction probabilities of all descendents) times the inverse of its range-extent.

Gudde et al. (2013) claimed to “quantify where on the landscape at-risk evolutionary history is concentrated.” However, their “imperilled phylogenetic endemism” (IPE) index appears to have the weakness that it could highlight places that have no threatened branches at all. As a revealing example, suppose that area A has 20 species, all of IUCN “least concern” (see IUCN 2006, 2012). Suppose that this corresponds to a low probability of extinction of 0.025 (for methods and discussion, see Mooers et al. 2008; Faith and Richards 2012). Each species is found in only ten areas. Suppose that area B has five species, all IUCN “critically endangered” (probability of extinction assumed to be a higher 0.4). Each species is found in 50 areas, but all are found together in this one area. Suppose also that each species is at the end of a branch of some unit length. Also, for simplicity, I will ignore deeper branches (assuming that all species have numerous secure sisters).

IPE in this simple case is equal to the product of the number of branches, the probability of extinction and the inverse of the number of cells containing a given branch. Application of IPE gives area A the higher priority; the IPE score equals 20 times 0.025 times 1/10 or 0.05. IPE gives area B the lower priority; the IPE score equals 5 times 0.4 times 1/50 or 0.04. Application of IPE therefore would ignore the opportunity to save, with a reserve based around area B, five critically endangered species. Instead, IPE would give preference to an area with 20 non-threatened species! This reveals the key limitation of the approach. IPE is supposed to reflect a concentration of range restricted, threatened species. Gudde et al. (2013) argued that “our mapping does indeed quantify where at risk PD is concentrated”. However, IPE, in the example above, actually quantified where not-at-risk PD was concentrated!

This weakness of IPE is similar to that of EDGE (see above and Faith 2008). Both methods suffer the weakness that phylogenetic overlap of species is not effectively taken into account. For EDGE type assessments, an existing probabilistic PD approach (Witting and Loeschcke 1995) performs better (Faith 2008; see also May-Collado and Agnarsson 2011; Kuntner et al. 2011). In the final section, I examine the prospects for using this “expected PD” approach to address some conservation assessment problems that have been unsuccessfully treated by the ED type methods.

The PE measure is relevant to another study that attempts to integrate range extent and threat information into PD assessments. In their global study on conservation of phylogenetic diversity of birds, Jetz et al. (2014) devised a measure related to ED to provide scores for regions or areas. Their “EDR” score for a species is simply the ED value divided by the range (number of occupied cells) of the species. Total EDR for a given region then is the summed EDR of all species occurring in the region. Jetz et al. ask, “Under an objective of minimizing global PD loss, how do ED and EDR perform as metrics for a rule-based approach to taxonand area-based conservation priority setting?” They claim that EDR indicates high priority conservation areas. However, this modified ED score, when summed to produce EDR area scores, again will not reflect PD (Fig. 2), nor amount of PD that would be lost (Fig. 1).

An alternative, incorporating range information, is a modification of PE.

A threatened-PE (TPE) area score only counts up threatened branches (e.g. those having only threatened descendents; see also Faith 2015). If the range-extents of many species are declining, TPE may be an effective simple index to monitor over time. The TPE of an area will increase if more of its species/branches are threatened or if range extent decreases for some of its species.

 
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