Manson, K. | Search bioRxiv

bioRxiv2023

Spaces of phylogenetic diversity indices: combinatorial and geometric properties

Biodiversity is a concept most naturally quantified and measured across sets of species. However, for some applications, such as prioritising species for conservation efforts, a species-by-species approach is desirable. Phylogenetic diversity indices are functions that apportion the total biodiversity value of a set of species across its constituent members. As such, they aim to measure each species individual contribution to, and embodiment of, the diversity present in that set. However, no clear definition exists that encompasses the diversity indices in current use. This paper presents conditions that define diversity indices arising from the phylogenetic diversity measure on rooted phylogenetic trees. In this context, the diversity index score given to a species represents a measure of its unique and shared evolutionary history as displayed in the underlying phylogenetic tree. Our definition generalises the diversity index notion beyond the popular Fair Proportion and Equal-Splits indices. These particular indices may now be seen as two points in a convex space of possible diversity indices, for which the boundary conditions are determined by the underlying shape of each phylogenetic tree. We calculated the dimension of the convex space associated with each tree shape and described the extremal points.

evolutionary biology↗

bioRxiv2022

Information Accumulation and Loss as a Foundation for Sound Phylogenetic Biodiversity Metrics

AO_SCPLOWBSTRACTC_SCPLOWPhylogenetic metrics are essential tools used in the study of ecology, evolution and conservation. Phylogenetic diversity (PD) in particular is one of the most prominent measures of biodiversity, and is based on the idea that biological features accumulate along the edges of phylogenetic trees that are summed. We argue that PD and many other phylogenetic biodiversity metrics fail to capture an essential process that we term attrition. Attrition is the gradual loss of features through causes other than extinction. Here we introduce EvoHeritage, a generalisation of PD that is founded on the joint processes of accumulation and attrition of features. We argue that whilst PD measures evolutionary history, EvoHeritage is required to capture a more pertinent subset of evolutionary history including only components that have survived attrition. We show that EvoHeritage is not the same as PD on a tree with scaled edges; instead, accumulation and attrition interact in a more complex non-monophyletic way that cannot be captured by edge lengths alone. This leads us to speculate that the one dimensional edge lengths of classic trees may be insufficiently flexible to capture the nuances of evolutionary processes. We derive a measure of EvoHeritage and show that it elegantly reproduces species richness and PD at opposite ends of a continuum based on the intensity of attrition. We demonstrate the utility of EvoHeritage in ecology as a predictor of community productivity compared with species richness and PD. We also show how EvoHeritage can quantify living fossils and resolve their associated controversy. We suggest how the existing calculus of PD-based metrics and other phylogenetic biodiversity metrics can and should be recast in terms of EvoHeritage accumulation and attrition. Candidate cover image O_FIG O_LINKSMALLFIG WIDTH=186 HEIGHT=200 SRC="FIGDIR/small/499419v5_ufig1.gif" ALT="Figure 1"> View larger version (70K): org.highwire.dtl.DTLVardef@1a4b8cforg.highwire.dtl.DTLVardef@16145dborg.highwire.dtl.DTLVardef@1316b1eorg.highwire.dtl.DTLVardef@16fb06b_HPS_FORMAT_FIGEXP M_FIG C_FIG Artistic cover image prepared for this manuscript. The central tree depicts the gain and loss of Evolutionary Heritage (EvoHeritage) along each edge with its many coloured sections. EvoHeritage is proposed as an expansion of the concept of phylogenetic diversity. Around the outside of the tree are species that feature in our two practical applications of the EvoHeritage calculus: mammals identified as living fossils and plants included in our study of community productivity. The cover image was generated by James Rosin-dell following discussions with co-authors. The Caenolestes outline (representing shrew opossums) and Dromiciops outline (monito del monte) used as components of this image are credited to Sarah Werning and provided under a CC BY 3.0 license; both images were recoloured in brown and placed over a shaded circle. All other images used as components are from the public domain. We thank Mina Mincheva for useful feedback on earlier drafts of the cover image.

evolutionary biology↗

bioRxiv2022

The Robustness of Phylogenetic Diversity Indices

Phylogenetic diversity indices provide a formal way to apportion evolutionary history amongst living species. Understanding the properties of these measures is key to determining their applicability in conservation biology settings. In this work, we investigate some questions posed in a recent paper by Fischer, Francis & Wicke appearing in Systematic Biology (Vol. 72(3), 2023). In that paper, it is shown that under certain extinction scenarios, the ranking of the surviving species by their Fair Proportion index scores may be the complete reverse of their ranking beforehand. Our main results here show that this behaviour extends to a large class of phylogenetic diversity indices, including the Equal-Splits index. We also provide a necessary condition for reversals of Fair Proportion rankings to occur on phylogenetic trees whose edge lengths obey the ultrametric constraint. Specific examples of rooted phylogenetic trees displaying these behaviours are given and the impact of our results on the use of phylogenetic diversity indices more generally is discussed.

evolutionary biology↗