Neutral phylogenetic models and their role in tree-based biodiversity measures (2405.17833v3)
Abstract: A wide variety of stochastic models of cladogenesis (based on speciation and extinction) lead to an identical distribution on phylogenetic tree shapes once the edge lengths are ignored. By contrast, the distribution of the tree's edge lengths is generally quite sensitive to the underlying model. In this paper, we review the impact of different model choices on tree shape and edge length distribution, and its impact for studying the properties of phylogenetic diversity (PD) as a measure of biodiversity, and the loss of PD as species become extinct at the present. We also compare PD with a stochastic model of feature diversity, and investigate some mathematical links and inequalities between these two measures plus their predictions concerning the loss of biodiversity under extinction at the present.
- Kubatko L, Knowles LL. 2023 Species Tree Inference:A guide to methods and applications. Princeton University Press.
- Feller W. 1939 Die grundlagen der volterraschen theorie des kampfes ums dasein in wahrscheinlichkeitstheoretischer behandlung. Acta Biotheor. 5, 11–40.
- Kendall DG. 1948 On the generalized ‘birth-and-death’ process. Ann. Math. Stat. 19, 1–15.
- Jagers P. 1992 Stabilities and instabilities in population dynamics. J. Appl. Prob. 80, 770–780.
- Harding EF. 1971 The probability of rooted tree shapes generated by random bifurcation. Adv. Appl. Prob. 3, 44–77.
- Etherington IMH. 1940 On non-associative combinations. Proc. Roy. Soc. Edinburgh 59, 153–162.
- Mahmoud HM. 1992 Evolution of Random Search Trees. Wiley.
- Lynch M. 1965 More combinatorial properties of certain trees. Comput. J. 7, 299–302.
- Sanderson MJ. 1996 How many taxa must be aampled to identify the root node of a large clade?. Syst. Biol. 45, 168–173.
- Bienvenu F, Steel M. 2024 0–1 Laws for pattern occurrences in phylogenetic trees and networks. Arxiv 2402.04499 (Bull. Math. Biol. in press).
- Disanto F, Fuchs M. 2023 Distribution of external branch lengths in Yule histories. Elec. J. Combin. 30.
- Faith DP. 1992 Conservation evaluation and phylogenetic diversity. Biol. Conserv. 61, 1–10.
- Manson K. 2024 The robustness of phylogenetic diversity indices to extinctions. J. Math. Biol. In press.
- Raup DM. 1993 Extinction: Bad Genes or Bad Luck? Oxford University Press.
- Feller W. 1950 An Introduction to Probability Theory and Its Applications vol. 1. Wiley 3rd edition.
- Overwater M. 2023 On the mathematical links between phylogenetic and feature diversity. MSc Thesis, University of Canterbury.
- Pitman J. 2006 Combinatorial stochastic processes: École d’été de probabilités de Saint-Flour XXXII-2002. Springer-Verlag.