Abstract

How to define a partition of individuals into species is a long-standing question called the species problem in systematics. Here, we focus on this problem in the thought experiment where individuals reproduce clonally and both the differentiation process and the population genealogies are explicitly known. We specify three desirable properties of species partitions: (A) Heterotypy between species, (B) Homotypy within species and (M) Genealogical monophyly of each species. We then ask: How and when is it possible to delineate species in a way satisfying these properties? We point out that the three desirable properties cannot in general be satisfied simultaneously, but that any two of them can. We mathematically prove the existence of the finest partition satisfying (A) and (M) and the coarsest partition satisfying (B) and (M). For each of them, we propose a simple algorithm to build the associated phylogeny out of the genealogy. The ways we propose to phrase the species problem shed new light on the interaction between the genealogical and phylogenetic scales in modeling work. The two definitions centered on the monophyly property can readily be used at a higher taxonomic level as well, e.g., to cluster species into monophyletic genera.

Highlights

  • Models in macro-evolution have traditionally been centered on species

  • In the last two decades, a popular way of studying macro-evolution has followed, consisting in performing computer-intensive simulations of individual-based stochastic processes of species diversification (Jabot and Chave 2009; Aguilée et al 2011; Rosindell et al 2015; Gascuel et al 2015; Missa et al 2016). These models rely on three major steps: (i) The genealogy of individuals is produced under a fixed or stochastic scenario of population dynamics; (ii) A process of phenotypic differentiation superimposed on the genealogy generates a partition of individuals into phenotypic groups; (iii) A species definition is postulated and is used to cluster individuals into different species, in relation to both the genealogy and phenotypic groups

  • These three steps allow modelers to track the evolutionary history of species, where extinction and speciation events emerge from the genealogical history of individual organisms

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Summary

Introduction

Models in macro-evolution have traditionally been centered on species. The so-called lineage-based models of diversification form a wide class of models considering species as key evolutionary units, thought of as particles that can give birth to other particles (i.e., speciate) during a given lifetime (i.e., before extinction) (see Stadler 2013; Pyron and Burbrink 2013; Morlon 2014 for reviews). Rely on three major steps: (i) The genealogy of individuals is produced under a fixed or stochastic scenario of population dynamics; (ii) A process of phenotypic differentiation superimposed on the genealogy generates a partition of individuals into phenotypic groups; (iii) A species definition is postulated and is used to cluster individuals into different species, in relation to both the genealogy and phenotypic groups These three steps allow modelers to track the evolutionary history of species, where extinction and speciation events emerge from the genealogical history of individual organisms. We discuss the relevance of these propositions from both empirical and theoretical points of view

Five species definitions in individual-based models
Three desirable properties of species definitions
The lacy and loose species definitions
Discussion
B Proof of Theorem 1
Defining the supremum and the infimum of a set of X -partitions
C Construction of the lacy and loose phylogenies

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