Stochastic Models for the Inference of Life Evolution

SMILE | Stochastic Models for the Inference of Life Evolution | Collège de France


SMILE is an interdisciplinary research group gathering mathematicians, bio-informaticians and biologists.
SMILE is affiliated to the Institut de Biologie de l'ENS, in Paris.
SMILE is hosted within the CIRB (Center for Interdisciplinary Research in Biology) at Collège de France.
SMILE is supported by Collège de France and CNRS.
Visit also our homepage at CIRB.


SMILE is hosted at Collège de France in the Latin Quarter of Paris. To reach us, go to 11 place Marcelin Berthelot (stations Luxembourg or Saint-Michel on RER B).
Our working spaces are rooms 107, 121 and 122 on first floor of building B1 (ask us for the code). Building B1 is facing you upon exiting the traversing hall behind Champollion's statue.


You can reach us by email (amaury.lambert - at - ; (guillaume.achaz - at - or (smile - at -

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The species problem from the modeler’s point of view

How to define and delineate species is a long-standing question sometimes called the species problem. In modern systematics, species should be groups of individuals sharing characteristics inherited from a common ancestor which distinguish them from other such groups. A good species definition should thus satisfy the following three desirable properties: (A) Heterotypy between species, (B) Homotypy within species and (E) Exclusivity, or monophyly, of each species. In practice, systematists seek to discover the very traits for which these properties are satisfied, without the a priori knowledge of the traits which have been responsible for differentiation and speciation nor of the true ancestral relationships between individuals. Here to the contrary, we focus on individual-based models of macro-evolution, where both the differentiation process and the population genealogies are explicitly modeled, and we ask: How and when is it possible, with this significant information, to delineate species in a way satisfying most or all of the three desirable properties (A), (B) and (E)? Surprisingly, despite the popularity of this modeling approach in the last two decades, there has been little progress or agreement on answers to this question. We prove that the three desirable properties are not in general satisfied simultaneously, but that any two of them can. We show mathematically the existence of two natural species partitions: the finest partition satisfying (A) and (E) and the coarsest partition satisfying (B) and (E). For each of them, we propose a simple algorithm to build the associated phylogeny. We stress that these two procedures can readily be used at a higher level, namely to cluster species into monophyletic genera. The ways we propose to phrase the species problem and to solve it should further refine models and our understanding of macro-evolution.



The genealogical decomposition of a matrix population model with applications to the aggregation of stages

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population models to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.

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