0-1 Laws for Pattern Occurrences in Phylogenetic Trees and Networks.

In a recent paper, the question of determining the fraction of binary trees that contain a fixed pattern known as the snowflake was posed. We show that this fraction goes to 1, providing two very different proofs: a purely combinatorial one that is quantitative and specific to this problem; and a proof using branching process techniques that is less explicit, but also much more general, as it applies to any fixed patterns and can be extended to other trees and networks. In particular, it follows immediately from our second proof that the fraction of d-ary trees (resp. level-k networks) that contain a fixed d-ary tree (resp. level-k network) tends to 1 as the number of leaves grows.

The kinship matrix: inferring the kinship structure of a population from its demography.

The familial structure of a population and the relatedness of its individuals are determined by its demography. There is, however, no general method to infer kinship directly from the life cycle of a structured population. Yet, this question is central to fields such as ecology, evolution and conservation, especially in contexts where there is a strong interdependence between familial structure and population dynamics. Here, we give a general formula to compute, from any matrix population model, the expected number of arbitrary kin (sisters, nieces, cousins, etc) of a focal individual ego, structured by the class of ego and of its kin. Central to our approach are classic but little-used tools known as genealogical matrices. Our method can be used to obtain both individual-based and population-wide metrics of kinship, as we illustrate. It also makes it possible to analyse the sensitivity of the kinship structure to the traits implemented in the model.

Revisiting Shao and Sokal's [Formula: see text] index of phylogenetic balance.

Measures of phylogenetic balance, such as the Colless and Sackin indices, play an important role in phylogenetics. Unfortunately, these indices are specifically designed for phylogenetic trees, and do not extend naturally to phylogenetic networks (which are increasingly used to describe reticulate evolution). This led us to consider a lesser-known balance index, whose definition is based on a probabilistic interpretation that is equally applicable to trees and to networks. This index, known as the [Formula: see text] index, was first proposed by Shao and Sokal (Syst Zool 39(3): 266-276, 1990). Surprisingly, it does not seem to have been studied mathematically since. Likewise, it is used only sporadically in the biological literature, where it tends to be viewed as arcane. In this paper, we study mathematical properties of [Formula: see text] such as its expectation and variance under the most common models of random trees and its extremal values over various classes of phylogenetic networks. We also assess its relevance in biological applications, and find it to be comparable to that of the Colless and Sackin indices. Altogether, our results call for a reevaluation of the status of this somewhat forgotten measure of phylogenetic balance.

The Equivocal Mean Age of Parents in a Cohort.

The mean age at which parents give birth is an important notion in demography, ecology, and evolution, where it is used as a measure of generation time. A standard way to quantify it is to compute the mean age of the parents of all offspring produced by a cohort, and the resulting measure is thought to represent the mean age at which a typical parent produces offspring. In this note, I explain why this interpretation is problematic. I also introduce a new measure of the mean age at reproduction and show that it can be very different from the mean age of parents of offspring of a cohort. In particular, the mean age of parents of offspring of a cohort systematically overestimates the mean age at reproduction and can even be greater than the expected life span of parents.

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 model 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.

A new approach to the generation time in matrix population models.

The generation time is commonly defined as the mean age of mothers at birth. In matrix population models, a general formula is available to compute this quantity. However, it is complex and hard to interpret. Here, we present a new approach where the generation time is envisioned as a return time in an appropriate Markov chain. This yields surprisingly simple results, such as the fact that the generation time is the inverse of the sum of the elasticities of the growth rate to changes in the fertilities. This result sheds new light on the interpretation of elasticities (which as we show correspond to the frequency of events in the ancestral lineage of the population), and we use it to generalize a result known as Lebreton's formula. Finally, we also show that the generation time can be seen as a random variable, and we give a general expression for its distribution.

Cultural transmission of reproductive success impacts genomic diversity, coalescent tree topologies, and demographic inferences.

Cultural transmission of reproductive success has been observed in many human populations as well as other animals. Cultural transmission of reproductive success consists of a positive correlation of nongenetic origin between the progeny size of parents and children. This correlation can result from various factors, such as the social influence of parents on their children, the increase of children's survival through allocare from uncles and aunts, or the transmission of resources. Here, we study the evolution of genomic diversity over time under cultural transmission of reproductive success. Cultural transmission of reproductive success has a threefold impact on population genetics: (1) the effective population size decreases when cultural transmission of reproductive success starts, mimicking a population contraction, and increases back to its original value when cultural transmission of reproductive success stops; (2) coalescent tree topologies are distorted under cultural transmission of reproductive success, with higher imbalance and a higher number of polytomies; and (3) branch lengths are reduced nonhomogenously, with a higher impact on older branches. Under long-lasting cultural transmission of reproductive success, the effective population size stabilizes but the distortion of tree topology and the nonhomogenous branch length reduction remain, yielding U-shaped site frequency spectra under a constant population size. We show that this yields a bias in site frequency spectra-based demographic inference. Considering that cultural transmission of reproductive success was detected in numerous human and animal populations worldwide, one should be cautious because inferring population past histories from genomic data can be biased by this cultural process.

Thrombosis revealing POEMS syndrome. About a case.

POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, skin changes) is a rare paraneoplastic disorder due to an underlying plasma cell dyscrasia. The diagnosis of POEMS syndrome requires a chronic polyneuropathy and a monoclonal lambda plasma cell-proliferative disorder (mandatory criteria), and various systematic symptoms such as sclerotic bone lesions, Castleman's disease, organomegaly, endocrinopathy, skin changes, papilloedema and biological abnormalities such as elevated vascular endothelial growth factor (VEGF), thrombocytosis or polycythaemia. We describe an observation of a patient with recurrent thrombosis with thrombocytosis that, after excluding a myeloproliferative neoplasm, proved to be due to POEMS syndrome. This case is unusual compared to the foreground thrombotic symptomatology. POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, skin changes) is a rare multi-systematic paraneoplastic disorder due to an underlying plasma cell disorder. The diagnosis of POEMS syndrome requires the presence of both mandatory criteria (a chronic polyneuropathy and a monoclonal plasma cell-proliferative disorder, always lambda restricted); at least one major (among sclerotic bone lesions, Castleman's disease, elevated VEGF (vascular endothelial growth factor)) and one minor criterion (among organomegaly, endocrinopathy, skin changes (haemangiomas, hypertrichosis, hyperpigmentation), papilloedema and thrombocytosis or polycythaemia. We describe an unusual observation of a young patient with recurrent thrombosis with thrombocytosis that, after excluding a myeloproliferative neoplasm, proved to be due to POEMS syndrome.

Factors Associated with Ocular and Extraocular Recovery in 143 Patients with Sarcoid Uveitis.

BACKGROUND: Sarcoidosis is one of the leading causes of uveitis. To date, no studies have assessed the factors specifically related with recovery in ocular sarcoidosis. In this study, we aimed to determine factors associated with ocular and extraocular recovery in patients with sarcoid uveitis. METHODS: A retrospective study of sarcoid uveitis, with a three-year minimum follow-up in Lyon University Hospital between December 2003 and December 2019. Patients presented biopsy-proven sarcoidosis or presumed sarcoid. Recovery was defined by a disease-free status, spontaneously or despite being off all treatments for three years or more. RESULTS: 143 patients were included: 110 with biopsy-proven and 33 with presumed sarcoid uveitis. Seventy-one percent were women, the median age at presentation was 53 years, and 71% were Caucasian. Chronic uveitis was the main clinical presentation (75%), mostly panuveitis (48%) with bilateral involvement (82%). After a median follow-up of 83.5 months, recovery was reported in 26% of patients. In multivariable analysis, Caucasian ethnicity (p = 0.007) and anterior uveitis (p = 0.008) were significantly associated with recovery, while increased intraocular pressure was negatively associated (p = 0.039). CONCLUSION: In this large European cohort, one quarter of patients recovered. Caucasian ethnicity and anterior uveitis are associated with ocular and extraocular recovery.