Prediction of the time evolution of the COVID-19 disease in Guadeloupe with a stochastic evolutionary model

Predictions on the time-evolution of the number of severe and critical cases of COVID-19 patients in Guadeloupe are presented. A stochastic model is purposely developed to explicitly account for the entire population (≃400000 inhabitants) of Guadeloupe. The available data for Guadeloupe are analysed and combined with general characteristics of the COVID-19 to constrain the parameters of the model. The time-evolution of the number of cases follows the well-known exponential-like model observed at the very beginning of a pandemic outbreak. The exponential growth of the number of infected individuals is controlled by the so-called basic reproductive number, R0, defined as the likely number of additional cases generated by a single infectious case during its infectious period TI. Because of the rather long duration of infectious period (≃14 days) a high rate of contamination is sustained during several weeks after the beginning of the containment period. This may constitute a source of discouragement for people restrained to respect strict containment rules. It is then unlikely that, during the containment period, R0 falls to zero. Fortunately, our models shows that the containment effects are not much sensitive to the exact value of R0 provided we have R0 < 0.6. For such conditions, we show that the number of severe and critical cases is highly tempered about 4 to 6 weeks after the beginning of the containment. Also, the maximum number of critical cases (i.e. the cases that may exceed the hospital’s intensive care capacity) remains near 30 when R0 < 0.6. For a larger R0 = 0.8 a slower decrease of the number of critical cases occurs, leading to a larger number of deceased patients. This last example illustrates the great importance to maintain an as low as possible R0 during and after the containment period. The rather long delay between the beginning of the containment and the appearance of the slowing-down of the rate of contamination puts a particular strength on the communication and sanitary education of people. To be mostly efficient, this communication must be done by a locally recognised medical staff. We believe that this point is a crucial matter of success.

Interplay of Driver, Mini-Driver, and Deleterious Passenger Mutations on Cancer Progression

Cancer is caused by the accumulation of a critical number of somatic mutations (drivers) that offer fitness advantage to tumor cells. Moderately deleterious passengers, suppressing cancer progression, and mini-drivers, mildly beneficial to tumors, can profoundly alter the cancer evolutionary landscape. This observation prompted us to develop a stochastic evolutionary model intended to probe the interplay of drivers, mini-drivers and deleterious passengers in tumor growth over a broad range of fitness values and mutation rates. Below a (small) threshold number of drivers tumor growth exhibits a plateau (dormancy) with large burst occurring when a driver achieves fixation, reminiscent of intermittency in dissipative dynamical systems. The predictions of the model, in particular the relationship between the average number of passenger mutations versus drivers in a tumor, is in accord with clinical data on several cancers. When deleterious drivers are included, we predict a non-monotonic growth of tumors as the mutation rate is varied with shrinkage and even reversal occurring at very large mutation rates. This surprising finding explains the paradoxical observation that high chromosomal instability (CIN) correlates with improved prognosis in a number of cancers compared with intermediate CIN.

Genomic plasticity and rapid host switching promote the evolution of generalism in the zoonotic pathogen Campylobacter

Horizontal gene transfer accelerates bacterial adaptation to novel environments, allowing selection to act on genes that have evolved in multiple genetic backgrounds. This can lead to ecological specialization. However, little is known about how zoonotic bacteria maintain the ability to colonize multiple hosts whilst competing with specialists in the same niche. Here we develop a stochastic evolutionary model and show how genetic transfer of niche specifying genes and the opportunity for host transition can interact to promote the emergence of host generalist lineages of the zoonotic bacterium Campylobacter. Using a modelling approach we show that increasing levels of recombination enhance the efficiency with which selection can fix combinations of beneficial alleles, speeding adaptation. We then show how these predictions change in a multi-host system, with low levels of recombination, consistent with real r/m estimates, increasing the standing variation in the population, allowing a more effective response to changes in the selective landscape. Our analysis explains how observed gradients of host specialism and generalism can evolve in a multihost system through the transfer of ecologically important loci among coexisting strains.

Phylogenetic confidence intervals for the optimal trait value

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

Phylogenetic confidence intervals for the optimal trait value

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part I: Theoretical basis

BackgroundInsertions and deletions (indels) account for more nucleotide differences between two related DNA sequences than substitutions do, and thus it is imperative to develop a stochastic evolutionary model that enables us to reliably calculate the probability of the sequence evolution through indel processes. Recently, such probabilistic models are mostly based on either hidden Markov models (HMMs) or transducer theories, both of which give the indel component of the probability of a given sequence alignment as a product of either probabilities of column-to-column transitions or block-wise contributions along the alignment. However, it is not a priori clear how these models are related with any genuine stochastic evolutionary model, which describes the stochastic evolution of an entire sequence along the time-axis. Moreover, none of these models can fully accommodate biologically realistic features, such as overlapping indels, power-law indel-length distributions, and indel rate variation across regions.ResultsHere, we theoretically tackle the ab initio calculation of the probability of a given sequence alignment under a genuine evolutionary model, more specifically, a general continuous-time Markov model of the evolution of an entire sequence via insertions and deletions. Our model allows general indel rate parameters including length distributions but does not impose any unrealistic restrictions on indels. Using techniques of the perturbation theory in physics, we expand the probability into a series over different numbers of indels. Our derivation of this perturbation expansion elegantly bridges the gap between Gillespie’s (1977) intuitive derivation of his own stochastic simulation method, which is now widely used in evolutionary simulators, and Feller’s (1940) mathematically rigorous theorems that underpin Gillespie′s method. We find a sufficient and nearly necessary set of conditions under which the probability can be expressed as the product of an overall factor and the contributions from regions separated by gapless columns of the alignment. The indel models satisfying these conditions include those with some kind of rate variation across regions, as well as space-homogeneous models. We also prove that, though with a caveat, pairwise probabilities calculated by the method of Miklós et al. (2004) are equivalent to those calculated by our ab initio formulation, at least under a space-homogenous model.ConclusionsOur ab initio perturbative formulation provides a firm theoretical ground that other indel models can rest on.[This paper and three other papers (Ezawa, Graur and Landan 2015a,b,c) describe a series of our efforts to develop, apply, and extend the ab initio perturbative formulation of a general continuous-time Markov model of indels.]

Phylogenetic confidence intervals for the optimal trait value

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein-Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.