arXiv subjects

Vitor M. Marquioni

Publications and source records attributed to Vitor M. Marquioni.

5 recordsLinked to original sources

arXiv2026

What sets the critical genome length for sympatric speciation? A closed form and asymptotic theory

In the Derrida--Higgs model of sympatric speciation, a sexually reproducing population with finite binary genomes can mate only when the genetic overlap between two individuals exceeds a threshold $q_{\min}$. Depending on the genome length $L$, the population either remains genetically connected or fragments into reproductively isolated species. A central problem is therefore to predict the critical genome length $L_c$ at which fragmentation begins. At finite $L$, fluctuations broaden the overlap distribution and allow genetically distant regions of the population to remain connected. A previously proposed transient variance criterion captures this effect, but its evaluation requires numerical iteration of coupled moment equations. Here we first correct the unrestricted moment equations by removing a previously implicit assumption and then derive an explicit closed form expression for $L_c$. The resulting formula shows that the critical genome length is determined, at the time the mean overlap reaches $q_{\min}$, by the competition between deterministic separation from the unrestricted equilibrium and the transient genealogical variance of the overlap distribution. This expression permits a systematic asymptotic analysis. When the deterministic contribution dominates, $L_c$ becomes essentially independent of the population size $M$ and scales as $μ^{-2}$. When the transient genealogical variance dominates, $L_c$ grows as $M^{3/2}$ or as $\sqrt{M}/μ$, depending on how $M$ and the mutation rate $μ$ jointly vary. Simulations support all predicted behaviors. Our results identify transient genealogical variance as the principal mechanism linking finite genome fluctuations to the onset of reproductive fragmentation and provide a practical analytical prediction for the critical genome length.

q-bio.PE↗

arXiv2024

The transition to speciation in the finite genome Derrida-Higgs model: a heuristic solution

The process of speciation, where an ancestral species divides in two or more new species, involves several geographic, environmental and genetic components that interact in a complex way. Understanding all these elements at once is challenging and simple models can help unveiling the role of each factor separately. The Derrida-Higgs model describes the evolution of a sexually reproducing population subjected to mutations in a well mixed population. Individuals are characterized by a string with entries $\pm1$ representing a haploid genome with biallelic genes. If mating is restricted by genetic similarity, so that only individuals that are sufficiently similar can mate, sympatric speciation, i.e. the emergence of species without geographic isolation, can occur. Only four parameters rule the dynamics: population size $N$, mutation rate $μ$, minimum similarity for mating $q_{min}$ and genome size $B$. In the limit $B\rightarrow\infty$, speciation occurs if the simple condition $q_{min}>(1+4μN)^{-1}$ is satisfied. However, this condition fails for finite genomes, and speciation does not occur if the genome size is too small. This indicates the existence of a critical genome size for speciation. In this work, we develop an analytical theory of the distribution of similarities between individuals, a quantity that defines how tight or spread out is the genetic content of the population. This theory is carried out in the absence of mating restrictions, where evolution equations for the mean and variance of the similarity distribution can be derived. We then propose a heuristic description of the speciation transition which allows us to numerically calculate the critical genome size for speciation as a function of the other model parameters. The result is in good agreement with the simulations of the model and may guide further investigations on theoretical conditions for species formation.

q-bio.PE↗

arXiv2021

Modeling viral mutations in the spread of epidemics

Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains of nucleotides that can mutate inside the host. Under the hypothesis of neutral evolution we compute analytically the average pairwise genetic distance between all infecting viruses over time. We also derive a mean-field version of this equation that can be added directly to compartmental models such as SIR or SEIR to estimate the genetic evolution. We compare our results with the inferred genetic evolution of SARS-CoV-2 at the beginning of the epidemic in China and found good agreement with the analytical solution of our model. Finally, using genetic distance as a proxy for different strains, we use numerical simulations to show that the lower the connectivity between communities, e.g., cities, the higher the probability of reinfection.

q-bio.PE↗

arXiv2020

Quantifying the effects of quarantine using an IBM SEIR model on scalefree networks

The COVID-19 pandemic led several countries to resort to social distancing, the only known way to slow down the spread of the virus and keep the health system under control. Here we use an individual based model (IBM) to study how the duration, start date and intensity of quarantine affect the height and position of the peak of the infection curve. We show that stochastic effects, inherent to the model dynamics, lead to variable outcomes for the same set of parameters, making it crucial to compute the probability of each result. To simplify the analysis we divide the outcomes in only two categories, that we call {best and worst scenarios. Although long and intense quarantine is the best way to end the epidemic, it is very hard to implement in practice. Here we show that relatively short and intense quarantine periods can also be very effective in flattening the infection curve and even killing the virus, but the likelihood of such outcomes are low. Long quarantines of relatively low intensity, on the other hand, can delay the infection peak and reduce its size considerably with more than 50% probability, being a more effective policy than complete lockdown for short periods.

q-bio.PE↗

arXiv2019

Multi-Dimensional Elephant Random Walk with Coupled Memory

The elephant random walk (ERW) is a microscopic, one-dimensional, discrete-time, non-Markovian random walk, which can lead to anomalous diffusion due to memory effects. In this study, I propose a multi-dimensional generalization in which the probability of taking a step in a certain direction depends on the previous steps in other directions. The original model is generalized in a straightforward manner by introducing coefficients that couple the probability of moving in one direction with the previous steps in all directions. I motivate the model by first introducing a two-elephant system and then elucidating it with a specific coupling. With the explicit calculation of the first moments, I show the existence of two newsworthy relative movement behaviours: one in which one elephant follows the other, and another in which they go in opposite directions. With the aid of a Fokker-Planck equation, the second moment is evaluated and two new super-diffusion regimes appear, not found in other ERWs. Then, I re-interpret the equations as a bidimensional elephant random walk model, and further generalize it to $N-$dimensions. I argue that the introduction of coupling coefficients is a way of extending any one-dimensional ERW to many dimensions.

cond-mat.stat-mech↗