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Register a new userAltruism in populations at the extinction transition
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We study the evolution of cooperation as a birth-death process in spatially extended populations. The benefit from the altruistic behavior of a cooperator is implemented by decreasing the death rate of its direct neighbors. The cost of cooperation is the increase of a cooperators death rate proportional to the number of its neighbors. When cooperation has higher cost than benefit, cooperators disappear. Then the dynamics reduces to the contact process with defectors as the single particle type. Increasing the benefit-cost ratio above 1, the extinction transition of the contact process splits into a set of nonequilibrium transitions between four regimes when increasing the baseline death rate $p$ as a control parameter: (i) defection only, (ii) coexistence, (iii) cooperation only, (iv) extinction. We investigate the transitions between these regimes. As the main result, we find that full cooperation is established at the extinction transition as long as benefit is strictly larger than cost. Qualitatively identical phase diagrams are obtained for populations on square lattices and in pair approximation. Spatial correlations with nearest neighbors only are thus sufficient for sustained cooperation.
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The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August---which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015.
We consider non-demographic noise in the form of uncertainty in the reaction step size, and reveal a dramatic effect this noise may have on the stability of self-regulating populations. Employing the reaction scheme mA->kA, but allowing, e.g., the product number k to be a-priori unknown and sampled from a given distribution, we show that such non-demographic noise can greatly reduce the populations extinction risk compared to the fixed k case. Our analysis is tested against numerical simulations, and by using empirical data of different species, we argue that certain distributions may be more evolutionary beneficial than others.
Establishing the conditions that guarantee the spreading or the sustenance of altruistic traits in a population is the main goal of intergroup selection models. Of particular interest is the balance of the parameters associated to group size, migration and group survival against the selective advantage of the non-altruistic individuals. Here we use Kimuras diffusion model of intergroup selection to determine those conditions in the case the group survival probability is a nonlinear non-decreasing function of the proportion of altruists in a group. In the case this function is linear, there are two possible steady states which correspond to the non-altruistic and the altruistic phases. At the discontinuous transition line separating these phases there is a non-ergodic coexistence phase. For a continuous concave survival function, we find an ergodic coexistence phase that occupies a finite region of the parameter space in between the altruistic and the non-altruistic phases, and is separated from these phases by continuous transition lines. For a convex survival function, the coexistence phase disappears altogether but a bistable phase appears for which the choice of the initial condition determines whether the evolutionary dynamics leads to the altruistic or the non-altruistic steady state.
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete lattice-based random walk model where individuals undergo movement, birth and death events. The discrete model is defined on a two-dimensional hexagonal lattice with periodic boundary conditions. A key feature of the discrete model is that crowding effects are introduced by specifying two different crowding functions that govern how local agent density influences movement events and birth/death events. The continuum limit description of the discrete model is a nonlinear reaction-diffusion equation, and we focus on crowding functions that lead to linear diffusion and a bistable source term that is often associated with the strong Allee effect. Using both the discrete and continuum modelling tools we explore the complicated relationship between the long-term survival or extinction of the population and the initial spatial arrangement of the population. In particular, we study different spatial arrangements of initial distributions: (i) a well-mixed initial distribution where the initial density is independent of position in the domain; (ii) a vertical strip initial distribution where the initial density is independent of vertical position in the domain; and, (iii) several forms of two-dimensional initial distributions where the initial population is distributed in regions with different shapes. Our results indicate that the shape of the initial spatial distribution of the population affects extinction of bistable populations. All software required to solve the discrete and continuum models used in this work are available on GitHub.
Since the onset of the COVID-19 outbreak in Wuhan, China, numerous forecasting models have been proposed to project the trajectory of coronavirus infection cases. We propose a new discrete-time Markov chain transition matrix model that directly incorporates stochastic behavior and for which parameter estimation is straightforward from available data. Using such data from Chinas Hubei province (for which Wuhan is the provincial capital city), the model is shown to be flexible, robust, and accurate. As a result, it has been adopted by the first Shanghai assistance medical team in Wuhans Jinyintan Hospital, which was the first designated hospital to take COVID-19 patients in the world. The forecast has been used for preparing medical staff, intensive care unit (ICU) beds, ventilators, and other critical care medical resources and for supporting real-time medical management decisions. Empirical data from Chinas first two months (January/February) of fighting COVID-19 was collected and used to enhance the model by embedding NPI efficiency into the model. We applied the model to forecast Italy, South Korea, and Iran on March 9. Later we made forecasts for Spain, Germany, France, US on March 24. Again, the model has performed very well, proven to be flexible, robust, and accurate for most of these countries/regions outside China.
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