Stochastic Birth Research Articles

Pervasive within-species spatial repulsion among adult tropical trees.

For species to coexist, performance must decline as the density of conspecific individuals increases. Although evidence for such conspecific negative density dependence (CNDD) exists in forests, the within-species spatial repulsion it should produce has rarely been demonstrated in adults. In this study, we show that in comparison to a null model of stochastic birth, death, and limited dispersal, the adults of dozens of tropical forest tree species show strong spatial repulsion, some to surprising distances of approximately 100 meters. We used simulations to show that such strong repulsion can only occur if CNDD considerably exceeds heterospecific negative density dependence-an even stronger condition required for coexistence-and that large-scale repulsion can indeed result from small-scale CNDD. These results demonstrate substantial niche differences between species that may stabilize species diversity.

Solving the stochastic dynamics of population growth.

Population growth is a fundamental process in ecology and evolution. The population size dynamics during growth are often described by deterministic equations derived from kinetic models. Here, we simulate several population growth models and compare the size averaged over many stochastic realizations with the deterministic predictions. We show that these deterministic equations are generically bad predictors of the average stochastic population dynamics. Specifically, deterministic predictions overestimate the simulated population sizes, especially those of populations starting with a small number of individuals. Describing population growth as a stochastic birth process, we prove that the discrepancy between deterministic predictions and simulated data is due to unclosed-moment dynamics. In other words, the deterministic approach does not consider the variability of birth times, which is particularly important with small population sizes. We show that some moment-closure approximations describe the growth dynamics better than the deterministic prediction. However, they do not reduce the error satisfactorily and only apply to some population growth models. We explicitly solve the stochastic growth dynamics, and our solution applies to any population growth model. We show that our solution exactly quantifies the dynamics of a community composed of different strains and correctly predicts the fixation probability of a strain in a serial dilution experiment. Our work sets the foundations for a more faithful modeling of community and population dynamics. It will allow the development of new tools for a more accurate analysis of experimental and empirical results, including the inference of important growth parameters.

Increased habitat connectivity induces diversity via noise-induced symmetry breaking.

Stochasticity or noise is omnipresent in ecosystems that mediates community dynamics. The beneficial role of stochasticity in enhancing species coexistence and, hence, in promoting biodiversity is well recognized. However, incorporating stochastic birth and death processes in excitable slow-fast ecological systems to study its response to biodiversity is largely unexplored. Considering an ecological network of excitable consumer-resource systems, we study the interplay of network structure and noise on species' collective dynamics. We find that noise drives the system out of the excitable regime, and high habitat patch connectance in the ordered as well as random networks promotes species' diversity by inducing new steady states via noise-induced symmetry breaking.

Liquid-hexatic-solid phases in active and passive Brownian particles determined by stochastic birth and death events.

We study the effects of stochastic birth and death processes on the structural phases of systems of active and passive Brownian particles subject to volume exclusion. The total number of particles in the system is a fluctuating quantity, determined by the birth and death parameters and on the activity of the particles. As the birth and death parameters are varied, we find liquid, hexatic, and solid phases. For passive particles, these phases are found to be spatially homogeneous. For active particles, motility-induced phase separation (coexisting hexatic and liquid phases) occurs for large activity and sufficiently small birth rates. We also observe a reentrant transition to the hexatic phase when the birth rate is increased. This results from a balance of an increasing number of particles filling the system, and a larger number of defects resulting from the birth and death dynamics.

Deterministic Factors Determine the Comammox Community Composition in the Pearl River Estuary Ecosystem.

ABSTRACTComplete ammonia oxidizers (comammox) have been widely detected in riverine and estuarine ecosystems. However, knowledge about the process of comammox community assembly from freshwater to marine environments is still limited. Here, based on deep sequencing, we investigated the community composition of comammox along a salinity gradient in the Pearl River Estuary (PRE), South China. Our results showed that comammox microorganisms in the PRE sediments were extremely diverse and displayed distinct distributional patterns between upstream and downstream habitats. Quantitative PCR demonstrated that comammox was the dominant ammonia-oxidizing microorganism (AOM) in the PRE upstream sediments, and ammonia-oxidizing archaea (AOA) dominated the PRE downstream sediments, while ammonia-oxidizing bacteria (AOB) were not dominant in any section of the PRE. Neutral modeling revealed that stochastic processes explained a limited part of the variation in the comammox community. The majority of beta nearest-taxon index values were higher than 2, indicating that comammox community assembly in the PRE sediments was better explained through a deterministic process than through a stochastic process. Salinity and total nitrogen were the most important contributing factors that shaped the comammox community. This study expanded the current knowledge of the diversity and niche preference of comammox in the estuarine ecosystem, and further enhances our understanding of the assembly of comammox community from freshwater to marine environments.IMPORTANCE Microbial communities are shaped by stochastic (emigration, immigration, birth, death, and genetic drift of species) and deterministic (e.g., environmental factors) processes. However, it remains unknown as to which type of process is more important in influencing the comammox community assembly from freshwater to marine environments. In this study, we compared the relative importance of stochastic and deterministic processes in shaping the assembly of the comammox community, which demonstrated that the deterministic process was more important in determining the community assembly patterns in the PRE ecosystem.

Moderate immigration may promote a peak of cooperation among natives.

In a world of hardening borders, nations may deprive themselves of enjoying the benefits of cooperative immigrants. Here we analyze the effect of efficient cooperative immigrants on a population playing public goods games. We considered a population structured on a square lattice with individuals playing public goods games with their neighbors. The demographics are determined by stochastic birth, death, and migration. The strategies spread through imitation dynamics. Our model shows that cooperation among natives can emerge due to social contagion of good role-model agents that can provide better quality public goods. Only a small fraction of efficient cooperators, among immigrants, is enough to trigger cooperation across the native population. We see that native cooperation achieves its peak at moderate values of immigration rate. Such efficient immigrant cooperators act as nucleation centers for the growth of cooperative clusters, which eventually dominate defection.

Analysis of Stochastic Birth – Death Process with Mean, Variance and Matrix Models

Analysis of Stochastic Birth – Death Process with Mean, Variance and Matrix Models

Application of growth rate from kinetic model to calculate stochastic growth of a bacteria population at low contamination level

Traditional predictive microbiology is not suited for cell growth predictions for low-level contamination, where individual cell heterogeneity becomes apparent. Accordingly, we simulated a stochastic birth process of bacteria population using kinetic parameters. We predicted the variation in behavior of Salmonella enterica serovar Typhimurium cells at low inoculum density. The modeled cells were grown in tryptic soy broth at 25 °C. Kinetic growth parameters were first determined empirically for an initial cell number of 104 cells. Monte Carlo simulation based on the growth kinetics and Poisson distribution for different initial cell numbers predicted the results of 50 replicate growth experiments with the initial cell number of 1, 10, and 64 cells. Indeed, measured behavior of 85% cells fell within the 95% prediction area of the simulation. The calculations link the kinetic and stochastic birth process with Poisson distribution. The developed model can be used to calculate the probability distribution of population size for exposure assessment and for the evaluation of a probability that a pathogen would exceed critical contamination level during food storage.

Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games

This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection-as a result of competition fashioned by game-theoretic consideration-into the Wright-Fisher process, a stochastic birth-death process. The process is further considered to be active in a generation-wise nonoverlapping finite population where individuals play a two-strategy bimatrix population game. Subsequently, connections among the corresponding master equation, the Fokker-Planck equation, and the Langevin equation are exploited to arrive at the deterministic discrete replicator maps in the limit of infinite population size.

Parallel responses of species diversity and functional diversity to changes in patch size are driven by distinct processes

Abstract Do species and functional trait diversity respond similarly to deterministic and random processes? Theory predicts that the contributions of random and deterministic processes to species diversity depend on patch size. Smaller patches are more strongly influenced by random sampling effects, by having fewer individuals, as well as ecological drift, which propagates the effects of small samples through stochastic birth and death processes. These random processes decrease species richness and increase compositional differences among small patches. Larger patches are predicted to be more deterministically assembled, with greater species richness and greater predictability of composition for a particular environment. The consequences of patch size for the diversity of functional traits, however, are poorly understood. Species diversity may be a poor proxy for functional diversity due to trait redundancies among species, making it unclear how random and deterministic processes alter functional diversity within patches of differing size, and how these differences scale up to determine among‐patch functional diversity. We report a novel experimental study of species and functional diversity across spatial scales. We manipulated patch area in an experimental plant metacommunity and used a nested sampling design to distinguish the effects of deterministic processes, ecological drift and sampling effects on species and functional trait diversity. Our study revealed a pervasive influence of ecological drift and sampling effects on diversity, with distinct influences on functional traits and species composition within and among patches. Overall, drift and sampling effects caused a two‐ to threefold decrease in the importance of deterministic processes in small fragments. Species and functional diversity showed similar patterns with patch size; larger patches had greater within‐patch (alpha) diversity and lower among‐patch (beta) diversity, consistent with theory. However, our nested sampling design revealed that sampling effects (i.e. the size of the sample area) largely determined alpha species diversity and beta functional diversity, while ecological drift had a stronger influence on alpha functional diversity and beta species diversity. Synthesis. The compositions of species and functional diversity in a community are influenced by distinct processes, resulting in divergent spatial scaling of species and their traits within patches and across landscapes.

Invasion Rate Versus Diversity in Population Dynamics with Catastrophes

A key question in the current diversity crisis is how diversity has been maintained throughout evolution and how to preserve it. Modern coexistence theories suggest that a high invasion rate of rare new types is directly related to diversity. We show that adding almost any mechanism of catastrophes to a stochastic birth, death, and mutation process with limited carrying capacity induces a novel phase transition characterized by a positive invasion rate but a low diversity. In this phase, new types emerge and grow rapidly, but the resulting growth of very large types decreases diversity. This model also resolves two major drawbacks of neutral evolution models: their failure to explain balancing selection without resorting to fitness differences and the unrealistic time required for the creation of the observed large types. We test this model on a classical case of genetic polymorphism: the HLA locus.

Dynamics of a birth–death process based on combinatorial innovation

A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of these items may also disappear (extinction). We model this process by a simple stochastic birth–death model, with non-linear combinatorial terms in the growth coefficients to capture the propensity of subsets of items to give rise to new items. In its simplest form, this model involves just two parameters (P, α). This process exhibits a characteristic ‘hockey-stick’ behaviour: a long period of relatively little growth followed by a relatively sudden ‘explosive’ increase. We provide exact expressions for the mean and variance of this time to explosion and compare the results with simulations. We then generalise our results to allow for more general parameter assignments, and consider possible applications to data involving human productivity and creativity.

Duality in stochastic processes from the viewpoint of basis expansions

A new derivation method of duality relations in stochastic processes is proposed. The current focus is on the duality between stochastic differential equations and birth–death processes. Although previous derivation methods have been based on the viewpoint of time-evolution operators, the current derivation is based on basis expansions. In addition, only the tool needed for the derivation is the integration by parts, which is rather simple and understandable. The viewpoint of basis expansions enables us to obtain various dual stochastic processes. As a demonstration, dual processes based on Taylor-type and Hermite polynomials are derived.

A simple spatially explicit neutral model explains the range size distribution of reef fishes

AbstractAimThe great variation in range sizes among species has fascinated ecologists for decades. Reef‐associated fish species live in highly spatially structured habitats and adopt a wide range of dispersal strategies. We consequently expect species with greater dispersal ability to occupy larger ranges. However, empirical evidence for such a positive relationship between dispersal and range size remains scarce. Here, we unveil the role of dispersal on the range size distribution of reef‐associated fishes using empirical data and a novel spatially explicit model.LocationTropical Eastern Pacific.Major taxa studiedReef‐associated fishes.Time periodUnderlying records are from the 20th and 21st centuries.MethodsWe estimated range size distributions for all reef‐associated fishes separated into six guilds, each with different dispersal abilities. We used a one‐dimensional spatially explicit neutral model, which simulates the distribution of species along a linear and contiguous coastline, to explore the effect of dispersal, speciation and sampling on the distribution of range sizes. Our model incorporates biologically important long‐distance dispersal events with a fat‐tailed dispersal kernel and also adopts a more realistic gradual “protracted” speciation process than originally used in neutral theory. We fitted the model to the empirical data using an approximate Bayesian computation approach, with a sequential Monte Carlo algorithm.ResultsStochastic birth, death, speciation and dispersal events alone can accurately explain empirical range size distributions for six different guilds of tropical, reef‐associated fishes. Variation in range size distributions among guilds are explained purely by differences in dispersal ability with the best dispersers being distributed over larger ranges.Main conclusionsNeutral processes and guild‐specific dispersal ability provide a general explanation for both within‐ and across‐guild range size variation. Our results support the theoretically expected, but empirically much debated, hypothesis that high dispersal capacity promotes the establishment of large range size.

A Marked Point Process Model Incorporating Active Contours Boundary Energy

In this paper we incorporate an active contours energy into the Marked Point Process (MPP) framework. The addition of this energy allows the MPP model to detect objects with irregular shapes. This energy accounts for the elasticity and curvature properties of the detected objects. We employ the balloon method to prevent the contour from stagnating at local minima. We use calculus of variations to evolve each individual contour and we use stochastic multiple birth and death dynamics to optimize the MPP energy function. We demonstrate that our method successfully models components with irregular shape in material images, but the model can be extended to other applications.

Modelo estocástico para la infección con VIH de las células T CD4+ del sistema inmune

En este trabajo se estudia la dinámica de infección por VIH, a través de los procesos estocásticos de nacimiento y muerte y los sistemas de ecuaciones diferenciales que representan un sistema real. Para éste caso en específico, se describe un proceso estocástico que interpreta la dinámica de infección del VIH al interior del organismo de una persona en sus etapas iniciales de infección (post exposición o periodo de ventana); es decir, se considera que el momento mismo en que el virus ingresa en el organismo corresponde al tiempo inicial para el modelo, y a partir de entonces se tiene en cuenta el proceso de replicación y las incidencias que el virus genera cuando ataca las células T CD4+, las cuales, son pieza fundamental en el sistema inmunológico del paciente. El proceso estocástico permite deducir a partir de primeros principios, un modelo básico para la infección por VIH, similar a los estudiados en la literatura; es decir, un sistema basado en ecuaciones diferenciales ordinarias de variable estocástica, donde las variables de estado corresponden a valores esperados (promedios) y en ese sentido se encuentran también ecuaciones diferenciales para la varianza de esas variables de estado, lo que proporcionará información adicional sobre el sistema. Finalmente se presenta el estudio analítico local del modelo completo y un estudio numérico de las soluciones del sistema usando valores de los parámetros obtenidos de fuentes secundarias, con el fin de ilustrar los resultados analíticos.

A null model for microbial diversification

Whether prokaryotes (Bacteria and Archaea) are naturally organized into phenotypically and genetically cohesive units comparable to animal or plant species remains contested, frustrating attempts to estimate how many such units there might be, or to identify the ecological roles they play. Analyses of gene sequences in various closely related prokaryotic groups reveal that sequence diversity is typically organized into distinct clusters, and processes such as periodic selection and extensive recombination are understood to be drivers of cluster formation ("speciation"). However, observed patterns are rarely compared with those obtainable with simple null models of diversification under stochastic lineage birth and death and random genetic drift. Via a combination of simulations and analyses of core and phylogenetic marker genes, we show that patterns of diversity for the genera Escherichia, Neisseria, and Borrelia are generally indistinguishable from patterns arising under a null model. We suggest that caution should thus be taken in interpreting observed clustering as a result of selective evolutionary forces. Unknown forces do, however, appear to play a role in Helicobacter pylori, and some individual genes in all groups fail to conform to the null model. Taken together, we recommend the presented birth-death model as a null hypothesis in prokaryotic speciation studies. It is only when the real data are statistically different from the expectations under the null model that some speciation process should be invoked.

A stochastic model for the normal tissue complication probability (NTCP) and applicationss.

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth-death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction.

Defectors Can Create Conditions That Rescue Cooperation.

Cooperation based on the production of costly common goods is observed throughout nature. This is puzzling, as cooperation is vulnerable to exploitation by defectors which enjoy a fitness advantage by consuming the common good without contributing fairly. Depletion of the common good can lead to population collapse and the destruction of cooperation. However, population collapse implies small population size, which, in a structured population, is known to favor cooperation. This happens because small population size increases variability in cooperator frequency across different locations. Since individuals in cooperator-dominated locations (which are most likely cooperators) will grow more than those in defector-dominated locations (which are most likely defectors), cooperators can outgrow defectors globally despite defectors outgrowing cooperators in each location. This raises the possibility that defectors can lead to conditions that sometimes rescue cooperation from defector-induced destruction. We demonstrate multiple mechanisms through which this can occur, using an individual-based approach to model stochastic birth, death, migration, and mutation events. First, during defector-induced population collapse, defectors occasionally go extinct before cooperators by chance, which allows cooperators to grow. Second, empty locations, either preexisting or created by defector-induced population extinction, can favor cooperation because they allow cooperator but not defector migrants to grow. These factors lead to the counterintuitive result that the initial presence of defectors sometimes allows better survival of cooperation compared to when defectors are initially absent. Finally, we find that resource limitation, inducible by defectors, can select for mutations adaptive to resource limitation. When these mutations are initially present at low levels or continuously generated at a moderate rate, they can favor cooperation by further reducing local population size. We predict that in a structured population, small population sizes precipitated by defectors provide a “built-in” mechanism for the persistence of cooperation.

New steady-state microbial community compositions and process performances in biogas reactors induced by temperature disturbances.

BackgroundThe microbial community in a biogas reactor greatly influences the process performance. However, only the effects of deterministic factors (such as temperature and hydraulic retention time (HRT)) on the microbial community and performance have been investigated in biogas reactors. Little is known about the manner in which stochastic factors (for example, stochastic birth, death, colonization, and extinction) and disturbance affect the stable-state microbial community and reactor performances.ResultsIn the present study, three replicate biogas reactors treating cattle manure were run to examine the role of stochastic factors and disturbance in shaping microbial communities. In the triplicate biogas reactors with the same inoculum and operational conditions, similar process performances and microbial community profiles were observed under steady-state conditions. This indicated that stochastic factors had a minor role in shaping the profile of the microbial community composition and activity in biogas reactors. On the contrary, temperature disturbance was found to play an important role in the microbial community composition as well as process performance for biogas reactors. Although three different temperature disturbances were applied to each biogas reactor, the increased methane yields (around 10% higher) and decreased volatile fatty acids (VFAs) concentrations at steady state were found in all three reactors after the temperature disturbances. After the temperature disturbance, the biogas reactors were brought back to the original operational conditions; however, new steady-state microbial community profiles were observed in all the biogas reactors.ConclusionsThe present study demonstrated that temperature disturbance, but not stochastic factors, played an important role in shaping the profile of the microbial community composition and activity in biogas reactors. New steady-state microbial community profiles and reactor performances were observed in all the biogas reactors after the temperature disturbance.Electronic supplementary materialThe online version of this article (doi:10.1186/s13068-014-0182-y) contains supplementary material, which is available to authorized users.