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Metapopulation structure and site jump dynamics. (a) Example of the metapopulation structure. It consists of 25 lattices, each one defined by a diffusion D. We use a fully connected network for the simulations. (b) Example of two subpopulations at a given time. Each node has a probability λΔt/N of jumping. (c) A site (highlighted in yellow) in the first subpopulation is randomly selected according to the previous probability to jump to the second subpopulation. (d) For each node that jumps, a target node in the second subpopulation is selected. (e) The state of the two nodes is swapped.
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Pathogen transmission and virulence are main evolutionary variables broadly assumed to be linked through trade-offs. In well-mixed populations, these trade-offs are often ascribed to physiological restrictions, while populations with spatial self-structuring might evolve emergent trade-offs. Here, we reexamine a model of the latter kind proposed by...
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We revisit a seminal paper by Levin (Am Nat 108:207–228, 1974), where spatially mediated coexistence and spatial pattern formation were described. We do so by reviewing and explaining the mathematical tools used to evaluate the dynamics of ecological systems in space, from the perspective of recent developments in spatial population dynamics. We st...
Citations
... 47 In population dynamics, also dominated by multiplicative (demographic) growth processes, the fast, local extinction of a population is often followed by "reinjection" in the form of a small number of migrating individuals. This situation could describe parasitic infection bursts in metapopulations 48 and explain the persistence of populations that would otherwise become extinct. 49 Resets could be also rephrased as any process that finishes the multiplicative growth, since the properties described do not depend on whether the reset is repeatedly applied to realizations that have a continuity in time or to many different realizations that are independently "born," and then terminated at the time of resetting. ...
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main goal is to provide a series of exact results on the dynamics and asymptotic behaviour of increasingly complex versions of a basic multiplicative process with resets, including discrete and continuous-time variants and several degrees of randomness in the parameters that control the process. In particular, we show how the power-law distributions are built up as time elapses, how their moments behave with time, and how their stationary profiles become quantitatively determined by those parameters. Our discussion emphasizes the connection with financial systems, but these stochastic processes are also expected to be fruitful in modeling a wide variety of social and biological phenomena.
... In addition, evolutionary processes can be seen as the driving force that allows biological systems to self-organize to an optimal critical-like point [18]. Concepts such as "self-evolved criticality" [173,174] could thus be used to explain the evolutionary pathway of specific organisms and/or the emergence of specific traits, or adaptive responses to shortor long-term perturbations. The latter would provide important insight on the resilience of key biological systems, as it could help assess whether the self-organizing mechanisms present in a focal system are robust enough for it to cope with the rapid environmental changes occurring in the anthropocene. ...
Scale-free outbursts of activity are commonly observed in physical, geological, and biological systems. The idea of self-organized criticality (SOC), introduced back in 1987 by Bak, Tang, and Wiesenfeld suggests that, under certain circumstances, natural systems can seemingly self-tune to a critical state with its concomitant power-laws and scaling. Theoretical progress allowed for a rationalization of how SOC works by relating its critical properties to those of a standard non-equilibrium second-order phase transition that separates an active state in which dynamical activity reverberates indefinitely, from an absorbing or quiescent state where activity eventually ceases. The basic mechanism underlying SOC is the alternation of a slow driving process and fast dynamics with dissipation, which generates a feedback loop that tunes the system to the critical point of an absorbing-active continuous phase transition. Here, we briefly review these ideas as well as a recent closely-related concept: self-organized bistability (SOB). In SOB, the very same type of feedback operates in a system characterized by a discontinuous phase transition, which has no critical point but instead presents bistability between active and quiescent states. SOB also leads to scale-invariant avalanches of activity but, in this case, with a different type of scaling and coexisting with anomalously large outbursts. Moreover, SOB explains experiments with real sandpiles more closely than SOC. We review similarities and differences between SOC and SOB by presenting and analyzing them under a common theoretical framework, covering recent results as well as possible future developments. We also discuss other related concepts for “imperfect” self-organization such as “self-organized quasi-criticality” and “self-organized collective oscillations,” of relevance in e.g., neuroscience, with the aim of providing an overview of feedback mechanisms for self-organization to the edge of a phase transition.
... 47 In population dynamics, also dominated by multiplicative (demographic) growth processes, the fast, local extinction of a population is often followed by "reinjection" in the form of a small number of migrating individuals. This situation could describe parasitic infection bursts in metapopulations 48 and explain the persistence of populations that would otherwise become extinct. 49 Resets could be also rephrased as any process that finishes the multiplicative growth, since the properties described do not depend on whether the reset is repeatedly applied to realizations that have a continuity in time or to many different realizations that are independently "born," and then terminated at the time of resetting. ...
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails—ubiquitous in the statistics of social, economic, and ecological systems. Our main goal is to provide a series of exact results on the dynamics and asymptotic behavior of increasingly complex versions of a basic multiplicative process with resets, including discrete and continuous-time variants and several degrees of randomness in the parameters that control the process. In particular, we show how the power-law distributions are built up as time elapses, how their moments behave with time, and how their stationary profiles become quantitatively determined by those parameters. Our discussion emphasizes the connection with financial systems, but these stochastic processes are also expected to be fruitful in modeling a wide variety of social and biological phenomena.
... Then, for each network model we characterized 62 the structure of pathogen population at the equilibrium through ecological diversity 63 measures, including species richness and evenness/dominance indices [52,53]. 64 We show sample epidemic trajectories in Fig 1A and average quantities in panels heterogeneities lower the transmissibility threshold above which total prevalence is 68 significantly above zero, thus allowing the spread of pathogens with low-transmissibility. 69 At the same time, however, heterogeneities hamper the epidemic spread when is large, 70 reducing the equilibrium prevalence [35]. Fig 1 shows that richness (i.e. the number of 71 distinct strains co-circulating) is not linked to the prevalence in a straightforward way. ...
... Many of these works addressed, for instance, the 268 co-existence between susceptible and resistant strains of S. pneumoniae [11,68]. 269 However, this assumption was rarely adopted in network models, that consider for the 270 majority strains with different epidemiological traits with the aim of describing 271 pathogen selection and evolution [47][48][49]70]. Strains were assumed to have the same 272 infection parameters in [50,51], where the role of community structure and clustering . ...
The interaction among multiple microbial strains affects the spread of infectious diseases and the efficacy of interventions. Genomic tools have made it increasingly easy to observe pathogenic strains diversity, but the best interpretation of such diversity has remained difficult because of relationships with host and environmental factors. Here, we focus on host-to-host contact behavior and study how it changes populations of pathogens in a minimal model of multi-strain interaction. We simulated a population of identical strains competing by mutual exclusion and spreading on a dynamical network of hosts according to a stochastic susceptible-infectious-susceptible model. We computed ecological indicators of diversity and dominance in strain populations for a collection of networks illustrating various properties found in real-world examples. Heterogeneities in the number of contacts among hosts were found to reduce diversity and increase dominance by making the repartition of strains among infected hosts more uneven, while strong community structure among hosts increased strain diversity. We found that the introduction of strains associated with hosts entering and leaving the system led to the highest pathogenic richness at intermediate turnover levels. These results were finally illustrated using the spread of Staphylococcus aureus in a long-term health-care facility where close proximity interactions and strain carriage were collected simultaneously. We found that network structural and temporal properties could account for a large part of the variability observed in strain diversity. These results show how stochasticity and network structure affect the population ecology of pathogens and warns against interpreting observations as unambiguous evidence of epidemiological differences between strains.
Author summary
Pathogens are structured in multiple strains that interact and co-circulate on the same host population. This ecological diversity affects, in many cases, the spread dynamics and the efficacy of vaccination and antibiotic treatment. Thus understanding its biological and host-behavioral drivers is crucial for outbreak assessment and for explaining trends of new-strain emergence. We used stochastic modeling and network theory to quantify the role of host contact behavior on strain richness and dominance. We systematically compared multi-strain spread on different network models displaying properties observed in real-world contact patterns. We then analyzed the real-case example of Staphylococcus aureus spread in a hospital, leveraging on a combined dataset of carriage and close proximity interactions. We found that contact dynamics has a profound impact on a strain population. Contact heterogeneity, for instance, reduces strain diversity by reducing the number of circulating strains and leading few strains to dominate over the others. These results have important implications in disease ecology and in the epidemiological interpretation of biological data.
The interaction among multiple microbial strains affects the spread of infectious diseases and the efficacy of interventions. Genomic tools have made it increasingly easy to observe pathogenic strains diversity, but the best interpretation of such diversity has remained difficult because of relationships with host and environmental factors. Here, we focus on host-to-host contact behavior and study how it changes populations of pathogens in a minimal model of multi-strain interaction. We simulated a population of identical strains competing by mutual exclusion and spreading on a dynamical network of hosts according to a stochastic susceptible-infectious-susceptible model. We computed ecological indicators of diversity and dominance in strain populations for a collection of networks illustrating various properties found in real-world examples. Heterogeneities in the number of contacts among hosts were found to reduce diversity and increase dominance by making the repartition of strains among infected hosts more uneven, while strong community structure among hosts increased strain diversity. We found that the introduction of strains associated with hosts entering and leaving the system led to the highest pathogenic richness at intermediate turnover levels. These results were finally illustrated using the spread of Staphylococcus aureus in a long-term health-care facility where close proximity interactions and strain carriage were collected simultaneously. We found that network structural and temporal properties could account for a large part of the variability observed in strain diversity. These results show how stochasticity and network structure affect the population ecology of pathogens and warn against interpreting observations as unambiguous evidence of epidemiological differences between strains.
