A 'rich-get-richer' mechanism drives patchy dynamics and resistance evolution in antibiotic-treated bacteria.

Bacteria in nature often form surface-attached communities that initially comprise distinct subpopulations, or patches. For pathogens, these patches can form at infection sites, persist during antibiotic treatment, and develop into mature biofilms. Evidence suggests that patches can emerge due to heterogeneity in the growth environment and bacterial seeding, as well as cell-cell signaling. However, it is unclear how these factors contribute to patch formation and how patch formation might affect bacterial survival and evolution. Here, we demonstrate that a 'rich-get-richer' mechanism drives patch formation in bacteria exhibiting collective survival (CS) during antibiotic treatment. Modeling predicts that the seeding heterogeneity of these bacteria is amplified by local CS and global resource competition, leading to patch formation. Increasing the dose of a non-eradicating antibiotic treatment increases the degree of patchiness. Experimentally, we first demonstrated the mechanism using engineered Escherichia coli and then demonstrated its applicability to a pathogen, Pseudomonas aeruginosa. We further showed that the formation of P. aeruginosa patches promoted the evolution of antibiotic resistance. Our work provides new insights into population dynamics and resistance evolution during surface-attached bacterial growth.

Population genetics in microchannels.

SignificanceMany microbial populations proliferate in small channels. In such environments, reproducing cells organize in parallel lanes. Reproducing cells shift these lanes, potentially expelling other cells from the channel. In this paper, we combine theory and experiments to understand how these dynamics affects the diversity of a microbial population. We theoretically predict that genetic diversity is quickly lost along lanes of cells. Our experiments confirm that a population of proliferating Escherichia coli in a microchannel organizes into lanes of genetically identical cells within a few generations. Our findings elucidate the effect of lane formation on populations evolution, with potential applications ranging from microbial ecology in soil to dynamics of epithelial tissues in higher organisms.

Temperature-dependent dispersal and ectotherm species' distributions in a warming world.

Dispersal is a crucial component of species' responses to climate warming. Warming-induced changes in species' distributions are the outcome of how temperature affects dispersal at the individual level. Yet, there is little or no theory that considers the temperature dependence of dispersal when investigating the impacts of warming on species' distributions. Here I take a first step towards filling this key gap in our knowledge. I focus on ectotherms, species whose body temperature depends on the environmental temperature, not least because they constitute the majority of biodiversity on the planet. I develop a mathematical model of spatial population dynamics that explicitly incorporates mechanistic descriptions of ectotherm life history trait responses to temperature. A novel feature of this framework is the explicit temperature dependence of all phases of dispersal: emigration, transfer and settlement. I report three key findings. First, dispersal, regardless of whether it is random or temperature-dependent, allows both tropical and temperate ectotherms to track warming-induced changes in their thermal environments and to expand their distributions beyond the lower and upper thermal limits of their respective climate envelopes. In the absence of dispersal mortality, warming does not alter these new distributional limits. Second, an analysis based solely on trait response data predicts that tropical ectotherms should be able to expand their distributions polewards to a greater degree than temperate ectotherms. Analysis of the dynamical model confirms this prediction. Tropical ectotherms have an advantage when moving to cooler climates because they experience lower within-patch and dispersal mortality, and their higher thermal optima and maximal birth rates allow them to take advantage of the warmer parts of the year. Previous theory has shown that tropical ectotherms are more successful in invading and adapting the temperate climates than vice versa. This study provides the key missing piece, by showing how temperature-dependent dispersal could facilitate both invasion and adaptation. Third, dispersal mortality does not affect the poleward expansion of ectotherm distributions. But, it prevents both tropical and temperate ectotherms from maintaining sink populations in localities that are too warm to be viable in the absence of dispersal. Dispersal mortality also affects species' abundance patterns, causing a larger decline in abundance throughout the range when species disperse randomly rather than in response to thermal habitat suitability. In this way, dispersal mortality can facilitate the evolution of dispersal modes that maximize fitness in warmer thermal environments.

Spatial metapopulation dynamics with local and global colonization.

We revisit a spatial metapopulation model on continuous space as a stochastic point pattern dynamics. In the model, local patches as points are distributed with a certain spatial configuration and status of each patch changes stochastically between occupied and empty: an occupied patch becomes empty by local extinction and an empty patch becomes occupied both by local and global colonization. We carry out simulation analysis and derive an analytical model in terms of singlet, pair and triplet probabilities that describe the stochastic dynamics. Using a simple closure that approximates triplet probabilities by singlet and pair probabilities, we show that equilibrium singlet and pair probabilities can be analytically derived. The derived equilibrium properties successfully describe simulation results under a certain condition where the range of local colonization and the proportion of global colonization play key roles. Our model is an extension of the classical non-spatial Levins model to a spatially explicit metapopulation model. We appeal the advantage of point pattern approach to study spatial dynamics in general ecology and call for the need to deepen our understanding of mathematical tools to explore point pattern dynamics.

Rate of coalescence of lineage pairs in the Spatial Λ-Fleming-Viot process.

We revisit the Spatial Λ-Fleming-Viot process introduced in Barton and Kelleher (2010). Particularly, we are interested in the time T0 to the most recent common ancestor for two lineages. We distinguish between the cases where the process acts on the two-dimensional plane and on a finite rectangle. Utilizing a differential equation linking T0 with the physical distance between the lineages, we arrive at computationally efficient and reasonably accurate approximation schemes for both cases. Furthermore, our analysis enables us to address the question of whether the genealogical process of the model "comes down from infinity", which has been partly answered before in Véber and Wakolbinger (2015).

SLiM 3: Forward Genetic Simulations Beyond the Wright-Fisher Model.

With the desire to model population genetic processes under increasingly realistic scenarios, forward genetic simulations have become a critical part of the toolbox of modern evolutionary biology. The SLiM forward genetic simulation framework is one of the most powerful and widely used tools in this area. However, its foundation in the Wright-Fisher model has been found to pose an obstacle to implementing many types of models; it is difficult to adapt the Wright-Fisher model, with its many assumptions, to modeling ecologically realistic scenarios such as explicit space, overlapping generations, individual variation in reproduction, density-dependent population regulation, individual variation in dispersal or migration, local extinction and recolonization, mating between subpopulations, age structure, fitness-based survival and hard selection, emergent sex ratios, and so forth. In response to this need, we here introduce SLiM 3, which contains two key advancements aimed at abolishing these limitations. First, the new non-Wright-Fisher or "nonWF" model type provides a much more flexible foundation that allows the easy implementation of all of the above scenarios and many more. Second, SLiM 3 adds support for continuous space, including spatial interactions and spatial maps of environmental variables. We provide a conceptual overview of these new features, and present several example models to illustrate their use.

Among-individual and within-individual variation in seasonal migration covaries with subsequent reproductive success in a partially migratory bird.

Within-individual and among-individual variation in expression of key environmentally sensitive traits, and associated variation in fitness components occurring within and between years, determine the extents of phenotypic plasticity and selection and shape population responses to changing environments. Reversible seasonal migration is one key trait that directly mediates spatial escape from seasonally deteriorating environments, causing spatio-seasonal population dynamics. Yet, within-individual and among-individual variation in seasonal migration versus residence, and dynamic associations with subsequent reproductive success, have not been fully quantified. We used novel capture-mark-recapture mixture models to assign individual European shags (Phalacrocorax aristotelis) to 'resident', 'early migrant', or 'late migrant' strategies in two consecutive years, using year-round local resightings. We demonstrate substantial among-individual variation in strategy within years, and directional within-individual change between years. Furthermore, subsequent reproductive success varied substantially among strategies, and relationships differed between years; residents and late migrants had highest success in the 2 years, respectively, matching the years in which these strategies were most frequently expressed. These results imply that migratory strategies can experience fluctuating reproductive selection, and that flexible expression of migration can be partially aligned with reproductive outcomes. Plastic seasonal migration could then potentially contribute to adaptive population responses to currently changing forms of environmental seasonality.

Advection exacerbates population decline from habitat loss: maintaining threatened taxa while restoring natural river flow regimes.

Modification of flow regimes and habitat degradation are the strongest, most common, and often co-occurring human activities affecting riverine populations. Ongoing efforts to restore peak flow events found under pristine flow regimes could increase advection-driven dispersal for many species. In rivers with extensive habitat loss, increased advection could transport individuals from remnant populations into degraded downstream areas, causing restored flow regimes to decrease persistence of threatened species. To demonstrate such possible 'washout' effects across imperiled taxa, we evaluate population growth in spatial models of insect, fish, and mollusc taxa that experience advective dispersal and either long-term habitat loss or temporary drought disturbances. As a case study to quantify advective dispersal in threatened species, we use intensive mark-recapture methods in a Rio Grande population of the endangered mussel Popenaias popeii belonging to the Unionida order, the most threatened faunal taxa worldwide. Our mark-recapture models estimate high levels of annual downstream emigration (16-51%) and immigration from upstream habitats (32-48%) of adult P. popeii, a result consistent with hydrodynamic experiments. Across taxa where such advective dispersal occurs in specific life stages, our population model suggests that washout effects might strongly reduce population recovery under high levels of habitat loss, especially for sessile or shorter lived species. Averting this potential negative consequence of restoring hydrology requires simultaneously restoring or protecting long, contiguous stretches of suitable habitats. In heavily impacted systems, we suggest integrating hydrodynamic studies and field surveys to detect the presence of advective dispersal and prioritize areas for habitat restoration to enhance population persistence.

Equilibrium properties of the spatial SIS model as a point pattern dynamics - How is infection distributed over space?

We revisit the classical epidemiological SIS model as a stochastic point pattern dynamics with special focus on its spatial distribution at equilibrium. In this model, each point on a continuous space is either susceptible S or infectious I, and infection occurs with an infection kernel as a function of distance from I to S. This stochastic process has been mathematically described by the hierarchical dynamics of the probabilities that a point, a pair made by two points, and a triplet made by three points, etc., is in a specific configuration of status. Using a simple closure thereby triplet probabilities that appear in the dynamics are approximated, we show that the average singlet probabilities and the pair probabilities that describe spatial distributions of Ss and Is at equilibrium can be explicitly derived using the infection kernel; Is are spatially clustered in the same order of the infection kernel. The results highlight the advantage of point pattern approach to model spatial population dynamics in general ecology where local interactions among individuals likely depend on distance between them.

Spatial synchrony and harvesting in fluctuating populations:Relaxing the small noise assumption.

In spatio-temporal population dynamic models, the most important concept, in addition to mean and variance of local density fluctuations, is the spatial scale of fluctuations in density expressed by studying the spatial autocovariance function. Analytical formulas for this scale in models with local density regulation, dispersal and spatially autocorrelated noise, are rather simple when based on asymptotic theory giving linear models in the limit as the environmental variance approaches zero. The accuracy of these analytical small noise approximations has, however, not been investigated theoretically. Here, we work out improved approximations for the scale as well the spatial autocorrelation function using non-linear logistic local dynamics and going to the next order of approximation with respect to the environmental variance. Generally, it turns out that the asymptotic results are remarkably accurate under moderate fluctuations in density but may be inaccurate for very large fluctuations. For populations with small dispersal capacity, the main error comes from the fact that the logistic dynamics is non-linear, and this error is partly wiped out as dispersal increases. Proportional harvesting has a large effect on the dynamics in spatial as well as non-spatial models, increasing population fluctuations and their spatial scale. The optimal harvesting rate with respect to expected yield per time unit, however, is only to a small extent affected by the magnitude of population fluctuations unless these are very large, so that asymptotic results are applicable over a large range of population fluctuations.

The plant in the labyrinth: Adaptive growth and branching in heterogeneous environments.

The "ant in the labyrinth" problem describes spatial constraints upon a moving agent in a disordered medium. In contrast with an animal-like agent (an "ant"), a clonal plant can stay in a place and move at the same time: some parts develop roots, while others continue moving by horizontal growth and branching. Hereby we present a spatially explicit, dynamic model for the study of percolation by plant growth rules in lattices that consist of open and closed sites. Growth always starts from a single seed in an open percolation cluster (patch). By increasing the proportion of open sites (p), we describe a new kind of threshold (the "tracking threshold", approximately pt=0.73), which is higher than the site percolation threshold (pc=0.5 in this lattice). At pc

Simple settlement decisions explain common dispersal patterns in territorial species.

Dispersal is one of the least-understood aspects of animal behaviour. For example, little is known of the mechanisms that determine how individuals express different dispersal behaviours in response to different circumstances. Uncovering these mechanisms is important for our understanding of spatial population dynamics. Using agent-based simulations, we examine how simple decision rules generate individual-level dispersal plasticity, and how this can influence population-scale dispersal dynamics. We model a territorial, monogamous population inhabiting a completely homogeneous environment. Dispersal variability therefore emerges solely as a result of between-individual interactions (competition, settlement, reproduction), which are governed by simple decision-making algorithms. We show that complex dispersal dynamics, including sex biases and strong density dependence, emerge naturally from simple rule-based behaviours. Dispersal is particularly sensitive to the inclusion of mate availability as a criterion for settlement: if neither sex evaluates mate availability, dispersal distances tend to decline at low densities, leading to a strong Allee effect from reduced pairing success. If one sex evaluates mate availability (females), Allee effects are largely avoided, but female-biased dispersal generates increasingly male-biased adult sex ratios at low densities. Sex biases are eliminated if both sexes evaluate mate availability, but population growth rates tend to be reduced due to survival costs and reduced pairing success. Our models suggest that simple decision mechanisms can explain several dynamic patterns that are commonly observed among territorial species. Importantly, these patterns emerge in the absence of environmental heterogeneity or between-individual variation in dispersal phenotypes, two conditions that are often invoked to explain dispersal heterogeneity in nature. This has implications for studies seeking to examine the causes of dispersal variability in wild populations, suggesting that observed patterns could be largely driven by the social and demographic conditions experienced by sampled individuals. Further insights could be gained by examining how selection operates on decision rules in different life-history and environmental circumstances, and how this might interact with selection on other demographic traits. Uncovering the decision rules used during settlement should be a priority for those wishing to understand and predict dispersal patterns in nature.

Modeling abundance, distribution, movement and space use with camera and telemetry data.

Studies of animal abundance and distribution are often conducted independently of research on movement, despite the important links between processes. Movement can cause rapid changes in spatial variation in density, and movement influences detection probability and therefore estimates of abundance from inferential methods such as spatial capture-recapture (SCR). Technological developments including camera traps and GPS telemetry have opened new opportunities for studying animal demography and movement, yet statistical models for these two data types have largely developed along parallel tracks. We present a hierarchical model in which both datasets are conditioned on a movement process for a clearly defined population. We fitted the model to data from 60 camera traps and 23,572 GPS telemetry locations collected on 17 male white-tailed deer in the Big Cypress National Preserve, Florida, USA during July 2015. Telemetry data were collected on a 3-4 h acquisition schedule, and we modeled the movement paths of all individuals in the region with a Ornstein-Uhlenbeck process that included individual-specific random effects. Two of the 17 deer with GPS collars were detected on cameras. An additional 20 male deer without collars were detected on cameras and individually identified based on their unique antler characteristics. Abundance was 126 (95% CI: 88-177) in the 228 km2 region, only slightly higher than estimated using a standard SCR model: 119 (84-168). The standard SCR model, however, was unable to describe individual heterogeneity in movement rates and space use as revealed by the joint model. Joint modeling allowed the telemetry data to inform the movement model and the SCR encounter model, while leveraging information in the camera data to inform abundance, distribution and movement. Unlike most existing methods for population-level inference on movement, the joint SCR-movement model can yield unbiased inferences even if non-uniform sampling is used to deploy transmitters. Potential extensions of the model include the addition of resource selection parameters, and relaxation of the closure assumption when interest lies in survival and recruitment. These developments would contribute to the emerging holistic framework for the study of animal ecology, one that uses modern technology and spatio-temporal statistics to learn about interactions between behavior and demography.

Modeling and simulation of the spatial population dynamics of the Aedes aegypti mosquito with an insecticide application.

BACKGROUND: The Aedes aegypti mosquito is the primary vector for several diseases. Its control requires a better understanding of the mosquitoes' live cycle, including the spatial dynamics. Several models address this issue. However, they rely on many hard to measure parameters. This work presents a model describing the spatial population dynamics of Aedes aegypti mosquitoes using partial differential equations (PDEs) relying on a few parameters. METHODS: We show how to estimate model parameter values from the experimental data found in the literature using concepts from dynamical systems, genetic algorithm optimization and partial differential equations. We show that our model reproduces some analytical formulas relating the carrying capacity coefficient to experimentally measurable quantities as the maximum number of mobile female mosquitoes, the maximum number of eggs, or the maximum number of larvae. As an application of the presented methodology, we replicate one field experiment numerically and investigate the effect of different frequencies in the insecticide application in the urban environment. RESULTS: The numerical results suggest that the insecticide application has a limited impact on the mosquitoes population and that the optimal application frequency is close to one week. CONCLUSIONS: Models based on partial differential equations provide an efficient tool for simulating mosquitoes' spatial population dynamics. The reduced model can reproduce such dynamics on a sufficiently large scale.

Spatial synchrony in population dynamics: The effects of demographic stochasticity and density regulation with a spatial scale.

We generalize a previous simple result by Lande et al. (1999) on how spatial autocorrelated noise, dispersal rate and distance as well as strength of density regulation determine the spatial scale of synchrony in population density. It is shown how demographic noise can be incorporated, what effect it has on variance and spatial scale of synchrony, and how it interacts with the point process for locations of individuals under random sampling. Although the effect of demographic noise is a rather complex interaction with environmental noise, migration and density regulation, its effect on population fluctuations and scale of synchrony can be presented in a transparent way. This is achieved by defining a characteristic area dependent on demographic and environmental variances as well as population density, and subsequently using this area to define a spatial demographic coefficient. The demographic noise acts through this coefficient on the spatial synchrony, which may increase or decrease with increasing demographic noise depending on other parameters. A second generalization yields the modeling of density regulation taking into account that regulation at a given location does not only depend on the density at that site but also on densities in the whole territory or home range of individuals. It is shown that such density regulation with a spatial scale reduces the scale of synchrony in population fluctuations relative to the simpler model with density regulation at each location determined only by the local point density, and may even generate negative spatial autocorrelations.

Dispersal-Dependent Oviposition and the Aggregation of Parasitism.

The prediction that parasitoid foraging effort should increase with distance traversed to reach or to locate hosts has had little experimental attention. Consistent with a number of models of foraging behavior, we found that the per capita number of ovipositions by the minute fairyfly-egg parasitoid Anagrus sophiae increased significantly with dispersal distance to planthopper hosts in the field in experimental patches of many host eggs. In large continuous stands of cordgrass host plants, after dispersal of decimeters or less, female wasps laid approximately 18% of their average of 18.6 eggs. After dispersal to plants isolated 10 m from other cordgrass, they laid approximately 84%, and they laid virtually all of their eggs after dispersal of 250 m to experimental floating islands of cordgrass. The increased oviposition following dispersal tripled the CV2 index of aggregation of parasitism to a level theoretically sufficient to promote locally stable parasitoid-host dynamics in isolated patches. At the same time, the change in wasp behavior did not affect the relationship between parasitism and host density, which was consistently density independent. Our results suggest that increased foraging effort with distance traversed can counter Allee effects in colonization and increase spatial spread of populations of natural enemies.