Implicit versus explicit vector management strategies in models for vector-borne disease epidemiology.

Throughout the vector-borne disease modeling literature, there exist two general frameworks for incorporating vector management strategies (e.g. area-wide adulticide spraying and larval source reduction campaigns) into vector population models, namely, the "implicit" and "explicit" control frameworks. The more simplistic "implicit" framework facilitates derivation of mathematically rigorous results on disease suppression and optimal control, but the biological connection of these results to real-world "explicit" control actions that could guide specific management actions is vague at best. Here, we formally define a biological and mathematical relationship between implicit and explicit control, and we provide mathematical expressions relating the strength of implicit control to management-relevant properties of explicit control for four common intervention strategies. These expressions allow the optimal control and basic reproduction number analyses typically utilized in implicit control modeling to be interpreted directly in terms of real-world actions and real-world monetary costs. Our methods reveal that only certain sub-classes of explicit control protocols are able to be represented as implicit controls, and that implicit control is a meaningful approximation of explicit control only when resonance-like synergistic effects between multiple explicit controls have negligible effects on population reduction. When non-negligible synergy exists, implicit control results, despite their mathematical tidiness, fail to provide accurate predictions regarding vector control and disease spread. Collectively, these elements build an effective bridge between analytically interesting and mathematically tractable implicit control and the challenging, action-oriented explicit control.

Exploring the functional composition of the human microbiome using a hand-curated microbial trait database.

BACKGROUND: Even when microbial communities vary wildly in their taxonomic composition, their functional composition is often surprisingly stable. This suggests that a functional perspective could provide much deeper insight into the principles governing microbiome assembly. Much work to date analyzing the functional composition of microbial communities, however, relies heavily on inference from genomic features. Unfortunately, output from these methods can be hard to interpret and often suffers from relatively high error rates. RESULTS: We built and analyzed a domain-specific microbial trait database from known microbe-trait pairs recorded in the literature to better understand the functional composition of the human microbiome. Using a combination of phylogentically conscious machine learning tools and a network science approach, we were able to link particular traits to areas of the human body, discover traits that determine the range of body areas a microbe can inhabit, and uncover drivers of metabolic breadth. CONCLUSIONS: Domain-specific trait databases are an effective compromise between noisy methods to infer complex traits from genomic data and exhaustive, expensive attempts at database curation from the literature that do not focus on any one subset of taxa. They provide an accurate account of microbial traits and, by limiting the number of taxa considered, are feasible to build within a reasonable time-frame. We present a database specific for the human microbiome, in the hopes that this will prove useful for research into the functional composition of human-associated microbial communities.

Managing disease outbreaks: The importance of vector mobility and spatially heterogeneous control.

Management strategies for control of vector-borne diseases, for example Zika or dengue, include using larvicide and/or adulticide, either through large-scale application by truck or plane or through door-to-door efforts that require obtaining permission to access private property and spray yards. The efficacy of the latter strategy is highly dependent on the compliance of local residents. Here we develop a model for vector-borne disease transmission between mosquitoes and humans in a neighborhood setting, considering a network of houses connected via nearest-neighbor mosquito movement. We incorporate large-scale application of adulticide via aerial spraying through a uniform increase in vector death rates in all sites, and door-to-door application of larval source reduction and adulticide through a decrease in vector emergence rates and an increase in vector death rates in compliant sites only, where control efficacies are directly connected to real-world experimentally measurable control parameters, application frequencies, and control costs. To develop mechanistic insight into the influence of vector motion and compliance clustering on disease controllability, we determine the basic reproduction number R0 for the system, provide analytic results for the extreme cases of no mosquito movement, infinite hopping rates, and utilize degenerate perturbation theory for the case of slow but non-zero hopping rates. We then determine the application frequencies required for each strategy (alone and combined) in order to reduce R0 to unity, along with the associated costs. Cost-optimal strategies are found to depend strongly on mosquito hopping rates, levels of door-to-door compliance, and spatial clustering of compliant houses, and can include aerial spray alone, door-to-door treatment alone, or a combination of both. The optimization scheme developed here provides a flexible tool for disease management planners which translates modeling results into actionable control advice adaptable to system-specific details.

Trait-based analysis of the human skin microbiome.

BACKGROUND: The past decade of microbiome research has concentrated on cataloging the diversity of taxa in different environments. The next decade is poised to focus on microbial traits and function. Most existing methods for doing this perform pathway analysis using reference databases. This has both benefits and drawbacks. Function can go undetected if reference databases are coarse-grained or incomplete. Likewise, detection of a pathway does not guarantee expression of the associated function. Finally, function cannot be connected to specific microbial constituents, making it difficult to ascertain the types of organisms exhibiting particular traits-something that is important for understanding microbial success in specific environments. A complementary approach to pathway analysis is to use the wealth of microbial trait information collected over years of lab-based, culture experiments. METHODS: Here, we use journal articles and Bergey's Manual of Systematic Bacteriology to develop a trait-based database for 971 human skin bacterial taxa. We then use this database to examine functional traits that are over/underrepresented among skin taxa. Specifically, we focus on three trait classes-binary, categorical, and quantitative-and compare trait values among skin taxa and microbial taxa more broadly. We compare binary traits using a Chi-square test, categorical traits using randomization trials, and quantitative traits using a nonparametric relative effects test based on global rankings using Tukey contrasts. RESULTS: We find a number of traits that are over/underrepresented within the human skin microbiome. For example, spore formation, acid phosphatase, alkaline phosphatase, pigment production, catalase, and oxidase are all less common among skin taxa. As well, skin bacteria are less likely to be aerobic, favoring, instead, a facultative strategy. They are also less likely to exhibit gliding motility, less likely to be spirillum or rod-shaped, and less likely to grow in chains. Finally, skin bacteria have more difficulty at high pH, prefer warmer temperatures, and are much less resilient to hypotonic conditions. CONCLUSIONS: Our analysis shows how an approach that relies on information from culture experiments can both support findings from pathway analysis, and also generate new insights into the structuring principles of microbial communities.

Detecting interaction networks in the human microbiome with conditional Granger causality.

Human microbiome research is rife with studies attempting to deduce microbial correlation networks from sequencing data. Standard correlation and/or network analyses may be misleading when taken as an indication of taxon interactions because "correlation is neither necessary nor sufficient to establish causation"; environmental filtering can lead to correlation between non-interacting taxa. Unfortunately, microbial ecologists have generally used correlation as a proxy for causality although there is a general consensus about what constitutes a causal relationship: causes both precede and predict effects. We apply one of the first causal models for detecting interactions in human microbiome samples. Specifically, we analyze a long duration, high resolution time series of the human microbiome to decipher the networks of correlation and causation of human-associated microbial genera. We show that correlation is not a good proxy for biological interaction; we observed a weak negative relationship between correlation and causality. Strong interspecific interactions are disproportionately positive, whereas almost all strong intraspecific interactions are negative. Interestingly, intraspecific interactions also appear to act at a short timescale causing vast majority of the effects within 1-3 days. We report how different taxa are involved in causal relationships with others, and show that strong interspecific interactions are rarely conserved across two body sites whereas strong intraspecific interactions are much more conserved, ranging from 33% between the gut and right-hand to 70% between the two hands. Therefore, in the absence of guiding assumptions about ecological interactions, Granger causality and related techniques may be particularly helpful for understanding the driving factors governing microbiome composition and structure.

Dynamic modelling of personal protection control strategies for vector-borne disease limits the role of diversity amplification.

Personal protection measures, such as bed nets and repellents, are important tools for the suppression of vector-borne diseases like malaria and Zika, and the ability of health agencies to distribute protection and encourage its use plays an important role in the efficacy of community-wide disease management strategies. Recent modelling studies have shown that a counterintuitive diversity-driven amplification in community-wide disease levels can result from a population's partial adoption of personal protection measures, potentially to the detriment of disease management efforts. This finding, however, may overestimate the negative impact of partial personal protection as a result of implicit restrictive model assumptions regarding host compliance, access to and longevity of protection measures. We establish a new modelling methodology for incorporating community-wide personal protection distribution programmes in vector-borne disease systems which flexibly accounts for compliance, access, longevity and control strategies by way of a flow between protected and unprotected populations. Our methodology yields large reductions in the severity and occurrence of amplification effects as compared to existing models.

Disentangling social interactions and environmental drivers in multi-individual wildlife tracking data.

While many animal species exhibit strong conspecific interactions, movement analyses of wildlife tracking datasets still largely focus on single individuals. Multi-individual wildlife tracking studies provide new opportunities to explore how individuals move relative to one another, but such datasets are frequently too sparse for the detailed, acceleration-based analytical methods typically employed in collective motion studies. Here, we address the methodological gap between wildlife tracking data and collective motion by developing a general method for quantifying movement correlation from sparsely sampled data. Unlike most existing techniques for studying the non-independence of individual movements with wildlife tracking data, our approach is derived from an analytically tractable stochastic model of correlated movement. Our approach partitions correlation into a deterministic tendency to move in the same direction termed 'drift correlation' and a stochastic component called 'diffusive correlation'. These components suggest the mechanisms that coordinate movements, with drift correlation indicating external influences, and diffusive correlation pointing to social interactions. We use two case studies to highlight the ability of our approach both to quantify correlated movements in tracking data and to suggest the mechanisms that generate the correlation. First, we use an abrupt change in movement correlation to pinpoint the onset of spring migration in barren-ground caribou. Second, we show how spatial proximity mediates intermittently correlated movements among khulans in the Gobi desert. We conclude by discussing the linkages of our approach to the theory of collective motion.This article is part of the theme issue 'Collective movement ecology'.

How Phenological Variation Affects Species Spreading Speeds.

In this paper, we develop a phenologically explicit reaction-diffusion model to analyze the spatial spread of a univoltine insect species. Our model assumes four explicit life stages: adult, two larval, and pupa, with a fourth, implicit, egg stage modeled as a time delay between oviposition and emergence as a larva. As such, our model is broadly applicable to holometabolous insects. To account for phenology (seasonal biological timing), we introduce four time-dependent phenological functions describing adult emergence, oviposition and larval conversion, respectively. Emergence is defined as the per-capita probability of an adult emerging from the pupal stage at a particular time. Oviposition is defined as the per-capita rate of adult egg deposition at a particular time. Two functions deal with the larva stage 1 to larva stage 2, and larva stage 2 to pupa conversion as per-capita rate of conversion at a particular time. This very general formulation allows us to accommodate a wide variety of alternative insect phenologies and lifestyles. We provide the moment-generating function for the general linearized system in terms of phenological functions and model parameters. We prove that the spreading speed of the linearized system is the same as that for nonlinear system. We then find explicit solutions for the spreading speed of the insect population for the limiting cases where (1) emergence and oviposition are impulsive (i.e., take place over an extremely narrow time window), larval conversion occurs at a constant rate, and larvae are immobile, (2) emergence and oviposition are impulsive (i.e., take place over an extremely narrow time window), larval conversion occurs at a constant rate starting at a delayed time from egg hatch, and larvae are immobile, and (3) emergence, oviposition, and larval conversion are impulsive. To consider other biological scenarios, including cases with emergence and oviposition windows of finite width as well as mobile larvae, we use numerical simulations. Our results provide a framework for understanding how phenology can interact with spatial spread to facilitate (or hinder) species expansion. This is an important area of research within the context of global change, which brings both new invasive species and range shifts for native species, all the while causing perturbations to species phenology that may impact the abilities of native and invasive populations to spread.

Metabolic division of labor in microbial systems.

Metabolic pathways are often engineered in single microbial populations. However, the introduction of heterologous circuits into the host can create a substantial metabolic burden that limits the overall productivity of the system. This limitation could be overcome by metabolic division of labor (DOL), whereby distinct populations perform different steps in a metabolic pathway, reducing the burden each population will experience. While conceptually appealing, the conditions when DOL is advantageous have not been rigorously established. Here, we have analyzed 24 common architectures of metabolic pathways in which DOL can be implemented. Our analysis reveals general criteria defining the conditions that favor DOL, accounting for the burden or benefit of the pathway activity on the host populations as well as the transport and turnover of enzymes and intermediate metabolites. These criteria can help guide engineering of metabolic pathways and have implications for understanding evolution of natural microbial communities.

Statistical analysis of co-occurrence patterns in microbial presence-absence datasets.

Drawing on a long history in macroecology, correlation analysis of microbiome datasets is becoming a common practice for identifying relationships or shared ecological niches among bacterial taxa. However, many of the statistical issues that plague such analyses in macroscale communities remain unresolved for microbial communities. Here, we discuss problems in the analysis of microbial species correlations based on presence-absence data. We focus on presence-absence data because this information is more readily obtainable from sequencing studies, especially for whole-genome sequencing, where abundance estimation is still in its infancy. First, we show how Pearson's correlation coefficient (r) and Jaccard's index (J)-two of the most common metrics for correlation analysis of presence-absence data-can contradict each other when applied to a typical microbiome dataset. In our dataset, for example, 14% of species-pairs predicted to be significantly correlated by r were not predicted to be significantly correlated using J, while 37.4% of species-pairs predicted to be significantly correlated by J were not predicted to be significantly correlated using r. Mismatch was particularly common among species-pairs with at least one rare species (<10% prevalence), explaining why r and J might differ more strongly in microbiome datasets, where there are large numbers of rare taxa. Indeed 74% of all species-pairs in our study had at least one rare species. Next, we show how Pearson's correlation coefficient can result in artificial inflation of positive taxon relationships and how this is a particular problem for microbiome studies. We then illustrate how Jaccard's index of similarity (J) can yield improvements over Pearson's correlation coefficient. However, the standard null model for Jaccard's index is flawed, and thus introduces its own set of spurious conclusions. We thus identify a better null model based on a hypergeometric distribution, which appropriately corrects for species prevalence. This model is available from recent statistics literature, and can be used for evaluating the significance of any value of an empirically observed Jaccard's index. The resulting simple, yet effective method for handling correlation analysis of microbial presence-absence datasets provides a robust means of testing and finding relationships and/or shared environmental responses among microbial taxa.

Invasion dynamics of competing species with stage-structure.

The spread of an invasive species often results in a decline and subsequent disappearance of native competitors. Several models, primarily based on spatially explicit Lotka-Volterra competition dynamics, have been developed to understand this phenomenon. In general, the goal of these models is to relate fundamental life history traits, for example dispersal ability and competition strength, to the rate of spread of the invasive species, which is also the rate at which the invasive species displaces its native competitor. Stage-structure is often an important determinant of population dynamics, but it has received little attention within the context of Lotka-Volterra invasion models. For many species, behaviors like dispersal and competition depend on life-stage. To describe the processes of invasion in these species, it is important to understand how behaviors that vary as a function of life-stage can impact spread rate. In this paper, we develop a spatially explicit, stage-structured Lotka-Volterra competition model. By comparing spread speed predictions from this model to spread speed predictions from an analogous single-stage model, we are able to determine when stage-structure is important and how stage-dependent behavior can alter the characteristics of an invasion.

A Stoichioproteomic Analysis of Samples from the Human Microbiome Project.

Ecological stoichiometry (ES) uses organism-specific elemental content to explain differences in species life histories, species interactions, community organization, environmental constraints and even ecosystem function. Although ES has been successfully applied to a range of different organisms, most emphasis on microbial ecological stoichiometry focuses on lake, ocean, and soil communities. With the recent advances in human microbiome research, however, large amounts of data are being generated that describe differences in community composition across body sites and individuals. We suggest that ES may provide a framework for beginning to understand the structure, organization, and function of human microbial communities, including why certain organisms exist at certain locations, and how they interact with both the other microbes in their environment and their human host. As a first step, we undertake a stoichioproteomic analysis of microbial communities from different body sites. Specifically, we compare and contrast the elemental composition of microbial protein samples using annotated sequencing data from 690 gut, vaginal, oral, nares, and skin samples currently available through the Human Microbiome Project. Our results suggest significant differences in both the median and variance of the carbon, oxygen, nitrogen, and sulfur contents of microbial protein samples from different locations. For example, whereas proteins from vaginal sites are high in carbon, proteins from skin and nasal sites are high in nitrogen and oxygen. Meanwhile, proteins from stool (the gut) are particularly high in sulfur content. We interpret these differences in terms of the local environments at different human body sites, including atmospheric exposure and food intake rates.

Perceptual Ranges, Information Gathering, and Foraging Success in Dynamic Landscapes.

How organisms gather and utilize information about their landscapes is central to understanding land-use patterns and population distributions. When such information originates beyond an individual's immediate vicinity, movement decisions require integrating information out to some perceptual range. Such nonlocal information, whether obtained visually, acoustically, or via chemosensation, provides a field of stimuli that guides movement. Classically, however, models have assumed movement based on purely local information (e.g., chemotaxis, step-selection functions). Here we explore how foragers can exploit nonlocal information to improve their success in dynamic landscapes. Using a continuous time/continuous space model in which we vary both random (diffusive) movement and resource-following (advective) movement, we characterize the optimal perceptual ranges for foragers in dynamic landscapes. Nonlocal information can be highly beneficial, increasing the spatiotemporal concentration of foragers on their resources up to twofold compared with movement based on purely local information. However, nonlocal information is most useful when foragers possess both high advective movement (allowing them to react to transient resources) and low diffusive movement (preventing them from drifting away from resource peaks). Nonlocal information is particularly beneficial in landscapes with sharp (rather than gradual) patch edges and in landscapes with highly transient resources.

Invasion speeds in microbial systems with toxin production and quorum sensing.

The theory of invasions and invasion speeds has traditionally been studied in macroscopic systems. Surprisingly, microbial invasions have received less attention. Although microbes share many of the features associated with competition between larger-bodied organisms, they also exhibit distinctive behaviors that require new mathematical treatments to fully understand invasions in microbial systems. Most notable is the possibility for long-distance interactions, including competition between populations mediated by diffusible toxins and cooperation among individuals of a single population using quorum sensing. In this paper, we model bacterial invasion using a system of coupled partial differential equations based on Fisher's equation. Our model considers a competitive system with diffusible toxins that, in some cases, are expressed in response to quorum sensing. First, we derive analytical approximations for invasion speeds in the limits of fast and slow toxin diffusion. We then test the validity of our analytical approximations and explore intermediate rates of toxin diffusion using numerical simulations. Interestingly, we find that toxins should diffuse quickly when used offensively, but that there are two optimal strategies when toxins are used as a defense mechanism. Specifically, toxins should diffuse quickly when their killing efficacy is high, but should diffuse slowly when their killing efficacy is low. Our approach permits an explicit investigation of the properties and characteristics of diffusible compounds used in non-local competition, and is relevant for microbial systems and select macroscopic taxa, such as plants and corals, that can interact through biochemicals.

Epidemiology of La Crosse Virus Emergence, Appalachia Region, United States.

La Crosse encephalitis is a viral disease that has emerged in new locations across the Appalachian region of the United States. Conventional wisdom suggests that ongoing emergence of La Crosse virus (LACV) could stem from the invasive Asian tiger (Aedes albopictus) mosquito. Efforts to prove this, however, are complicated by the numerous transmission routes and species interactions involved in LACV dynamics. To analyze LACV transmission by Asian tiger mosquitoes, we constructed epidemiologic models. These models accurately predict empirical infection rates. They do not, however, support the hypothesis that Asian tiger mosquitoes are responsible for the recent emergence of LACV at new foci. Consequently, we conclude that other factors, including different invasive mosquitoes, changes in climate variables, or changes in wildlife densities, should be considered as alternative explanations for recent increases in La Crosse encephalitis.

Antibiotics as a selective driver for conjugation dynamics.

It is generally assumed that antibiotics can promote horizontal gene transfer. However, because of a variety of confounding factors that complicate the interpretation of previous studies, the mechanisms by which antibiotics modulate horizontal gene transfer remain poorly understood. In particular, it is unclear whether antibiotics directly regulate the efficiency of horizontal gene transfer, serve as a selection force to modulate population dynamics after such gene transfer has occurred, or both. Here, we address this question by quantifying conjugation dynamics in the presence and absence of antibiotic-mediated selection. Surprisingly, we find that sublethal concentrations of antibiotics from the most widely used classes do not significantly increase the conjugation efficiency. Instead, our modelling and experimental results demonstrate that conjugation dynamics are dictated by antibiotic-mediated selection, which can both promote and suppress conjugation dynamics. Our findings suggest that the contribution of antibiotics to the promotion of horizontal gene transfer may have been overestimated. These findings have implications for designing effective antibiotic treatment protocols and for assessing the risks of antibiotic use.

Persistence and Spreading Speeds of Integro-Difference Equations with an Expanding or Contracting Habitat.

We study an integro-difference equation model that describes the spatial dynamics of a species in an expanding or contracting habitat. We give conditions under which the species disperses to a region of poor quality where the species eventually becomes extinct. We show that when the species persists in the habitat, the rightward and leftward spreading speeds are determined by c, the speed at which the habitat quality increases or decreases in time, as well as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which are formulated in terms of the dispersal kernel and species growth rates in both directions. We demonstrate that in the case that the species grows everywhere in space, the rightward spreading speed is [Formula: see text] if c is relatively small and is [Formula: see text] if c is large, and the leftward spreading speed is one of [Formula: see text], [Formula: see text], or [Formula: see text]. We also show that it is possible for a solution to form a two-layer wave, with the propagation speeds of the two layers analytically determined.

A dynamical model for bark beetle outbreaks.

Tree-killing bark beetles are major disturbance agents affecting coniferous forest ecosystems. The role of environmental conditions on driving beetle outbreaks is becoming increasingly important as global climatic change alters environmental factors, such as drought stress, that, in turn, govern tree resistance. Furthermore, dynamics between beetles and trees are highly nonlinear, due to complex aggregation behaviors exhibited by beetles attacking trees. Models have a role to play in helping unravel the effects of variable tree resistance and beetle aggregation on bark beetle outbreaks. In this article we develop a new mathematical model for bark beetle outbreaks using an analogy with epidemiological models. Because the model operates on several distinct time scales, singular perturbation methods are used to simplify the model. The result is a dynamical system that tracks populations of uninfested and infested trees. A limiting case of the model is a discontinuous function of state variables, leading to solutions in the Filippov sense. The model assumes an extensive seed-bank so that tree recruitment is possible even if trees go extinct. Two scenarios are considered for immigration of new beetles. The first is a single tree stand with beetles immigrating from outside while the second considers two forest stands with beetle dispersal between them. For the seed-bank driven recruitment rate, when beetle immigration is low, the forest stand recovers to a beetle-free state. At high beetle immigration rates beetle populations approach an endemic equilibrium state. At intermediate immigration rates, the model predicts bistability as the forest can be in either of the two equilibrium states: a healthy forest, or a forest with an endemic beetle population. The model bistability leads to hysteresis. Interactions between two stands show how a less resistant stand of trees may provide an initial toe-hold for the invasion, which later leads to a regional beetle outbreak in the resistant stand.

How Resource Phenology Affects Consumer Population Dynamics.

Climate change drives uneven phenology shifts across taxa, and this can result in changes to the phenological match between interacting species. Shifts in the relative phenology of partner species are well documented, but few studies have addressed the effects of such changes on population dynamics. To explore this, we develop a phenologically explicit model describing consumer-resource interactions. Focusing on scenarios for univoltine insects, we show how changes in resource phenology can be reinterpreted as transformations in the year-to-year recursion relationships defining consumer population dynamics. This perspective provides a straightforward path for interpreting the long-term population consequences of phenology change. Specifically, by relating the outcome of phenological shifts to species traits governing recursion relationships (e.g., consumer fecundity or competitive scenario), we demonstrate how changes in relative phenology can force systems into different dynamical regimes, with major implications for resource management, conservation, and other areas of applied dynamics.

How Oviposition Behavior Determines Persistence in Small Patches and Changing Climates.

Habitat loss and climate change jointly threaten a large fraction of earth's biodiversity. A key goal is to understand how these threats play out differentially across species. Focusing on insects that undergo an ontogenetic shift in habitat requirements, we use critical patch size models to examine how breeding strategy influences the abilities of different kinds of species to persist in small habitat patches. In general, we find that income breeders require larger habitat patches for population persistence than do capital breeders. However, increases in patch size requirements as a result of factors that limit oviposition (e.g., resource availability, weather conditions) are more severe for capital breeders than for income breeders. From a conservation perspective, our work suggests that a species' sensitivity to habitat loss, both today and in the future, can depend critically on evolved behavioral strategies. Explicit consideration of such behavioral strategies, including a careful accounting of their relationship with dispersal and survival, provides a map linking life-history spectra, spatial requirements, and management.