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Changes to migration routes and phenology create novel contact patterns among hosts and pathogens. These novel contact patterns can lead to pathogens spilling over between resident and migrant populations. Predicting the consequences of such pathogen spillover events requires understanding how pathogen evolution depends on host movement behaviour. Following spillover, pathogens may evolve changes in their transmission rate and virulence phenotypes because different strategies are favoured by resident and migrant host populations. There is conflict in current theoretical predictions about what those differences might be. Some theory predicts lower pathogen virulence and transmission rates in migrant populations because migrants have lower tolerance to infection. Other theoretical work predicts higher pathogen virulence and transmission rates in migrants because migrants have more contacts with susceptible hosts. We aim to understand how differences in tolerance to infection and host pace of life act together to determine the direction of pathogen evolution following pathogen spillover from a resident to a migrant population. We constructed a spatially implicit model in which we investigate how pathogen strategy changes following the addition of a migrant population. We investigate how differences in tolerance to infection and pace of life between residents and migrants determine the effect of spillover on pathogen evolution and host population size. When the paces of life of the migrant and resident hosts are equal, larger costs of infection in the migrants lead to lower pathogen transmission rate and virulence following spillover. When the tolerance to infection in migrant and resident populations is equal, faster migrant paces of life lead to increased transmission rate and virulence following spillover. However, the opposite can also occur: when the migrant population has lower tolerance to infection, faster migrant paces of life can lead to decreases in transmission rate and virulence. Predicting the outcomes of pathogen spillover requires accounting for both differences in tolerance to infection and pace of life between populations. It is also important to consider how movement patterns of populations affect host contact opportunities for pathogens. These results have implications for wildlife conservation, agriculture and human health.
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Animais Selvagens , Interações Hospedeiro-Patógeno , Animais , Humanos , VirulênciaRESUMO
Our ability to understand population spread dynamics is complicated by rapid evolution, which renders simple ecological models insufficient. If dispersal ability evolves, more highly dispersive individuals may arrive at the population edge than less dispersive individuals (spatial sorting), accelerating spread. If individuals at the low-density population edge benefit (escape competition), high dispersers have a selective advantage (spatial selection). These two processes are often described as forming a positive feedback loop; they reinforce each other, leading to faster spread. Although spatial sorting is close to universal, this form of spatial selection is not: low densities can be detrimental for organisms with Allee effects. Here, we present two conceptual models to explore the feedback loops that form between spatial sorting and spatial selection. We show that the presence of an Allee effect can reverse the positive feedback loop between spatial sorting and spatial selection, creating a negative feedback loop that slows population spread.
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Modelos Biológicos , Modelos Teóricos , Humanos , Dinâmica PopulacionalRESUMO
Animal migration impacts organismal health and parasite transmission: migrants are simultaneously exposed to parasites and able to reduce infection for both individuals and populations. However, these dynamics are difficult to study; empirical studies reveal disparate results while existing theory makes assumptions that simplify natural complexity. Here, we systematically review empirical studies of migration and infection across taxa, highlighting key gaps in our understanding. Next, we develop a unified evolutionary framework incorporating different selective pressures of parasite-migration interactions while accounting for ecological complexity that goes beyond previous theory. Our framework generates diverse migration-infection patterns paralleling those seen in empirical systems, including partial and differential migration. Finally, we generate predictions about which mechanisms dominate which empirical systems to guide future studies. Our framework provides an overarching understanding of selective pressures shaping migration patterns in the context of animal health and disease, which is critical for predicting how environmental change may threaten migration.
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Parasitos , Doenças Parasitárias , Humanos , Animais , Migração Animal , Ecossistema , Evolução BiológicaRESUMO
This investigation seeks to integrate LAPONITE® clay gels with thermoresponsive branched copolymer surfactants (BCSs) to develop advanced functional materials with temperature-induced sol-gel behaviour. It is known that a diverse range of molecules adsorb strongly to clays which may be used to control liberation of the species in healthcare applications, and as such the development of polymer/clay hybrid materials which can add function to the native clay behaviour are of great interest. BCS were synthesised with a structure that encompasses poly(ethylene glycol)methacrylate (PEGMA), ethylene glycol dimethacrylate (EGDMA), and dodecanethiol (DDT), conferring versatile and tuneable thermoresponsive attributes. Systematic modulation of the monomer : DDT/initiator ratio was used to facilitate the synthesis of BCS architectures spanning a range of molecular weights. Through application of small-amplitude oscillatory shear (SAOS) rheology and small-angle neutron scattering (SANS) in conjunction with controlled temperature variations, the sol-gel transition dynamics of these nanocomposite materials were elucidated. Complementary insights into the mechanisms underpinning this transition and temperature-induced alterations in the constituents are gleaned through the utilization of SANS techniques employing contrast-matching methodologies to mitigate clay and polymer scattering interference. It is found that heating systems from room- to body- temperature induces self-assembly of BCS in the bulk aqueous phase with concurrent structuration of clay in gel-forming samples with lower number average molecular weight (Mn). SANS study unpicks this phenomenon to find that gelation occurs with concurrent aggregation of BCS in the bulk, inducing clay-clay interactions only in lower Mn BCS systems with large nanoaggregates.
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The rate at which a species responds to natural selection is a central predictor of the species' ability to adapt to environmental change. It is well-known that spatially-structured environments slow the rate of adaptation due to increased intra-genotype competition. Here, we show that this effect magnifies over time as a species becomes better adapted and grows faster. Using a reaction-diffusion model, we demonstrate that growth rates are inextricably coupled with effective spatial scales, such that higher growth rates cause more localized competition. This has two effects: selection requires more generations for beneficial mutations to fix, and spatially-caused genetic drift increases. Together, these effects diminish the value of additional growth rate mutations in structured environments.
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Adaptação Biológica/genética , Modelos Genéticos , Mutação/genética , Crescimento Demográfico , Seleção Genética/genética , Deriva Genética , GenótipoRESUMO
Numerous theoretical models have demonstrated that migration, a seasonal animal movement behaviour, can minimize the risks and costs of parasite infection. Past work on migration-infection interactions assumes migration is the only strategy available to organisms for dealing with the parasite infection, that is they migrate to a different environment to recover or escape from infection. Thus, migration is similar to the non-spatial strategy of resistance, where hosts prevent infection or kill parasites once infected. However, an alternative defence strategy is to tolerate the infection and experience a lower cost to the infection. To our knowledge, no studies have examined how migration can change based on combining two host strategies (migration and tolerance) for dealing with parasites. In this paper, we aim to understand how both parasite transmission and infection tolerance can influence the host's migratory behaviour. We constructed a model that incorporates two host strategies (migration and tolerance) to understand whether allowing for tolerance affects the proportion of the population that migrates at equilibrium in response to infection. We show that the benefits of tolerance can either decrease or increase the host's migration. Also, if the benefit of migration is great, then individuals are more likely to migrate regardless of the presence of tolerance. Finally, we find that the transmission rate of parasite infection can either decrease or increase the tolerant host's migration, depending on the cost of migration. These findings highlight that adopting two defence strategies is not always beneficial to the hosts. Instead, a single strategy is often better, depending on the costs and benefits of the strategies and infection pressures. Our work further suggests that multiple host-defence strategies as a potential explanation for the evolution of migration to minimize the parasite infection. Moreover, migration can also affect the ecological and evolutionary dynamics of parasite-host interactions.
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Parasitos , Doenças Parasitárias , Migração Animal , Animais , Interações Hospedeiro-Parasita , Modelos TeóricosRESUMO
Habitat loss and fragmentation can negatively influence population persistence and biodiversity, but the effects can be mitigated if species successfully disperse between isolated habitat patches. Network models are the primary tool for quantifying landscape connectivity, yet in practice, an overly simplistic view of species dispersal is applied. These models often ignore individual variation in dispersal ability under the assumption that all individuals move the same fixed distance with equal probability. We developed a modeling approach to address this problem. We incorporated dispersal kernels into network models to determine how individual variation in dispersal alters understanding of landscape-level connectivity and implemented our approach on a fragmented grassland landscape in Minnesota. Ignoring dispersal variation consistently overestimated a population's robustness to local extinctions and underestimated its robustness to local habitat loss. Furthermore, a simplified view of dispersal underestimated the amount of habitat substructure for small populations but overestimated habitat substructure for large populations. Our results demonstrate that considering biologically realistic dispersal alters understanding of landscape connectivity in ecological theory and conservation practice.
Consecuencias de la Omisión de la Variación en la Dispersión en los Modelos de Redes para la Conectividad de Paisajes Resumen La pérdida y la fragmentación del hábitat pueden influir negativamente la persistencia de poblaciones y biodiversidad. Sin embargo, estos efectos pueden ser mitigados si las especies tienen una dispersión exitosa entre los fragmentos aislados de hábitat. Los modelos de redes son la herramienta principal para la cuantificación de la conectividad del paisaje, no obstante en la práctica, se tiende a usar una visión excesivamente simplista de la dispersión de especies. Es común que estos modelos ignoren la variación que existe entre individuos en sus habilidades de dispersión y que asuman que todos los individuos se pueden mover la misma distancia y con la misma probabilidad. En este estudio, desarrollamos una estrategia de modelaje para (minimizar o aminorar) estas limitaciones incorporando kernels de dispersión dentro de los modelos de redes para determinar cómo la variación individual de la dispersión altera el entendimiento de la conectividad a nivel de paisaje. Como un ejemplo, implementamos esta estrategia en un paisaje de pastizal fragmentado en Minnesota. Omitir la variación en la dispersión generó una sobreestimación sistemática de la robustez de la población ante las extinciones locales y una subestimación de la robustez ante la pérdida local del hábitat. Además, una visión simplificada de la dispersión subestimó la complejidad de hábitat para las poblaciones pequeñas, sin emgargo sobreestimó la complejidad para las poblaciones grandes. Nuestros resultados demuestran que incorporar parámetros que describan una dispersión biológica realista tiene implicaciones importantes en la teoría de conectividad de paisajes e implementación de practicas de conservación.
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Conservação dos Recursos Naturais , Ecossistema , Biodiversidade , HumanosRESUMO
Most of the classical theory on species coexistence has been based on species-level competitive trade-offs. However, it is becoming apparent that plant species display high levels of trait plasticity. The implications of this plasticity are almost completely unknown for most coexistence theory. Here, we model a competition-colonisation trade-off and incorporate trait plasticity to evaluate its effects on coexistence. Our simulations show that the classic competition-colonisation trade-off is highly sensitive to environmental circumstances, and coexistence only occurs in narrow ranges of conditions. The inclusion of plasticity, which allows shifts in competitive hierarchies across the landscape, leads to coexistence across a much broader range of competitive and environmental conditions including disturbance levels, the magnitude of competitive differences between species, and landscape spatial patterning. Plasticity also increases the number of species that persist in simulations of multispecies assemblages. Plasticity may generally increase the robustness of coexistence mechanisms and be an important component of scaling coexistence theory to higher diversity communities.
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Ecossistema , Plantas , Modelos Biológicos , FenótipoRESUMO
Climate change is an escalating threat facing populations around the globe, necessitating a robust understanding of the ecological and evolutionary mechanisms dictating population responses. However, populations respond to climate change not in isolation but rather in the context of their existing ranges. In particular, spatial population structure within a range (e.g., trait clines, starkness of range edges, etc.) likely interacts with other ecological and evolutionary processes during climate-induced range shifts. Here, we use an individual-based model to explore the interacting roles of several such factors in range shift dynamics. We show that increased spatial population structure (driven primarily by a steeper environmental gradient) severely increases a population's extinction risk. Further, we show that while evolution of heightened dispersal during range shifts can aid populations in tracking changing conditions, it can also interact negatively with adaptation to the environmental gradient, leading to reduced fitness and contributing to the increased extinction risk observed in populations structured along steep environmental gradients. Our results demonstrate that the effect of dispersal evolution on range-shifting populations is dependent on environmental context and that spatial population structure can substantially increase extinction risk in range shifts.
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Distribuição Animal , Mudança Climática , Clima , Extinção Biológica , Dispersão Vegetal , Animais , Modelos Biológicos , Plantas , Dinâmica Populacional , Análise EspacialRESUMO
Pathogen and parasite infections are increasingly recognized as powerful drivers of animal movement, including migration. Yet, infection-related migration benefits can result from a combination of environmental and/or social conditions, which can be difficult to disentangle. Here, we focus on two infection-related mechanisms that can favour migration: moving to escape versus recover from infection. By directly comparing the evolution of migration in response to each mechanism, we can evaluate the likely importance of changing abiotic conditions (linked to migratory recovery) with changing social conditions (linked to migratory escape) in terms of infection-driven migration. We built a mathematical model and analysed it using numerically simulated adaptive dynamics to determine when migration should evolve for each migratory recovery and social migratory escape. We found that a higher fraction of the population migrated under migratory recovery than under social migratory escape. We also found that two distinct migratory strategies (e.g. some individuals always migrate and others only occasionally migrate) sometimes coexisted within populations with social migratory escape, but never with migratory recovery. Our results suggest that migratory recovery is more likely to promote the evolution of migratory behaviour, rather than escape from infected conspecifics (social migratory escape).
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Migração Animal , Modelos Teóricos , AnimaisRESUMO
Diarylethenes (DAEs) represent an important class of photochromes with notable characteristics, like thermally irreversible photoisomerization and high fatigue resistance. Structural diversification of the DAE scaffold has enabled further refinement of photochromic properties and realization of new applications, ranging from advanced materials to tools for studying biological systems. In particular, methods for synthesizing non-symmetric DAE scaffolds, which are typically more challenging to synthesize than their symmetric counterparts, have grown over the past 20 years. These developments are surveyed in this review, with discussion of how access to these compounds has contributed to the improvement of photochromic properties and paved the way for exploring new applications of DAEs. First, non-symmetric DAE structures are classified and their uses and applications are overviewed. Subsequent sections discuss the main strategies that have been used to access non-symmetric DAEs with examples illustrating the impact of non-symmetric DAEs in the growing field of light-controlled molecular systems.
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Density dependence plays an important role in population regulation and is known to generate temporal fluctuations in population density. However, the ways in which density dependence affects spatial population processes, such as species invasions, are less understood. Although classical ecological theory suggests that invasions should advance at a constant speed, empirical work is illuminating the highly variable nature of biological invasions, which often exhibit nonconstant spreading speeds, even in simple, controlled settings. Here, we explore endogenous density dependence as a mechanism for inducing variability in biological invasions with a set of population models that incorporate density dependence in demographic and dispersal parameters. We show that density dependence in demography at low population densities-i.e., an Allee effect-combined with spatiotemporal variability in population density behind the invasion front can produce fluctuations in spreading speed. The density fluctuations behind the front can arise from either overcompensatory population growth or density-dependent dispersal, both of which are common in nature. Our results show that simple rules can generate complex spread dynamics and highlight a source of variability in biological invasions that may aid in ecological forecasting.
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Espécies Introduzidas , Modelos Biológicos , Dinâmica PopulacionalRESUMO
The spread of vector-borne pathogens depends on a complex set of interactions among pathogen, vector, and host. In single-host systems, pathogens can induce changes in vector preferences for infected vs. healthy hosts. Yet it is unclear if pathogens also induce changes in vector preference among host species, and how changes in vector behaviour alter the ecological dynamics of disease spread. Here, we couple multi-host preference experiments with a novel model of vector preference general to both single and multi-host communities. We show that viruliferous aphids exhibit strong preferences for healthy and long-lived hosts. Coupling experimental results with modelling to account for preference leads to a strong decrease in overall pathogen spread through multi-host communities due to non-random sorting of viruliferous vectors between preferred and non-preferred host species. Our results demonstrate the importance of the interplay between vector behaviour and host diversity as a key mechanism in the spread of vectored-diseases.
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Afídeos , Insetos Vetores , Animais , Vetores de Doenças , Ecologia , Doenças das PlantasRESUMO
Understanding the causes of larval dispersal is a major goal of marine ecology, yet most research focuses on proximate causes. Here we ask how ultimate, evolutionary causes affect dispersal. Building on Hamilton and May's classic 1977 article "Dispersal in Stable Habitats," we develop analytic and simulation models for the evolution of dispersal kernels in spatially structured habitats. First, we investigate dispersal in a world without edges and find that most offspring disperse as far as possible, opposite the pattern of empirical data. Adding edges to our model world leads to nearly all offspring dispersing short distances, again a mismatch with empirical data. Adding resource heterogeneity improves our results: most offspring disperse short distances with some dispersing longer distances. Finally, we simulate dispersal evolution in a real seascape in Belize and find that the simulated dispersal kernel and an empirical dispersal kernel from that seascape both have the same shape, with a high level of short-distance dispersal and a low level of long-distance dispersal. The novel contributions of this work are to provide a spatially explicit analytic extension of Hamilton and May's 1977 work, to demonstrate that our spatially explicit simulations and analytic models provide equivalent results, and to use simulation approaches to investigate the evolution of dispersal kernel shape in spatially complex habitats. Our model could be modified in various ways to investigate dispersal evolution in other species and seascapes, providing new insights into patterns of marine larval dispersal.
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Distribuição Animal , Evolução Biológica , Ecossistema , Modelos Genéticos , Seleção Genética , Animais , Larva , PerciformesRESUMO
Most studies on the evolution of migration focus on food, mates and/or climate as factors influencing these movements, whereas negative species interactions such as predators, parasites and pathogens are often ignored. Although infection and its associated costs clearly have the potential to influence migration, thoroughly studying these interactions is challenging without a solid theoretical framework from which to develop testable predictions in natural systems. Here, we aim to understand when parasites favour the evolution of migration. We develop a general model which enables us to explore a broad range of biological conditions and to capture population and infection dynamics over both ecological and evolutionary time-scales. We show that when migration evolves depends on whether the costs of migration and infection are paid in reduced fecundity or survival. Also important are the parasite transmission mode and spatiotemporal dynamics of infection and recovery (if it occurs). Finally, we find that partial migration (where only a fraction of the population migrates) can evolve but only when parasite transmission is density-dependent. Our results highlight the critical, if overlooked, role of parasites in shaping long-distance movement patterns, and suggest that infection should be considered alongside more traditional drivers of migration in both empirical and theoretical studies.
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Infecções , Parasitos , Animais , Ecologia , Interações Hospedeiro-Parasita , Modelos TeóricosRESUMO
The choice of a modeling approach is a critical decision in the modeling process, as it determines the complexity of the model and the phenomena that the model captures. In this paper, we developed an individual-based model (IBM) and compared it to a previously published ordinary differential equation (ODE) model, both developed to describe the same biological system although with slightly different emphases given the underlying assumptions and processes of each modeling approach. We used both models to examine the effect of insect vector life history and behavior traits on the spread of a vector-borne plant virus, and determine how choice of approach affects the results and their biological interpretation. A non-random distribution of insect vectors across plant hosts emerged in the IBM version of the model and was not captured by the ODE. This distribution led simultaneously to a slower-growing vector population and a faster spread of the pathogen among hosts. The IBM model also enabled us to test the effect of potential control measures to slow down virus transmission. We found that removing virus-infected hosts was a more effective strategy for controlling infection than removing vector-infested hosts. Our findings highlight the need to carefully consider possible modeling approaches before constructing a model.
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Modelos Biológicos , Doenças das Plantas/etiologia , Doenças Transmitidas por Vetores/etiologia , Animais , Análise por Conglomerados , Simulação por Computador , Interações entre Hospedeiro e Microrganismos , Insetos Vetores/virologia , Luteovirus/patogenicidade , Conceitos Matemáticos , Doenças das Plantas/prevenção & controle , Doenças das Plantas/virologia , Poaceae/virologia , Dinâmica Populacional/estatística & dados numéricos , Processos Estocásticos , Análise de Sistemas , Biologia de Sistemas , Doenças Transmitidas por Vetores/prevenção & controle , Doenças Transmitidas por Vetores/virologiaRESUMO
Parasites have long been thought to influence the evolution of migration, but precisely determining the conditions under which this occurs by quantifying costs of infection remains a challenge. Here we developed a model that demonstrates how the metric used to describe infection (richness/diversity, prevalence or intensity) shapes the prediction of whether migration will evolve. The model shows that predictions based on minimizing richness yield opposite results compared to those based on minimizing prevalence, with migration only selected for when minimizing prevalence. Consistent with these findings, empirical studies that measure parasite diversity typically find that migrants are worse off than residents, while those measuring prevalence or intensity find the opposite. Our own empirical analysis of fish parasite data finds that migrants (of all types) have higher parasite richness than residents, but with no significant difference in either prevalence or intensity.
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Migração Animal , Biodiversidade , Peixes/fisiologia , Peixes/parasitologia , Interações Hospedeiro-Parasita/fisiologia , Parasitos/fisiologia , Animais , Modelos Biológicos , PrevalênciaRESUMO
Species-level dispersal information can give mechanistic insights into how spatial processes impact plant communities. Unfortunately, field-based estimates of the dispersal abilities of multiple members of a community are often lacking for many plant systems. Here, we provide a simple method for measuring dispersal ability for large numbers of grassland plant species based on functional traits. Using this method, we estimated the dispersal ability of 50 co-occurring grassland species using the Wald Analytical Long-distance Dispersal (WALD) model. Grassland plants species are often used for developing community theory, yet species-level estimates of their dispersal abilities are comparatively rare. We use these dispersal measurements to examine the relationship between species dispersal abilities and successional dynamics using data from a 90-yr old field chronosequence. We find that our estimated dispersal measurements matched field-based establishment observations well, and estimated species colonization, competitive, and establishment abilities. We hope that this method for measuring dispersal ability of multiple species within a community, and its demonstrated ability to generate predictions for spatial ecology, will encourage more studies of the explicit role of dispersal in plant community ecology.
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Ecologia , Dispersão de Sementes , PlantasRESUMO
The rate at which a population grows and spreads can depend on individual behaviour and interactions with others. In many species with two sexes, males and females differ in key life-history traits (e.g. growth, survival and dispersal), which can scale up to affect population rates of growth and spread. In sexually reproducing species, the mechanics of locating mates and reproducing successfully introduce further complications for predicting the invasion speed (spread rate), as both can change nonlinearly with density. Most models of population spread are based on one sex, or include limited aspects of sex differences. Here we ask whether and how the dynamics of finding mates interact with sex-specific life-history traits to influence the rate of population spread. We present a hybrid approach for modelling invasions of populations with two sexes that links individual-level mating behaviour (in an individual-based model) to population-level dynamics (in an integrodifference equation model). We find that limiting the amount of time during which individuals can search for mates causes a demographic Allee effect which can slow, delay, or even prevent an invasion. Furthermore, any sex-based asymmetries in life history or behaviour (skewed sex ratio, sex-biased dispersal, and sex-specific mating behaviours) amplify these effects. In contrast, allowing individuals to mate more than once ameliorates these effects, enabling polygynandrous populations to invade under conditions where monogamously mating populations would fail to establish. We show that details of individuals' mating behaviour can impact the rate of population spread. Based on our results, we propose a stricter definition of a mate-finding Allee effect, which is not met by the commonly used minimum mating function. Our modelling approach, which links individual- and population-level dynamics in a single model, may be useful for exploring other aspects of individual behaviour that are thought to impact the rate of population spread.
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Distribuição Animal , Aptidão Genética , Preferência de Acasalamento Animal , Animais , Feminino , Masculino , Modelos Genéticos , Densidade Demográfica , Fatores SexuaisRESUMO
Plant viruses, often spread by arthropod vectors, impact natural and agricultural ecosystems worldwide. Intuitively, the movement behavior and life history of vectors influence pathogen spread, but the relative contribution of each factor has not been examined. Recent research has highlighted the influence of host infection status on vector behavior and life history. Here, we developed a model to explore how vector traits influence the spread of vector-borne plant viruses. We allowed vector life history (growth rate, carrying capacity) and movement behavior (departure and settlement rates) parameters to be conditional on whether the plant host is infected or healthy and whether the vector is viruliferous (carrying the virus) or not. We ran simulations under a wide range of parameter combinations and quantified the fraction of hosts infected over time. We also ran case studies of the model for Barley yellow dwarf virus, a persistently transmitted virus, and for Potato virus Y, a non-persistently transmitted virus. We quantified the relative importance of each parameter on pathogen spread using Latin hypercube sampling with the statistical partial rank correlation coefficient technique. We found two general types of mechanisms in our model that increased the rate of pathogen spread. First, increasing factors such as vector intrinsic growth rate, carrying capacity, and departure rate from hosts (independent of whether these factors were condition-dependent) led to more vectors moving between hosts, which increased pathogen spread. Second, changing condition-dependent factors such as a vector's preference for settling on a host with a different infection status than itself, and vector tendency to leave a host of the same infection status, led to increased contact between hosts and vectors with different infection statuses, which also increased pathogen spread. Overall, our findings suggest that vector population growth rates had the greatest influence on rates of virus spread, but rates of vector dispersal from infected hosts and from hosts of the same infection status were also very important. Our model highlights the importance of simultaneously considering vector life history and behavior to better understand pathogen spread. Although developed for plant viruses, our model could readily be utilized with other vector-borne pathogen systems.