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Abstract: Abstract Previous work involving integro-difference equations of a single species in a homogenous environment has emphasized spreading behavior in unbounded habitats. We show that, under suitable conditions, a simple scalar integro-difference equation incorporating a strong Allee effect and overcompensation can produce solutions where the population persists in an essentially bounded domain without spread despite the homogeneity of the environment. These solutions are robust in that they occupy a region of full measure in parameter space. We develop orbit diagrams showing various patterns of nonspreading solutions from stable equilibria, period-two, to higher periodicity. We show that from a relatively uniform initial density with small stochastic perturbations, a population consisting of multiple isolated patches can emerge. In ecological terms, this work suggests a novel endogenous mechanism for the creation of patch boundaries. PubDate: 2023-12-01
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Abstract: Abstract Although past work has considered how evolution and Allee effects each shape population spread, these factors have rarely been considered together. We develop an integrodifference equation model that tracks individuals of multiple dispersal types (i.e., short- and long-distance dispersers) of male and female individuals subject to a strong Allee effect due to mate-finding process. We use our model to explore how mutation between different dispersal types affects the rate of population spread, since this evolutionary mechanism has been shown to lead to both faster and slower spread in a previous individual-based model. We ask, under what conditions does mutation cause the population to spread faster (or slower) than it spreads without mutation (from the same initial conditions)' We find that mutation can both speed up and slow down invasions. Speeding up occurs in a relatively small range of parameter space near the Allee threshold of the population. Slowing down occurs across a broad range of parameters. PubDate: 2023-12-01
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Abstract: Abstract Climate change and its consequences such as sea-level rise will modify environmental gradients, altering the spatial spread and persistence of plant populations. However, ecosystem engineers can also modify environmental gradients. To quantify the potential interactive effects of climate change and ecosystem engineering on population spread rates, we develop a spatial model that explicitly focuses on feedbacks between coastal vegetation growth and the environmental gradient of marsh elevation. We use the model to determine how sea-level rise could change how ecosystem engineering affects the spread rate of marsh populations. The model demonstrates that low levels of ecosystem engineering can produce the highest population spread rates in the absence of sea-level rise in initially low-elevation marshes. However, higher rates of ecosystem engineering and initially higher elevation marshes produce the highest population spread rates in the presence of sea-level rise. Sea-level rise can therefore reverse the conditions that drive high rates of spatial spread: engineers with low rates of spatial spread prior to sea-level rise may spread faster as sea levels rise. This result suggests that sea-level rise may promote the spread of invasive ecosystem engineers that previously experienced low rates of spatial spread. Moreover, ecosystem engineering can serve as a mechanism for adaptation to climate-driven changes in environmental gradients. Ecosystem engineering has the potential to rescue both native and exotic plant populations from climate-driven decreases in habitat suitability. PubDate: 2023-12-01
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Abstract: Abstract Growth in individual body size amongst different species can to a greater or lesser extent depend on environmental factors such as resource availability. Individual growth curves can therefore be largely fixed or more plastic. Classic theory about phenotypic plasticity assumes that such plasticity has associated costs. In contrast, according to dynamic energy budget theory, maintaining a fixed growth rate in the face of variable resource availability would incur additional energetic costs. In this article, we explore the simultaneous evolution of the degree of plasticity in individual growth curves and the rate of non-plastic, environment-independent individual growth. We explore different relations between possible additional energetic costs and the degree of growth curve plasticity. To do so, we use adaptive dynamics to analyze a size-structured population model that is based on dynamic energy budget theory to account for the energetic trade-offs within an individual. We show that simultaneous evolution of the degree of growth curve plasticity and the rate of non-plastic individual growth will drive these traits to intermediate values at first. Afterwards, the degree of growth curve plasticity might evolve slowly towards extreme values depending on whether energetic costs increase or decrease with the degree of plasticity. In addition, the analysis shows that it is unlikely to encounter species in which individual growth is entirely fixed or entirely plastic, opposing general assumptions in dynamic energy budget theory. PubDate: 2023-11-29
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Abstract: Abstract Integrodifference equations are a discrete-time spatially explicit model that describes the dispersal of ecological populations through space. This framework is useful to study spread dynamics of organisms and how ecological interactions can affect their spread. When studying interactions such as consumption, dispersal rates might vary with life cycle stage, such as in cases with dispersive juveniles and sessile adults. In the non-dispersive stage, resources may engage in group defense to protect themselves from consumption. These local nondispersive interactions may limit the number of dispersing recruits that are produced and therefore affect how fast populations can spread. We present a spatial consumer-resource system using an integrodifference framework with limited movement of their adult stages and group defense mechanisms in the resource population. We model group defense using a Type IV Holling functional response, which limits the survival of adult resource population and enhances juvenile consumer production. We find that high mortality levels for sessile adults can destabilize resource at carrying capacity. Furthermore, we find that at high resource densities, group defense leads to a slower local growth of resource in newly invaded regions due to intraspecific competition outweighing the effect of consumption on resource growth. PubDate: 2023-09-30
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Abstract: Abstract A central and fundamental issue in ecology is to understand the relationship between complexity and stability. Increased empirical evidences demonstrated no clear relationships between complexity metrics and stability, and recent food web loop analyses suggested that maximum loop weight as well as the summation ratio between 3- and 2-link feedback loop weights could be better estimators of system stability. However, the importance of longer loops than 3-link on the stability remains unclear. Here, we use 127 marine food webs and the matrix product and trace method to investigate the relationship between loops with maximum of 7 links and food web stability. We found that feedback metrics \( a_{2n+1}/a_{2n} \) , i.e., the ratio of the sums of (2n + 1)-link and 2n-link loop weights, are strongly related with stability. These sum weight ratios can be regarded as the coupling strength between omnivory loops and their one-species-delete subloops, including the smallest three species and high-level omnivory ones. Further theoretical simulations of bioenergetic consumer-resource models with allometric constraints strengthen this finding. These results suggest that both longer loops and omnivory are important drivers of the food web stability. PubDate: 2023-08-21 DOI: 10.1007/s12080-023-00568-y
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Abstract: Abstract Since the work of von Bertalanffy (Q Rev Boil 32:217–231, 1957), several models have been proposed that relate the ontogenetic scaling of energy assimilation and metabolism to growth, which are able to describe ontogenetic growth trajectories for living organisms and collapse them onto a single universal curve (West et al. in Nature 413:628–631, 2001; Barnavar et al. in Nature 420:626, 2002). Nevertheless, all these ontogenetic growth models critically depend on fitting parameters and on the allometric scaling of the metabolic rate. Using a new metabolic rate relation (Escala in Theor Ecol 12(4):415–425, 2019) applied to a Bertalanffy-type ontogenetic growth equation, we find that ontogenetic growth can also be described by a universal growth curve for all studied species, but without the aid of any fitting parameters (i.e., no fitting procedure is performed on individual growth curves). We find that the inverse of the heart frequency \(\mathrm f_H\) , rescaled by the ratio of the specific energies for biomass creation and metabolism, defines the characteristic timescale for ontogenetic growth. Moreover, our model also predicts a generation time and lifespan that explain the origin of several “Life History Invariants’ (Charnov in Oxford University Press, Oxford, 1993) and predict that the Malthusian parameter should be inversely proportional to both the generation time and lifespan, in agreement with the data in the literature (Duncan et al. in Ecology 88:324–333 2007; Dillingham et al. in Paper 535, 2016; Hatton et al. in PNAS 116(43):21616–21622 2019). In our formalism, several critical timescales and rates (lifespan, generation time, and intrinsic population growth rate) are all proportional to the heart frequency \(\mathrm f_H\) , and thus, their allometric scaling relations come directly from the allometry of the heart frequency, which is typically \(\mathrm f_H \propto M^{-0.25}\) under basal conditions. PubDate: 2023-08-09 DOI: 10.1007/s12080-023-00565-1
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Abstract: Abstract Finding the conditions that ensure the survival of species has occupied ecologists for decades. Theoretically, for mechanistic models such as MacArthur’s consumer-resource model, most of the efforts have concentrated on proving the stability of an equilibrium assuming that it is feasible, but overlooking the conditions that ensure its feasibility. Here, we address this gap by finding the range of conditions that lead to a feasible equilibrium of MacArthur’s consumer-resource model, where species competition is mediated by their consumption of similar resources, and study how changes in the system’s structural and parametric properties affect those ranges for communities of any size. We characterize the relationship between the loss of feasibility and the increase in complexity (measured by the system’s richness and connectance) by a power law that can be extended to random competition matrices. Focusing on the pool of consumers, we find that while the feasibility of the entire system decreases with the size of the pool, the expected fraction of feasible consumers increases—safety in consumer numbers. Focusing on the pool of resources, we find that if resources grow linearly, the larger the pool of resources, the lower the feasibility of the system and the expected fraction of feasible consumers—danger in resource numbers. However, if resources grow logistically, this pattern is reversed with a sublinear increase in feasibility, as it has been previously reported in experimental work. This work provides testable predictions for consumer-resource systems and is a gateway to exploring feasibility in other mechanistic models. PubDate: 2023-07-22 DOI: 10.1007/s12080-023-00566-0
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Abstract: Abstract Understanding how individuals come into contact with each other is important in many fields from biology and ecology to robotics and physics. Interaction dynamics are central in understanding how information is spread between agents, how disease spreads through a population, and how group movement or behaviour occurs. However, in many applications, the underlying mode of movement is not considered, and instead, contacts are considered a fraction of all possible contacts amongst a population. This gives rise to the mass-action law which in turn implies a negative quadratic relationship between contacts and individuals. Here we consider how a simple but often used movement model, the correlated random walk, affects the contact rate in a standard Susceptible-Infection (SI) epidemiological model. Via extensive simulation, we show that the contact rate is not always well described by the assumed negative quadratic relationship, \(I(N-I)\) (where \(I\) is the number of infected at a given time and \(N\) the total number of individuals). Instead, we find that a contact rate proportional to \({\left[I(N-I)\right]}^{\alpha }\) with \(0<\alpha \le 1\) is a better qualitative fit, where \(\alpha\) depends upon parameters such as the straightness of the movement and the density of individuals. We highlight that the expected contacts at low densities increase with straight line movement, whereas, at high densities, they increase with more random movement. PubDate: 2023-07-19 DOI: 10.1007/s12080-023-00567-z
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Abstract: Abstract Ecosystem dynamics is often considered driven by a coupling of species’ resource consumption and its population size dynamics. Such resource-population dynamics is captured by MacArthur-type models. One biologically relevant feature that would also need to be captured by such models is the introduction of new and different species. Speciation introduces a stochastic component in the otherwise deterministic MacArthur theory. We describe here how speciation can be implemented to yield a model that is consistent with current theory on equilibrium resource-consumer models, but also displays readily observable rank diversity metric changes. The model also reproduces a priority effect. Adding speciation to a MacArthur-style model provides an attractively simple extension to explore the rich dynamics in evolving ecosystems. PubDate: 2023-06-29 DOI: 10.1007/s12080-023-00564-2
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Abstract: Abstract For ectotherms, habitat temperature is one of the most fundamental factors responsible for disease dynamics. Therefore, temperature-dependent habitat selection of hosts could alter their susceptibility to pathogens. Here, we examined the effect of host behavior in the fluctuating thermal regime on disease dynamics, by a dynamical modeling with field surveys. Cyprinid herpesvirus 3 (CyHV-3) was used as a model disease, which is a mass mortality agent of common carp (Cyprinus carpio). Telemetry analysis revealed that carp shifted their location according to the temporal fluctuations of the thermal regime in the habitat, suggesting a preference for specific temperatures. Numerical simulation using a disease transmission model reproduced the characteristic bimodal seasonal trends of infection rate to CyHV-3. The simulation demonstrated that the temperature preference of individual carp was central in determining whether the temperature-dependent behavior ameliorates or exacerbates disease severity. Moreover, it also demonstrated that increases in the fraction of warmer coastal areas can mitigate the impact of CyHV-3 on the carp population by promoting the acquisition of immunity. Our findings suggest that the prevalence of infectious disease in poikilothermic animals can be regulated by the combined effects of the thermal regime of their habitat and the host’s thermally induced behavior. PubDate: 2023-06-20 DOI: 10.1007/s12080-023-00563-3
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Abstract: Abstract Nearly all wild populations live in seasonal environments in which they experience regular fluctuations in environmental conditions that drive population dynamics. Recent empirical evidence from experimental populations of Drosophila suggests that demographic signals inherent in the counts of seasonal populations, including reproduction and survival, can indicate when in the annual cycle habitat loss occurred. However, it remains unclear whether these signatures of season-specific decline are detectable under a wider range of demographic conditions and rates of habitat loss. Here, we use a bi-seasonal Ricker model to examine season-specific signals of population decline induced by different rates of habitat loss in the breeding or non-breeding season and different strengths of density dependence. Consistent with the findings in Drosophila, breeding habitat loss was accompanied by reduced reproductive output and a density-dependent increase in survival during the subsequent non-breeding period. Non-breeding habitat loss resulted in reduced non-breeding survival and a density-dependent increase in reproduction in the following breeding season. These season-specific demographic signals of decline were present under a wide range of habitat loss rates (2–25% per generation) and different density-dependent regimes (weak, moderate, and strong). We show that stronger density dependence can negatively influence time to extinction when non-breeding habitat is lost, whereas the strength of density dependence does not influence time to extinction with breeding habitat loss (although, in all cases, density dependence itself was an important modulator of population dynamics). Our results illustrate the need to incorporate seasonality in theoretical models to better understand when populations are being driven to decline. PubDate: 2023-06-13 DOI: 10.1007/s12080-023-00562-4
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Abstract: Abstract The growing shortfall in wild seafood and expansion of aquaculture can involve ecological and economic feedback between wild and farmed fish populations such as disease transmission and market competition. Here, we investigate the resilience of bioeconomically interacting fisheries and aquaculture systems by developing and analyzing mathematical models that capture the ecological suppression of wild fish survival by aquaculture, the management of fisheries for maximum sustainable yield, and aquaculture growth via two regulatory scenarios: perfect competition or rent optimization. Stability analysis of the models indicates that coexistence of productive fisheries and aquaculture is stable if the ecological impacts of aquaculture on wild fish are held below a bioeconomic threshold. Otherwise, the dynamics involve regime shifts between alternative stable states of fishery dominance with little aquaculture versus aquaculture dominance with collapsed fisheries. These regime shifts are difficult to reverse due to hysteresis. Coexistence and alternative stable states occur in both regulatory scenarios, but resilience is higher under rent optimization than perfect competition. Our results indicate that bioeconomic feedback can have important consequences for the resilience of aquaculture-fishery systems. PubDate: 2023-05-30 DOI: 10.1007/s12080-023-00561-5
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Abstract: Abstract Algal blooms are typical of many aquatic freshwater ecosystems in seasonal environments. Such blooms could derive from transient reactive dynamics of algae and limiting nutrients following seasonal perturbation events. Linking parameter estimates derived from previously published lab experiments with empirical estimates of algal density dependence, we modeled dynamic interactions between nutrients and the green algal species Chlorella vulgaris and tested model predictions in a dozen 140 L mesocosms supplied with bi-weekly inputs of liquid fertilizer. Consistent with the reactive nutrient-driven model, Chlorella populations exhibited an initial surge in abundance over the first month followed by collapse as they rapidly converged on stable equilibria. The reactive model suggests that the magnitude of transient blooms is positively related to the augmentation of nutrients and depression of algae over the winter period. The magnitude of both algal peaks and equilibrium abundance was positively related to fertilizer loading, as predicted by the reactive model. Our results suggest that transient reactive responses to climate-driven perturbation events can be an important contributor to seasonal algal blooms observed in many temperate freshwater ecosystems. Controlled experimental studies such as ours may be helpful in understanding and potentially mediating the impact of fertilizer run-off on freshwater systems in temperate agricultural landscapes. PubDate: 2023-05-09 DOI: 10.1007/s12080-023-00559-z
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Abstract: Abstract In the light of global climate change and biodiversity loss, understanding the role of functional diversity in the response of food webs to environmental change is growing ever more important. Using a tritrophic food web model, with a variable degree of functional diversity at each trophic level, we studied the role of functional diversity on the resistance of a system against press perturbations. Perturbations affected either nutrient availability or the mortality of the species, which can be interpreted as effects of eutrophication and warming, respectively. We compared food webs with different levels of functional diversity by investigating the species trait and biomass dynamics, the overall changes in the species’ standing biomass as measured by the warping distance, and the duration of the system transients after the onset of a press perturbation (transition time). We found that higher functional diversity increased resistance since it buffered trophic cascading effects and delayed the onset of oscillatory behaviour caused by either bottom-up forcing via perturbations to nutrient concentration or top-down forcing via perturbations to mortality rate. This increased resistance emerged from a higher top-down control of the intermediate species on the basal species. Functional diversity also promoted a higher top biomass, in particular via a higher proportion of top selective species undergoing high mortality rates. Additionally, functional diversity had context-dependent effects on warping distances, and increased transition times. Overall, this study encourages accounting for functional diversity in future investigations about the response of multitrophic systems to global change and in management strategies. PubDate: 2023-05-09 DOI: 10.1007/s12080-023-00558-0
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Abstract: Abstract The ongoing pandemic disease COVID‑19 has caused worldwide social and financial disruption. As many countries are engaged in designing vaccines, the harmful second and third waves of COVID‑19 have already appeared in many countries. To investigate changes in transmission rates and the effect of social distancing in the USA, we formulate a system of ordinary differential equations using data of confirmed cases and deaths in these states: California, Texas, Florida, Georgia, Illinois, Louisiana, Michigan, and Missouri. Our models and their parameter estimations show social distancing can reduce the transmission of COVID‑19 by 60% to 90%. Thus, obeying the movement restriction rules is crucial in reducing the magnitude of the outbreak waves. This study also estimates the percentage of people who were not social distancing ranges between 10% and 18% in these states. Our analysis shows the management restrictions taken by these states do not slow the disease progression enough to contain the outbreak. PubDate: 2023-04-25 DOI: 10.1007/s12080-023-00557-1
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Abstract: Abstract Ecologists have put forward many explanations for coexistence, but these are only partial explanations; nature is complex, so it is reasonable to assume that in any given ecological community, multiple mechanisms of coexistence are operating at the same time. Here, we present a methodology for quantifying the relative importance of different explanations for coexistence, based on an extension of the Modern Coexistence Theory. Current versions of Modern Coexistence Theory only allow for the analysis of communities that are affected by spatial or temporal environmental variation, but not both. We show how to analyze communities with spatiotemporal fluctuations, how to parse the importance of spatial variation and temporal variation, and how to measure everything with either mathematical expressions or simulation experiments. Our extension of Modern Coexistence Theory shows that many more species can coexist than originally thought. More importantly, it allows empiricists to use realistic models and more data to better infer the mechanisms of coexistence in real communities. PubDate: 2023-04-22 DOI: 10.1007/s12080-022-00549-7
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Abstract: Abstract Climate warming directly influences the developmental and feeding rates of organisms. Changes in these rates are likely to have consequences for species interactions, particularly for organisms affected by stage- or size-dependent predation. However, because of differences in species-specific responses to warming, predicting the impact of warming on predator and prey densities can be difficult. We present a general model of stage-dependent predation with temperature-dependent vital rates to explore the effects of warming when predator and prey have different thermal optima. We found that warming generally favored the interactor with the higher thermal optimum. Part of this effect occurred due to the stage-dependent nature of the interaction and part due to thermal asymmetries. Interestingly, below the predator and prey thermal optima, warming caused prey densities to decline, even as increasing temperature improved prey performance. We also parameterize our model using values from a well-studied system, Arctia virginalis and Formica lasioides, in which the predator has a warmer optimum. Overall, our results provide a general framework for understanding stage- and temperature-dependent predator–prey interactions and illustrate that the thermal niche of both predator and prey is important to consider when predicting the effects of climate warming. PubDate: 2023-04-03 DOI: 10.1007/s12080-023-00555-3
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Abstract: Abstract Population dynamics of migratory species can be modeled using spatial bipartite networks in which nodes representing breeding and winter regions are distributed longitudinally and connected by links representing migratory movements. Understanding the factors that influence the connectivity and population size of such networks is important for effective conservation. In migration ecology terminology, strong migratory connectivity is a network with low node degree and weak or diffuse connectivity is a network with high node degree. We present a model of migration networks using a Lotka-Volterra system of differential equations in which each winter-breeding link is represented as a subpopulation which competes with other subpopulations that share breeding or winter regions. We analyze how habitat distribution and relative costs of migration paths affect the coexistence of subpopulations and hence, the connectivity pattern (weak, moderate or strong). We find that, in the absence of dispersal among subpopulations, strong connectivity occurs when winter habitat has the same longitudinal distribution as breeding habitat, and/or costs of cross-longitudinal migration are high. Moderate connectivity arises otherwise. Total population size is maximized when each longitudinal region has the same amount of breeding habitat as winter habitat and decreases with the costs of migration. Including dispersal leads to weak connectivity and reduces population size. Our results suggest that actions that conserve habitat so as to preserve matching habitat distributions and minimize costs of migration would be most effective. PubDate: 2023-03-30 DOI: 10.1007/s12080-023-00554-4
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