Global potential distribution of mangroves: Taking into account salt marsh interactions along latitudinal gradients.

Mangrove is one of the most productive and sensitive ecosystems in the world. Due to the complexity and specificity of mangrove habitat, the development of mangrove is regulated by several factors. Species distribution models (SDMs) are effective tools to identify the potential habitats for establishing and regenerating the ecosystem. Such models usually include exclusively environmental factors. Nevertheless, recent studies have challenged this notion and highlight the importance of including biotic interactions. Both factors are necessary for a mechanistic understanding of the mangrove distribution in order to promote the protection and restoration of mangroves. Thus, we present a novel approach of combining environmental factors and interactions with salt marsh for projecting mangrove distributions at the global level and within latitudinal zones. To test the salt marsh interaction, we fit the MaxEnt model with two predicting sets: (1) environments only and (2) environments + salt marsh interaction index (SII). We found that both sets of models had good predictive ability, although the SII improved model performance slightly. Potential distribution areas of mangrove decrease with latitudes, and are controlled by biotic and abiotic factors. Temperature, precipitation and wind speed are generally critical at both global scale and ecotones along latitudes. SII is important on global scale, with a contribution of 5.9%, ranking 6th, and is particularly critical in the 10-30°S and 20-30°N zone. Interactions with salt marsh, including facilitation and competition, are shown to affect the distribution of mangroves at the zone of coastal ecotone, especially in the latitudinal range from 10° - 30°. The contribution of SII to mangrove distribution increases with latitudes due to the difference in the adaptive capacity of salt marsh plants and mangroves to environments. Totally, this study identified and quantified the effects of salt marsh on mangrove distribution by establishing the SII. The results not only facilitate to establish a more accurate mangrove distribution map, but also improve the efficiency of mangrove restoration by considering the salt marsh interaction in the mangrove management projects. In addition, the method of incorporating biotic interaction into SDMs through establish the biotic interaction index has contributed to the development of SDMs.

Directed movement changes coexistence outcomes in heterogeneous environments.

Understanding mechanisms of coexistence is a central topic in ecology. Mathematical analysis of models of competition between two identical species moving at different rates of symmetric diffusion in heterogeneous environments show that the slower mover excludes the faster one. The models have not been tested empirically and lack inclusions of a component of directed movement toward favourable areas. To address these gaps, we extended previous theory by explicitly including exploitable resource dynamics and directed movement. We tested the mathematical results experimentally using laboratory populations of the nematode worm, Caenorhabditis elegans. Our results not only support the previous theory that the species diffusing at a slower rate prevails in heterogeneous environments but also reveal that moderate levels of a directed movement component on top of the diffusive movement allow species to coexist. Our results broaden the theory of species coexistence in heterogeneous space and provide empirical confirmation of the mathematical predictions.

Towards Building a Sustainable Future: Positioning Ecological Modelling for Impact in Ecosystems Management.

As many ecosystems worldwide are in peril, efforts to manage them sustainably require scientific advice. While numerous researchers around the world use a great variety of models to understand ecological dynamics and their responses to disturbances, only a small fraction of these models are ever used to inform ecosystem management. There seems to be a perception that ecological models are not useful for management, even though mathematical models are indispensable in many other fields. We were curious about this mismatch, its roots, and potential ways to overcome it. We searched the literature on recommendations and best practices for how to make ecological models useful to the management of ecosystems and we searched for 'success stories' from the past. We selected and examined several cases where models were instrumental in ecosystem management. We documented their success and asked whether and to what extent they followed recommended best practices. We found that there is not a unique way to conduct a research project that is useful in management decisions. While research is more likely to have impact when conducted with many stakeholders involved and specific to a situation for which data are available, there are great examples of small groups or individuals conducting highly influential research even in the absence of detailed data. We put the question of modelling for ecosystem management into a socio-economic and national context and give our perspectives on how the discipline could move forward.

Effect of Stressors on the Carrying Capacity of Spatially Distributed Metapopulations.

Stressors such as antibiotics, herbicides, and pollutants are becoming increasingly common in the environment. The effects of stressors on populations are typically studied in homogeneous, nonspatial settings. However, most populations in nature are spatially distributed over environmentally heterogeneous landscapes with spatially restricted dispersal. Little is known about the effects of stressors in these more realistic settings. Here, we combine laboratory experiments with novel mathematical theory to rigorously investigate how a stressor's physiological effect and spatial distribution interact with dispersal to influence population dynamics. We prove mathematically that if a stressor increases the death rate and/or simultaneously decreases the population growth rate and yield, a homogeneous distribution of the stressor leads to a lower total population size than if the same amount of the stressor was heterogeneously distributed. We experimentally test this prediction on spatially distributed populations of budding yeast (Saccharomyces cerevisiae). We find that the antibiotic cycloheximide increases the yeast death rate but reduces the growth rate and yield. Consistent with our mathematical predictions, we observe that a homogeneous spatial distribution of cycloheximide minimizes the total equilibrium size of experimental metapopulations, with the magnitude of the effect depending predictably on the dispersal rate and the geographic pattern of antibiotic heterogeneity. Our study has implications for assessing the population risk posed by pollutants, antibiotics, and global change and for the rational design of strategies for employing toxins to control pathogens and pests.

Dispersal asymmetry in a two-patch system with source-sink populations.

This paper analyzes source-sink systems with asymmetric dispersal between two patches. Complete analysis on the models demonstrates a mechanism by which the dispersal asymmetry can lead to either an increased total size of the species population in two patches, a decreased total size with persistence in the patches, or even extinction in both patches. For a large growth rate of the species in the source and a fixed dispersal intensity, (i) if the asymmetry is small, the population would persist in both patches and reach a density higher than that without dispersal, in which the population approaches its maximal density at an appropriate asymmetry; (ii) if the asymmetry is intermediate, the population persists in both patches but reaches a density less than that without dispersal; (iii) if the asymmetry is large, the population goes to extinction in both patches; (iv) asymmetric dispersal is more favorable than symmetric dispersal under certain conditions. For a fixed asymmetry, similar phenomena occur when the dispersal intensity varies, while a thorough analysis is given for the low growth rate of the species in the source. Implications for populations in heterogeneous landscapes are discussed, and numerical simulations confirm and extend our results.

An overview of agent-based models in plant biology and ecology.

Agent-based modelling (ABM) has become an established methodology in many areas of biology, ranging from the cellular to the ecological population and community levels. In plant science, two different scales have predominated in their use of ABM. One is the scale of populations and communities, through the modelling of collections of agents representing individual plants, interacting with each other and with the environment. The other is the scale of the individual plant, through the modelling, by functional-structural plant models (FSPMs), of agents representing plant building blocks, or metamers, to describe the development of plant architecture and functions within individual plants. The purpose of this review is to show key results and parallels in ABM for growth, mortality, carbon allocation, competition and reproduction across the scales from the plant organ to populations and communities on a range of spatial scales to the whole landscape. Several areas of application of ABMs are reviewed, showing that some issues are addressed by both population-level ABMs and FSPMs. Continued increase in the relevance of ABM to environmental science and management will be helped by greater integration of ABMs across these two scales.

Energetic constraints and the paradox of a diffusing population in a heterogeneous environment.

Previous mathematical analyses have shown that, for certain parameter ranges, a population, described by logistic equations on a set of connected patches, and diffusing among them, can reach a higher equilibrium total population when the local carrying capacities are heterogeneously distributed across patches, than when carrying capacities having the same total sum are homogeneously distributed across the patches. It is shown here that this apparently paradoxical result is explained when the resultant differences in energy inputs to the whole multi-patch system are taken into account. We examine both Pearl-Verhulst and Original Verhulst logistic models and show that, when total input of energy or limiting resource, is constrained to be the same in the homogeneous and heterogeneous cases, the total population in the heterogeneous patches can never reach an asymptotic equilibrium that is greater than the sum of the carrying capacities over the homogeneous patches. We further show that, when the dynamics of the limiting resources are explicitly modeled, as in a chemostat model, the paradoxical result of the logistic models does not occur. These results have implications concerning the use of some ubiquitous equations of population ecology in modeling populations in space.

Global dynamics of a mutualism-competition model with one resource and multiple consumers.

Recent simulation modeling has shown that species can coevolve toward clusters of coexisting consumers exploiting the same limiting resource or resources, with nearly identical ratios of coefficients related to growth and mortality. This paper provides a mathematical basis for such as situation; a full analysis of the global dynamics of a new model for such a class of n-dimensional consumer-resource system, in which a set of consumers with identical growth to mortality ratios compete for the same resource and in which each consumer is mutualistic with the resource. First, we study the system of one resource and two consumers. By theoretical analysis, we demonstrate the expected result that competitive exclusion of one of the consumers can occur when the growth to mortality ratios differ. However, when these ratios are identical, the outcomes are complex. Either equilibrium coexistence or mutual extinction can occur, depending on initial conditions. When there is coexistence, interaction outcomes between the consumers can transition between effective mutualism, parasitism, competition, amensalism and neutralism. We generalize to the global dynamics of a system of one resource and multiple consumers. Changes in one factor, either a parameter or initial density, can determine whether all of the consumers either coexist or go to extinction together. New results are presented showing that multiple competing consumers can coexist on a single resource when they have coevolved toward identical growth to mortality ratios. This coexistence can occur because of feedbacks created by all of the consumers providing a mutualistic service to the resource. This is biologically relevant to the persistence of pollination-mutualisms.

A parasitism-mutualism-predation model consisting of crows, cuckoos and cats with stage-structure and maturation delays on crows and cuckoos.

In this paper, a parasitism-mutualism-predation model is proposed to investigate the dynamics of multi-interactions among cuckoos, crows and cats with stage-structure and maturation time delays on cuckoos and crows. The crows permit the cuckoos to parasitize their nestlings (eggs) on the crow chicks (eggs). In return, the cuckoo nestlings produce a malodorous cloacal secretion to protect the crow chicks from predation by the cats, which is apparently beneficial to both the crow and cuckoo population. The multi-interactions, i.e., parasitism and mutualism between the cuckoos (nestlings) and crows (chicks), predation between the cats and crow chicks are modeled both by Holling-type II and Beddington-DeAngelis-type functional responses. The existence of positive equilibria of three subsystems of the model are discussed. The criteria for the global stability of the trivial equilibrium are established by the Krein-Rutman theorem and other analysis methods. Moreover, the threshold dynamics for the coexistence and weak persistence of the model are obtained, and we show, both analytically and numerically, that the stabilities of the interior equilibria may change with the increasing maturation time delays. We find there exists an evident difference in the dynamical properties of the parasitism-mutualism-predation model based on whether or not we consider the effects of stage-structure and maturation time delays on cuckoos and crows. Inclusion of stage structure results in many varied dynamical complexities which are difficult to encompass without this inclusion.

Carrying capacity in a heterogeneous environment with habitat connectivity.

A large body of theory predicts that populations diffusing in heterogeneous environments reach higher total size than if non-diffusing, and, paradoxically, higher size than in a corresponding homogeneous environment. However, this theory and its assumptions have not been rigorously tested. Here, we extended previous theory to include exploitable resources, proving qualitatively novel results, which we tested experimentally using spatially diffusing laboratory populations of yeast. Consistent with previous theory, we predicted and experimentally observed that spatial diffusion increased total equilibrium population abundance in heterogeneous environments, with the effect size depending on the relationship between r and K. Refuting previous theory, however, we discovered that homogeneously distributed resources support higher total carrying capacity than heterogeneously distributed resources, even with species diffusion. Our results provide rigorous experimental tests of new and old theory, demonstrating how the traditional notion of carrying capacity is ambiguous for populations diffusing in spatially heterogeneous environments.

Moving forward in circles: challenges and opportunities in modelling population cycles.

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer-resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.

Dispersal and spatial heterogeneity: single species.

A recent result for a reaction-diffusion equation is that a population diffusing at any rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. This has so far been proven by Lou for the case in which the reaction term has only one parameter, m(x), varying with spatial location x, which serves as both the intrinsic growth rate coefficient and carrying capacity of the population. However, this striking result seems rather limited when applies to real populations. In order to make the model more relevant for ecologists, we consider a logistic reaction term, with two parameters, r (x) for intrinsic growth rate, and K(x) for carrying capacity. When r (x) and K(x) are proportional, the logistic equation takes a particularly simple form, and the earlier result still holds. In this paper we have established the result for the more general case of a positive correlation between r (x) and K(x) when dispersal rate is small. We review natural and laboratory systems to which these results are relevant and discuss the implications of the results to population theory and conservation ecology.

A spatial individual-based model predicting a great impact of copious sugar sources and resting sites on survival of Anopheles gambiae and malaria parasite transmission.

BACKGROUND: Agent-based modelling (ABM) has been used to simulate mosquito life cycles and to evaluate vector control applications. However, most models lack sugar-feeding and resting behaviours or are based on mathematical equations lacking individual level randomness and spatial components of mosquito life. Here, a spatial individual-based model (IBM) incorporating sugar-feeding and resting behaviours of the malaria vector Anopheles gambiae was developed to estimate the impact of environmental sugar sources and resting sites on survival and biting behaviour. METHODS: A spatial IBM containing An. gambiae mosquitoes and humans, as well as the village environment of houses, sugar sources, resting sites and larval habitat sites was developed. Anopheles gambiae behaviour rules were attributed at each step of the IBM: resting, host seeking, sugar feeding and breeding. Each step represented one second of time, and each simulation was set to run for 60 days and repeated 50 times. Scenarios of different densities and spatial distributions of sugar sources and outdoor resting sites were simulated and compared. RESULTS: When the number of natural sugar sources was increased from 0 to 100 while the number of resting sites was held constant, mean daily survival rate increased from 2.5% to 85.1% for males and from 2.5% to 94.5% for females, mean human biting rate increased from 0 to 0.94 bites per human per day, and mean daily abundance increased from 1 to 477 for males and from 1 to 1,428 for females. When the number of outdoor resting sites was increased from 0 to 50 while the number of sugar sources was held constant, mean daily survival rate increased from 77.3% to 84.3% for males and from 86.7% to 93.9% for females, mean human biting rate increased from 0 to 0.52 bites per human per day, and mean daily abundance increased from 62 to 349 for males and from 257 to 1120 for females. All increases were significant (P < 0.01). Survival was greater when sugar sources were randomly distributed in the whole village compared to clustering around outdoor resting sites or houses. CONCLUSIONS: Increases in densities of sugar sources or outdoor resting sites significantly increase the survival and human biting rates of An. gambiae mosquitoes. Survival of An. gambiae is more supported by random distribution of sugar sources than clustering of sugar sources around resting sites or houses. Density and spatial distribution of natural sugar sources and outdoor resting sites modulate vector populations and human biting rates, and thus malaria parasite transmission.

Exposures to a selective serotonin reuptake inhibitor (SSRI), sertraline hydrochloride, over multiple generations: changes in life history traits in Ceriodaphnia dubia.

Selective serotonin reuptake inhibitors (SSRIs) have been reported to range from low parts per trillion to parts per billion levels in surface waters, wastewater effluents, and sediments. These low levels have led to concern for their potential long-term risks to the survival, growth, and reproduction of aquatic organisms. We investigated the acute and chronic effects of sertraline on the life history traits of Ceriodaphnia dubia over the course of three generations under environmentally realistic concentrations. Acute toxicity of sertraline in C. dubia offspring resulted in a 48h median effective concentration of 126µgL(-1). Under chronic exposure, the lowest concentration to affect fecundity and growth was at 53.4µgL(-1) in the first two generations. These parameters become more sensitive during the third generation where the LOEC was 4.8µgL(-1). The median effective concentrations (EC50) for the number of offspring per female, offspring body size, and dry weight were 17.2, 21.2, and 26.2µgL(-1), respectively. Endpoints measured in this study demonstrate that chronic exposure of C. dubia to sertraline leads to effects that occur at concentrations only an order of magnitude higher than predicted environmental concentrations. However, this study also demonstrates that multigenerational effects should be considered in chronic exposure studies because standard toxicity tests do not account for increases in sensitivity in successive generations to toxicants.

Chronic effects of carbamazepine on life-history strategies of Ceriodaphnia dubia in three successive generations.

Trace quantities of pharmaceuticals are continuously being discharged into the environment through domestic and industrial wastewater effluents, causing concern among scientists and regulators regarding potential long-term impacts on aquatic ecosystems. These compounds and their metabolites are constantly interacting with organisms at various life-cycle stages and may differentially influence the development of embryonic, larval, juvenile, and adult stages. To understand the possible cumulative effects of exposure to carbamazepine (CBZ), a multigenerational approach was taken in which survival, reproduction, respiration, growth, brood size, and biomass of Ceriodaphnia dubia were assessed at sublethal concentrations over the course of three successive generations. CBZ exposure significantly decreased fecundity at 196.7 µg/L in the F0 and F1 generations over 2 weeks and acclimatized at 264.6 µg/L in the F2 generation. Similarly, a significant decrease of neonate dry weight was observed at the 196.7 µg/L CBZ treatment in the F1 generation, and it acclimatized at 264.6 µg/L treatment level in the F2 generation. Median time to first brood release was significantly delayed at 264.6 µg/L in the F2 generation, indicating slower maturation. Results over three successive generations are not different than what one would obtain by testing simply the F0 generation. Furthermore, the effects measured were observed at concentrations two orders of magnitude higher than are environmentally relevant, and it is unlikely that CBZ poses a substantial risk to the environment regarding the end points measured in this study. However, additional research through laboratory and field multigenerational studies may be required to understand the overall risk of CBZ to other nontarget organisms.

Towards a theory of ecotone resilience: coastal vegetation on a salinity gradient.

Ecotones represent locations where vegetation change is likely to occur as a result of climate and other environmental changes. Using a model of an ecotone vulnerable to such future changes, we estimated the resilience of the ecotone to disturbances. The specific ecotone is that between two different vegetation types, salinity-tolerant and salinity-intolerant, along a gradient in groundwater salinity. In the case studied, each vegetation type, through soil feedback loops, promoted local soil salinity levels that favor itself in competition with the other type. Bifurcation analysis was used to study the system of equations for the two vegetation types and soil salinity. Alternative stable equilibria, one for salinity-tolerant and one for salinity intolerant vegetation, were shown to exist over a region of the groundwater salinity gradient, bounded by two bifurcation points. This region was shown to depend sensitively on parameters such as the rate of upward infiltration of salinity from groundwater into the soil due to evaporation. We showed also that increasing diffusion rates of vegetation can lead to shrinkage of the range between the two bifurcation points. Sharp ecotones are typical of salt-tolerant vegetation (mangroves) near the coastline and salt-intolerant vegetation inland, even though the underlying elevation and groundwater salinity change very gradually. A disturbance such as an input of salinity to the soil from a storm surge could upset this stable boundary, leading to a regime shift of salinity-tolerant vegetation inland. We showed, however, that, for our model as least, a simple pulse disturbance would not be sufficient; the salinity would have to be held at a high level, as a 'press', for some time. The approach used here should be generalizable to study the resilience of a variety of ecotones to disturbances.

Uni-directional interaction and plant-pollinator-robber coexistence.

A mathematical model for the plant-pollinator-robber interaction is studied to understand the factors leading to the widespread occurrence and stability of such interactions. In the interaction, a flowering plant provides resource for its pollinator and the pollinator has both positive and negative effects on the plant. A nectar robber acts as a plant predator, consuming a common resource with the pollinator, but with a different functional response. Using dynamical systems theory, mechanisms of species coexistence are investigated to show how a robber could invade the plant-pollinator system and persist stably with the pollinator. In addition, circumstances are demonstrated in which the pollinator's positive and negative effects on the plant could determine the robber's invasibility and the three-species coexistence.

Modeling the dynamics of woody plant-herbivore interactions with age-dependent toxicity.

In this paper we study the effects that woody plant chemical defenses may have on interactions between boreal hares that in winter feed almost entirely on twigs. We focus particularly on the fact that toxin concentration often varies with the age of twig segments. The model incorporates the fact that the woody internodes of the youngest segments of the twigs of the deciduous angiosperm species that these hares prefer to eat are more defended by toxins than the woody internodes of the older segments that subtend and support the younger segments. Thus, the per capita daily intake of the biomass of the older segments of twigs by hares is much higher than their intake of the biomass of the younger segments of twigs. This age-dependent toxicity of twig segments is modeled using age-structured model equations which are reduced to a system of delay differential equations involving multiple delays in the woody plant-hare dynamics. A novel aspect of the modeling was that it had to account for mortality of non-consumed younger twig segment biomass when older twig biomass was bitten off and consumed. Basic mathematical properties of the model are established together with upper and lower bounds on the solutions. Necessary and sufficient conditions are found for the linear stability of the equilibrium in which the hare is extinct, and sufficient conditions are found for the global stability of this equilibrium. Numerical simulations confirmed the analytical results and demonstrated the existence of limit cycles over ranges of parameters reasonable for hares browsing on woody vegetation in boreal ecosystems. This showed that age dependence in plant chemical defenses has the capacity to cause hare-plant population cycles, a new result.

Wading bird foraging on a wetland landscape: a comparison of two strategies.

Tactile-feeding wading birds, such as wood storks and white ibises, require high densities of prey such as small fishes and crayfish to support themselves and their offspring during the breeding season. Prey availability in wetlands is often determined by seasonal hydrologic pulsing, such as in the subtropical Everglades, where spatial distributions of prey can vary through time, becoming heterogeneously clumped in patches, such as ponds or sloughs, as the wetland dries out. In this mathematical modeling study, we selected two possible foraging strategies to examine how they impact total energetic intake over a time scale of one day. In the first, wading birds sample prey patches without a priori knowledge of the patches' prey densities, moving from patch to patch, staying long enough to estimate the prey density, until they find one that meets a predetermined satisfactory threshold, and then staying there for a longer period. For this case, we solve for a wading bird's expected prey intake over the course of a day, given varying theoretical probability distributions of patch prey densities across the landscape. In the second strategy considered, it is assumed that the wading bird samples a given number of patches, and then uses memory to return to the highest quality patch. Our results show how total intake over a day is impacted by assumptions of the parameters governing the spatial distribution of prey among patches, which is a key source of parameter uncertainty in both natural and managed ecosystems. Perhaps surprisingly, the foraging strategy that uses a prey density threshold generally led to higher maximum potential prey intake than the strategy for using memory to return to the best patch sampled. These results will contribute to understanding the foraging of wading birds and to the management of wetlands.