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Don DeAngelis

Publications and source records attributed to Don DeAngelis.

At least 19 recordsLinked to original sources

Modeling the effects of temperature and limiting nutrients on the competition of an invasive floating plant, Pontederia crassipes, with submersed vegetation in a shallow lake

The potential for a non-native plant species to invade a new habitat depends on broadscale factors such as climate, local factors such as nutrient availability, and the biotic community of the habitat into which the plant species is introduced. We developed a spatially explicit model to assess the risk of expansion of a floating invasive aquatic plant species (FAV), the water hyacinth ( Pontederia crassipes ), an invader in the United States, beyond its present range. Our model used known data on growth rates and competition with a native submersed aquatic macrophyte (SAV). In particular, the model simulated an invasion into a habitat with a mean annual temperature different from its own growth optimum, in which we also simulated seasonal fluctuations in temperature. Twenty different nutrient concentrations and eight different temperature scenarios, with different mean annual amplitudes of seasonal temperature variation around the mean of the invaded habitat, were simulated. In each case, the ability of the water hyacinth to invade and either exclude or coexist with the native vegetation was determined. As the temperature pattern was changed from tropical towards increasingly cooler temperate levels, the competitive advantage shifted from the tropical FAV to the more temperate SAV, with a wide range in which coexistence occurred. High nutrient concentrations allowed the coexistence of FAV, even at cooler annual temperatures. But even at the highest nutrient concentrations in the model, the FAV was unlikely to persist under the current climates of latitudes in the Southeastern United States above that of Northern Alabama. This result may have some implications for where control efforts need to be concentrated.

Plants

Modeling the effects of spatial distribution on dynamics of an invading Melaleuca quinquenervia (Cav.) Blake population

To predict the potential success of an invading non-native species, it is important to understand its dynamics and interactions with native species in the early stages of its invasion. In spatially implicit models, mathematical stability criteria are commonly used to predict whether an invading population grows in number in an early time period. But spatial context is important for real invasions as an invading population may first occur as a small number of individuals scatter spatially. The invasion dynamics are therefore not describable in terms of population level state variables. A better approach is spatially explicit individual-based modeling (IBM). We use an established spatially explicit IBM to predict the invasion of the non-native tree, Melaleuca quinquenervia (Cav.) Blake, to a native community in southern Florida. We show that the initial spatial distribution, both the spatial density of individuals and the area they cover, affects its success in growing numerically and spreading. The formation of a cluster of a sufficient number and density of individuals may be needed for the invader to locally outcompete the native species and become established. Different initial densities, identical in number and density but differing in random positions of individuals, can produce very different trajectories of the invading population through time, even affecting invasion success and failure.

Forests

Spatial patterns as long transients in submersed-floating plant competition with biocontrol

A cellular automata model was developed and parameterized to test the effectiveness of application of biological control insects to water hyacinth ( Pontederia crassipes ), which is an invasive floating plant species in many parts of the world and outcompetes many submersed native aquatic species in southern Florida. In the model, P. crassipes was allowed to compete with Nuttall’s waterweed ( Elodea nuttallii ). In the absence of biocontrol acting on the P. crassipes , E. nuttallii excluded P. crassipes at low concentrations of the limiting nutrient (nitrogen), and the reverse occurred at high nutrient concentrations. At intermediate values, alternative stable states could occur; either P. crassipes alone or a mixture of the two species. When the biocontrol agent, the weevil Neochetina eichhorniae , was applied in the model, there was initially a rapid reduction of the P. crassipes , however, over time a regular striped pattern of moving spatially alternating stripes of P. crassipes and E. nuttallii emerged. -This pattern of moving stripes emerged and persisted over thousands of days but could quickly transform into an irregular pattern at some apparently random time, when either external stochasticity (added adult weevils) or only the weak internal stochasticity of weevil movements occurred. The cause of the end of the long transient can be traced to a single slightly irregular pixel within the striped pattern. Model parameters were varied to study effects of plant growth rate, nutrient concentration and nutrient diffusion rate on the dynamics of the system.

Theoretical Ecology

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.

Journal of Environmental Management

Effects of initial vegetation heterogeneity on competition of submersed and floating macrophytes

Non-spatial models of competition between floating aquatic vegetation (FAV) and submersed aquatic vegetation (SAV) predict a stable state of pure SAV at low total available limiting nutrient level, N , a stable state of only FAV for high N , and alternative stable states for intermediate N , as described by an S-shaped bifurcation curve. Spatial models that include physical heterogeneity of the waterbody show that the sharp transitions between these states become smooth. We examined the effects of heterogeneous initial conditions of the vegetation types. We used a spatially explicit model to describe the competition between the vegetation types. In the model, the FAV, duckweed ( L. gibba ), competed with the SAV, Nuttall's waterweed ( Elodea nuttallii ). Differences in the initial establishment of the two macrophytes affected the possible stable equilibria. When initial biomasses of SAV and FAV differed but each had the same initial biomass in each spatial cell, the S-shaped bifurcation resulted, but the critical transitions on the N -axis are shifted, depending on FAV:SAV biomass ratio. When the initial biomasses of SAV and FAV were randomly heterogeneously distributed among cells, the vegetation pattern of the competing species self-organized spatially, such that many different stable states were possible in the intermediate N region. If N was gradually increased or decreased through time from a stable state, the abrupt transitions of non-spatial models were changed into smoother transitions through a series of stable states, which resembles the Busse balloon observed in other systems.

Mathematical Biosciences and Engineering

Ecological benefits of integrative weed management of Melaleuca quinquenervia in Big Cypress National Preserve

The southern tip of North America coalesces into one of the world’s largest freshwater wetlands, the Everglades, Florida, USA. Though this region is much like an island, home to high biodiversity and endemism, it is also the site of a century of development and associated landscape-scale species invasions. Melaleuca quinquenervia (hereafter melaleuca), a tree native to tropical Australia, was planted extensively throughout south Florida as street trees, levee stabilizers, and later to reduce standing water in marshy areas. Through extensive cooperation with the United States Department of Agriculture’s Australian Biological Control Laboratory, several biological control agents were released, three of which later successfully established. Herein we examine evidence that plant community shifts determined from vegetation surveys and remotely sensed images reflect changes from melaleuca-dominated wetlands (before management) to native communities (after management). Melaleuca-dominated community types decreased from 1990 to 2020 by more than 99%. Vegetation surveys also reflect an increase in cypress wetlands, pinelands, and open water wetlands, all of which were dominated by melaleuca in previous decades. We also found the normalized difference vegetation index (NDVI) increased in melaleuca-invaded wetlands during peak infestations but decreased again after communities recovered to sawgrass-dominated wetlands. These responses are concomitant with the development of integrative management techniques for melaleuca that include mechanical, chemical, and biological control. Our results confirm previous findings that biological control likely augments conventional management methods by limiting recovery of invasive species.

Florida

Resource-driven pattern formation in consumer-resource systems with asymmetric dispersal on a plane

This paper considers resource-driven pattern formation in consumer-resource systems. Here, a planar pattern consists of many big patches, and a big patch can be regarded as combination of many patches on the plane. The consumer moves between patches asymmetrically, while the asymmetry is driven by the resource abundance. Based on experimental models with linearly-linked patches, we propose a planarly-linked-patch model with asymmetric dispersal. Using dynamical systems theory, we show global stability of equilibria in the model, and demonstrate how the resource-driven dispersal forms patterns. It is shown that appropriate asymmetry in dispersal would make the consumer persist in the system, even in sink patches. The asymmetry could also make the consumer’s total population abundance larger than that without dispersal. However, inappropriate asymmetry would make the consumer go into extinction, even in source patches. Dispersal rates are also shown to play a role in the persistence and abundance increase. Our results are consistent with experimental observations and provide new insights. Numerical simulations by the model reproduce various vegetation patterns in the real world. This work has potential applications in spatial pattern formation in biological research.

SIAM Journal on Applied Mathematics

Seed dispersal and tree legacies influence spatial patterns of plant invasion dynamics

Invasive plant species alter community dynamics and ecosystem properties, potentially leading to regime shifts. Here, the invasion of a non-native tree species into a stand of native tree species is simulated using an agent-based model. The model describes an invasive tree with fast growth and high seed production that produces litter with a suppressive effect on native seedlings, based loosely on Melaleuca quinquenervia , invasive to southern Florida. The effect of a biocontrol agent, which reduces the invasive tree's growth and reproductive rates, is included to study how effective biocontrol is in facilitating the recovery of native trees. Even under biocontrol, the invader has some advantages over native tree species, such as the ability to tolerate higher stem densities than the invaded species and its litter's seedling suppression effect. We also include a standing dead component of both species, where light interception from dead canopy trees influences neighboring tree demographics. The model is applied to two questions. The first is how the mean seedling dispersal rate affects the spread of the invading species into a pure stand of natives, assuming the same mean dispersal distance for both species. For assumed litter seedling suppression that roughly balances the fitness levels of the two species, which species dominates depends on the mean dispersal distance. The invader dominates at both very high and very low mean seedling dispersal distances, while the native tree dominates for dispersal distances in the intermediate range. The second question is how standing dead trees affect either the rate of spread of the invader or the rate of recovery of the native species. The legacy of standing dead invasive trees may delay the recovery of native vegetation. The results here are novel and show that agent-based modeling is essential in illustrating how the fine-scale modeling of local interactions of trees leads to effects at the population level.

Frontiers in Applied Mathematics and Statistics

Enhancing the predictability of ecology in a changing world: A call for an organism-based approach

Ecology is usually very good in making descriptive explanations of what is observed, but is often unable to make predictions of the response of ecosystems to change. This has implications in a human-dominated world where a suite of anthropogenic stresses are threatening the resilience and functioning of ecosystems that sustain mankind through a range of critical regulating and supporting services. In ecosystems, cause-and-effect relationships are difficult to elucidate because of complex networks of negative and positive feedbacks. Therefore, being able to effectively predict when and where ecosystems could pass into different (and potentially unstable) new states is vitally important under rapid global change. Here, we argue that such better predictions may be reached if we focus on organisms instead of species, because organisms are the principal biotic agents in ecosystems that react directly on changes in their environment. Several studies show that changes in ecosystems may be accurately described as the result of changes in organisms and their interactions. Organism-based theories are available that are simple and derived from first principles, but allow many predictions. Of these we discuss Trait-based Ecology, Agent Based Models, and Maximum Entropy Theory of Ecology and show that together they form a logical sequence of approaches that allow organism-based studies of ecological communities. Combining and extending them makes it possible to predict the spatiotemporal distribution of groups of organisms in terms of how metabolic energy is distributed over areas, time, and resources. We expect that this “Organism-based Ecology” (OE) ultimately will improve our ability to predict ecosystem dynamics.

Frontiers in Applied Mathematics and Statistics

Less is more: Less herbicide does more when biological control is present in Pontederia crassipes

An experiment along with simulation modeling was applied to study the combinations of herbicide treatment and biological control that best limit invasive water hyacinth ( Pontederia crassipes , formerly Eichhornia crassipes ) in freshwater aquatic systems. The experiment consisted of 14 different treatments of P. crassipes in 1.67 m 2 outdoor tank mesocosms. Seven treatments were with and seven were without insect biological control agents, Neochetina eichhorniae . In both of the sets of seven treatments, there was one no-herbicide treatment, a one-time full-strength herbicide treatment with 40 %, 80 % and 100 % coverage of the P. crassipes , and a one-time half-strength herbicide treatment with 40 %, 80 %, and 100 % surface area coverage. An overarching hypothesis was that leaving part of a tank unsprayed, providing habitat for the maintenance of biological control agents, would optimize control. Data from the experiment, measured on five days over the 167-day period, were used to calibrate a difference equation model of P. crassipes with and without the biological control agent. The model was then used to project longer term dynamics of the system. The model predicted that an initial one-time herbicide treatment, combined with application of the biocontrol agent at 80 % areal coverage, could maintain P. crassipes at levels lower than the carrying capacity of the plant's biomass over the long term, though not enough that N. eichhorniae would be considered, by itself, a highly effective control. However, the results suggest that a combination of biocontrol with 80 % spraying coverage every 600 days or so would be an effective integrated biocontrol strategy for maintaining decreased P. crassipes biomass at low levels over the long term.

Ecological Modelling

Book review: Quasispecies as a unifying concept in population dynamics

The quasispecies concept had two independent origins. One source was the theoretical ideas of Manfred Eigen and Peter Schuster in the 1970s. Studying the self-organization and evolution of primitive RNA molecules, they defined quasispecies as a distribution of mutant viral genomes generated by the mutation-selection process. In particular, the quasispecies nucleotide distribution consists of a singular fittest genotype, called the master sequence, surrounded by similar mutant spectra. The other source of the quasispecies concept can be traced to the growing empirical knowledge on RNA viruses formulated around the same time. Genomic sequencing of viral RNA indicated a variety of nucleotide sequences, or a distribution of sequences. Mutations in both Eigen’s theoretical system in the RNA viruses are not rare, as RNA is structurally less stable than RNA, but common, preventing the fittest genotype from becoming dominant. Virologists have adopted the quasispecies concept, with some papers on Covid-19 using the construct to explain that virus’s behavior.

Mathematical Biosciences

Aerial dispersal of Lygodium microphyllum spores within Arthur R. Marshall Loxahatchee National Wildlife Refuge

Native across the Old World tropics from Africa to Southeast Asia and Australia, Lygodium microphyllum (Cav.) R. Br. (Old World Climbing Fern) is one of the most invasive plant species threatening South Florida ecosystems (Rodgers et al. 2014). This invasive fern was first collected as a naturalized plant in South Florida in the late 1960s (Beckner 1968). Subsequent populations were observed in the late 1970s in both Martin and Palm Beach Counties (Nauman and Austin 1978). In 1989 L. microphyllum was observed by the South Florida Water Management District (SFWMD) in the Arthur R. Marshall Loxahatchee National Wildlife Refuge (LNWR). In 1995, a survey by SFWMD indicated that 12% of LNWR was colonized by L. microphyllum. By 1997 this had increased to 36% (Ferriter 2001). Ten years later, Systematic Reconnaissance Flights conducted over LNWR estimated that 44% of LNWR had sparse (> a single individual tree, shrub or stem to <50%) or dense (>50%) infestations of L. microphyllum

Florida Scientist

Hierarchical functional response of a forager on a wetland landscape

We show that for some foragers the form that a functional response takes depends on the temporal and spatial scales considered. In representing the consumption rate of an organism, it may be necessary to use a hierarchy of functional responses. Consider, for example, a wading bird foraging in wetland landscape characterized by a spatial distribution of potential foraging sites, such as ponds. At the smallest time scale of minutes or hours, during which a wading bird is foraging within a single site, the functional response will reflect the local density of prey, as well as features of the site that affect the feeding rate, such as water depth. At this short time scale, which is determined by the giving up time of the wading bird in a particular site, prey density may be relatively constant. The food intake from a particular pond is then the product of the time spent before giving-up time and moving to another site and the rate of prey consumption at that site. A prey-centered functional response is most appropriate for describing the prey consumption rate. We propose that over the longer time scale of a day, during which a wading bird may visit several foraging sites, the type of functional response can be considered to be patch centered. That is, it is influenced by the spatial configuration of sites with available prey and the wading bird’s strategy of choosing among different sites and decisions on how long to stay in any given sites. Over the time scale of a day, if the prey densities stay relatively constant, the patch-centered functional response for a constant environment is adequate. However, on the longer time scale of a breeding season, in which changing water levels result in temporal changes in the availability of prey in sites, a third hierarchical level may be relevant. At that scale, the way in which the landscape pattern changes through time, and how the wading bird responds, influences the functional response. This hierarchical concept applies to a colony of breeding wading birds foraging in wetlands such as the Everglades.

Frontiers in Ecology and Evolution

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.

Bulletin of Mathematical Biology

Modeling structural mechanics of oyster reef self-organization including environmental constraints and community interactions

Self-organization is a process of establishing and reinforcing local structures through feedbacks between internal population dynamics and external factors. In reef-building systems, substrate is collectively engineered by individuals that also occupy it and compete for space. Reefs are constrained spatially by the physical environment, and by mortality, which reduces production but exposes substrate for recruits. Reef self-organization therefore depends on efficient balancing of production and occupancy of substrate. To examine this, we develop a three-dimensional individual-based model (IBM) of oyster reef mechanics. Shell substrate is grown by individuals as valves, accumulates at the reef level, and degrades following mortality. Single restoration events and subsequent dynamics are simulated for a case study in South Carolina (USA). Variability in model processes is included on recruitment, spatial environmental constraints, and predation, over multiple independent runs and five predator community scenarios. The main goal for this study is to summarize trends in dynamics that are robust across this uncertainty, and from these generate new hypotheses and predictions for future studies. Simulation results demonstrate three phases following restoration: initial transient dynamics with considerable shell loss, followed by growth and saturation of the live population, and then saturation of settlement habitat several years later. Over half of simulations recoup initial shell losses as populations grow, while others continue in decline. The balance between population density, substrate supporting the reef, and exposed surfaces for settlement is mediated by overall population size and size structure, presence of predators, and relative amounts of live individuals and intact dead shells. The efficiency of settlement substrate production improves through time as population size structure becomes more complex, and the population of dead valves accumulates.

Ecological Modelling

Carrying capacity of spatially distributed metapopulations

Carrying capacity is a key concept in ecology. A body of theory, based on the logistic equation, has extended predictions of carrying capacity to spatially distributed, dispersing populations. However, this theory has only recently been tested empirically. The experimental results disagree with some theoretical predictions of when they are extended to a population dispersing randomly in a two-patch system. However, they are consistent with a mechanistic model of consumption on an exploitable resource (consumer–resource model). We argue that carrying capacity, defined as the total equilibrium population, is not a fundamental property of ecological systems, at least in the context of spatial heterogeneity. Instead, it is an emergent property that depends on the population’s intrinsic growth and dispersal rates.

Trends in Ecology and Evolution

Carrying capacity of a population diffusing in a heterogeneous environment

The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reaction-diffusion equations describing populations in space. Analysis of reaction-diffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space, conditions exist for which the total population size at equilibrium (i) exceeds the total population that which would occur in the absence of diffusion and (ii) exceeds that which would occur if the system were homogeneous and the total carrying capacity, computed as the integral over the local carrying capacities, was the same in the heterogeneous and homogeneous cases. We review here work over the past few years that has explained these apparently counter-intuitive results in terms of the way input of energy or another limiting resource (e.g., a nutrient) varies across the system. We report on both mathematical analysis and laboratory experiments confirming that total population size in a heterogeneous system with diffusion can exceed that in the system without diffusion. We further report, however, that when the resource of the population in question is explicitly modeled as a coupled variable, as in a reaction-diffusion chemostat model rather than a model with logistic growth, the total population in the heterogeneous system with diffusion cannot exceed the total population size in the corresponding homogeneous system in which the total carrying capacities are the same.

Mathematics and Computers in Modern Science - Acou

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.

The American Naturalist