Donald L. DeAngelis’s research while affiliated with United States Geological Survey and other places

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Publications (31)


Resource-Driven Pattern Formation in Consumer-Resource Systems with Asymmetric Dispersal on a Plane
  • Article

October 2023

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16 Reads

SIAM Journal on Applied Mathematics

Weiting Song

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Shikun Wang

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Yuanshi Wang

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Donald DeAngelis

A generically parameterized model of Lake eutrophication: The impact of Stoichiometric ratios and constraints on the abundance of natural phytoplankton communities (GPLake-S)

November 2022

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83 Reads

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4 Citations

Ecological Modelling

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Donald L. DeAngelis

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[...]

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Water quality improvement to avoid excessive phytoplankton blooms often requires eutrophication management where both phosphorus (P) and nitrogen (N) play a role. While empirical eutrophication studies and ecological resource competition theory both provide insight into phytoplankton abundance in response to nutrient loading, they are not seamlessly linked in the current state of eutrophication research. We argue that understanding species competition for multiple nutrients and light in natural phytoplankton communities is key to assessing phytoplankton abundance under changing nutrient supply. Here we present GPLake-S, a mechanistic model rooted in ecological resource competition theory, which has only eight parameters and can predict chlorophyll-a to nutrient relationships for phytoplankton communities under N, P, N+P colimitation and light limitation. GPLake-S offers a simple mechanistic tool to make first estimates of chlorophyll-a levels and nutrient thresholds for generic lake properties, accounting for variation in N:P ratio preferences of phytoplankton species. This makes the model supportive of water management and policy.


Periodic oscillation and tri-stability in mutualism systems with two consumers

February 2022

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28 Reads

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4 Citations

Journal of Mathematical Analysis and Applications

This paper considers mutualistic interactions between two consumers, in which one consumer can consume a resource only by exchange of service for service with the other. By rigorous analysis on the one-resource and two-consumer model with Holling-type I response, we show periodic oscillations and tri-stability in the mutualism system: when their initial densities decrease, the consumers' interaction outcomes would change from coexistence in periodic oscillation, to persistence at a steady state, and to extinction. Under certain conditions, we also show two types of bi-stability in the system: the consumers would change from coexisting in periodic oscillation (resp. at a steady state) to going to extinction when their initial densities decrease. Then we analyze a modified system with Holling-type II response. Based on theoretical analysis and numerical computation, we show that there also exist tri-stability and two types of bi-stability in this system. Moreover, it is shown that varying the degree of obligation can lead to transition of interaction outcomes between coexistence in periodic oscillation (resp. at a steady state) and extinction of both consumers. These results are important in understanding complexity in mutualism.


Schematic diagram of theoretical predictions. (a) Based on paired logistic equations with random diffusion. (b) Based on the paired consumer‐resource model with directed movement. (c) Representation of experimental design on ‘transfer event’. (d) Same initial population size was used in both heterogeneous and homogeneous environments, which started with the same level of total resource concentration. Worms were counted after four days of growth in four randomly selected fields on each entire plate. Micro‐graphed image with labelled strain (in orange boxes) and unlabelled strain (in blue boxes)
Dynamic change of proportion of slow mover (proportionslow) in the group with directed movement. (a, c) LX2004 (labelled) paired with MT1073 (roamer); (b, d) LX2004 (labelled) paired with CX14295 (dweller), over eight transfers in heterogeneous environments (dark dots) and in homogeneous environments (empty dots). Significance of difference in the final proportions of slow mover (proportionslow) between the different initial proportions in each condition were analysed using Analysis of Variance (ANOVA). p values indicate the significance of comparisons
Dynamic change of proportion of slow mover (proportionslow) in the group without directed movement. (a, c) MIA470 (labelled, no chemotaxis) paired with MIA472 (roamer, no chemotaxis); (b, d) MIA470 (labelled, no chemotaxis) paired with MIA471 (dweller, no chemotaxis), over nine transfers in heterogeneous environments (dark dots) and in homogeneous environments (empty dots). Significance of difference in the final proportions of slow mover (proportionslow) between the different initial proportions in each condition were analysed using Analysis of Variance (ANOVA). p values indicate the significance of comparisons
Simulations of population sizes of slow movers (U1 and U2) on Patches 1 and 2, respectively, and fast movers (V1 and V2), on Patches 1 and 2, respectively, as functions of the coefficient of directed movement coefficient, α
Simulations of the proportion of slow mover (proportionslow) over 20 transfer events with a series of initial proportions (0.1–0.9) in heterogeneous environments with (a) small α (≤0.1); (b) intermediate α (=0.125); (c) large α (≥0.35); and in homogeneous environments with (d) small α (≤0.1); (e) intermediate α (=0.125); (f) large α (≥0.35). Each dot represents the proportionslow of each transfer event, and colours represent different initial proportions. Initial resource levels in the three patches in heterogeneous environments are (200, 100 and 1) and in homogeneous environments are 100, 100 and 100, respectively. To evaluate the results, we used the proportion of slow mover as proportionslow = ∑i=13Ui/(∑i=13Ui+∑i=13Vi) to represent the dominance of slow mover
Directed movement changes coexistence outcomes in heterogeneous environments
  • Article
  • Full-text available

November 2021

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694 Reads

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16 Citations

Ecology Letters

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.

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Conceptual description of the model. (A) Schematic figure of the model. (B) The initial condition where native populations occupied all the 100 × 100 spatial cells and invasive population starts to invade from the center cell. DOI: https://doi.org/10.1525/elementa.2020.00181.f1
Population dynamics change under interaction of biological control and different frequencies of mechanical treatments. The description of the six treatment frequencies of mechanical treatments (A), the change of average proportion of invasive species over time steps with weak biological control (γ) = .002 (B), with intermediate biological control (γ) = .01 (C), and the final fraction of invasive species across the six treatment groups under weak and intermediate level of biological control (D). DOI: https://doi.org/10.1525/elementa.2020.00181.f2
Population dynamics change under different scenarios of biological control. The final population distribution pattern of native, invasive, and biological control agent with no biological control (A), with targeted and low frequency treatment of biological control (B), with targeted and high frequency treatment of biological control (C), with nontargeted and low frequency treatment of biological control (D), with nontargeted and high-frequency treatment of biological control (E), the change of average fraction of invasive species over time steps under the four sub-scenarios (F), and the final fraction of invasive species across the four treatments (G). Biological control efficiency level (γ) = .01. DOI: https://doi.org/10.1525/elementa.2020.00181.f3
Population dynamics change under interaction of biological control and mechanical treatments. The final population distribution pattern of native, invasive, and biological control agent with targeted biological control and low frequency mechanical treatments (A), targeted biological control and high frequency mechanical treatments (B), with nontargeted biological control and low frequency mechanical treatments (C), with nontargeted biological control and high frequency mechanical treatments (D), the change of average fraction of invasive species over time steps under the four sub-scenarios (E), and the final fraction of invasive species across the four treatments (F). Biological control efficiency level (γ) = .01. DOI: https://doi.org/10.1525/elementa.2020.00181.f4
Total times of mechanical treatment under different levels of biological control. Total times that mechanical treatment (i.e., handing removal) were added in each repetition (50 times; A, C, E, and G) and temporal change of average fraction of invasive species in each repetition (50 times; B, D, F, and H) in conditions of weak level of biological control (γ) = .002 with handling removing one row each time (A, B); weak level of biological control (γ) = .002 with handling removing 10 rows each time (C, D); intermediate level of biological control (γ) = .01 with handling removing one row each time (E, F); intermediate level of biological control (γ) = .01 with handling removing ten rows each time (G, H). Note that we used vertical lines to connect data points with corresponding repetition points in A, C, E, and G to give a better vision of the plot. The mean and standard deviation of total time points that mechanical treatment are shown in A, C, E, and G. DOI: https://doi.org/10.1525/elementa.2020.00181.f5
Integrating mechanical treatment and biological control to improve field treatment efficiency on invasions

June 2021

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187 Reads

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3 Citations

Projecting invasion treatment outcomes and determining controlling efficiency under various management strategies have important implications in field management. Different from herbicide usage that may cause environmental pollution and nontarget effects on native plants, nonchemical (i.e., mechanical) methods, such as mowing and hand weeding, have shown great targeted effectiveness on invasion. However, an interesting and important question that remains unclear is how to reduce the need for repeated applications of mechanical treatments. One possible approach is to integrate mechanical treatments with biological control agents, which can attack and limit invasion spread after being established in the field. We hypothesize that applying mechanical methods to remove invasive plants while establishing biological control agents, then using the established biological control agents to limit future regrowth of invasive plants, will decrease the use of mechanical treatments. To include vegetation dispersal, we developed a spatial modeling framework, using paired logistic equation models of both a resident native plant and an invasive plant, and a biological control agent, to capture the dynamics of native and invasive plants under different treatment scenarios. Specifically, we examined four factors, the initial application location of biological agents, their controlling efficiency, the treatment frequency (how often nonchemical treatment will be applied), and the areal extent of mechanical treatment. We found that explicitly targeted biological control agents showed significantly stronger controlling impacts on invasive plants than did nontargeted agents, whereas a higher treatment frequency could compensate for the drawback of untargeted treatment. Our results also suggested that adding mechanical treatment can further limit invasion spread with the cooperation of established biological control agents, and applying mechanical treatment in a lower frequency, but treating larger areas per time, is a more efficient approach than vice versa. We emphasize that a high biological control efficiency can continuously decrease the requirement of repeated treatment of nonchemical methods and maintain the invasive population at a low level. The model we developed here can be potentially extended and used by field managers on prioritizing controlling efforts to achieve a higher efficiency.


Development and validation of a spatially-explicit agent-based model for space utilization by African savanna elephants (Loxodonta africana) based on determinants of movement

May 2021

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326 Reads

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7 Citations

Ecological Modelling

African elephants (Loxodonta africana) are well-studied and inhabit diverse landscapes that are being transformed by both humans and natural forces. Most tools currently in use are limited in their ability to predict how elephants will respond to novel changes in the environment. Individual-, or agent-based modeling (ABM), may extend current methods in addressing and predicting spatial responses to environmental conditions over time. We developed a spatially explicit agent-based model to simulate elephant space use and validated the model with movement data from elephants in Kruger National Park (KNP) and Chobe National Park (CNP). We simulated movement at an hourly scale, as this scale can reflect switches in elephant behavior due to changes in internal states and short-term responses to the local availability and distribution of critical resources, including forage, water, and shade. Known internal drivers of elephant movement, including perceived temperature and the time since an individual last visited a water source, were linked to the external environment through behavior-based movement rules. Simulations were run on model landscapes representing the wet season and the hot, dry season for both parks. The model outputs, including home range size, daily displacement distance, net displacement distance, and maximum distance traveled from a permanent water source, were evaluated through qualitative and quantitative comparisons to actual elephant movement data from both KNP and CNP. The ABM was successful in reproducing the differences in daily displacements between seasons in each park, and in distances traveled from a permanent water source between parks and seasons. Other movement characteristics, including differences in home range sizes and net daily displacements, were partially reproduced. Out of the all the statistical comparisons made between the empirical and simulated movement patterns, the majority were classified as discrepancies of medium or small effect size. We have shown that a resource-driven model with relatively simple decision rules generates trajectories with movement characteristics that are mostly comparable to those calculated from empirical data. Simulating hourly movement (as our model does) may be useful in predicting how finer-scale patterns of space use, such as those created by foraging movements, are influenced by finer spatio-temporal changes in the environment.



Projecting the optimal control strategy on invasive plants combining effects of herbivores and native plants resistance

October 2020

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29 Reads

Understanding how to limit biological invasion is critical, especially in the context of accelerating anthropogenic ecological changes. Although biological invasion success could be explained by the lack of natural enemies in new regions, recent studies have revealed that resident herbivores often do have a substantial effect on both native and invasive plants. Very few studies have included consideration of native plant resistance while estimating methods of controlling invasion; hence, it is unclear to what extent the interactive effects of controlling approaches and native plants' resistance could slow down or even inhibit biological invasion. We developed a spatial modeling framework, using a paired logistic equation model, with considerations of the dispersal processes, to capture the dynamics change of native and invasive plants under various strategies of control. We found that when biocontrol agents could have a strong effect on invasive plant, that could almost completely limit the invasion, together with a high native plant resistance. However, a high application frequency is needed make an efficient impact, whereas, a low frequency treatment leads to nearly the same outcome as the no treatment case. Lastly, we showed that evenly controlling a larger area with a weaker effect still lead to a better outcome than focusing on small patches with a stronger effect. Overall, this study has some management implications, such as how to determine the optimal allocation strategy.


An Overview of Agent-Based Models in Plant Biology and Ecology

March 2020

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153 Reads

A c c e p t e d M a n u s c r i p t 2 Agent-based modeling (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 modeling 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 modeling, 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 scale 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.


Fig. 1. Types of ABMs with the ranges of spatial extent and resolution. (1) Functional structural plant models (FSPMs): for example, PEACH (Grossman and DeJong, 1994), and Tomato model (Sarlikioti et al., 2011). (2) FSPMs with plant-plant interactions: for example, PLATHO (Gayler et al., 2006), Virtual Grassland (Louarn et al., 2020, ROOTMAP (Diggle, 1988). (3) Gap phase models: for example, JABOWA (Botkin et al., 1972), FORET (Shugart and West, 1977), LINKAGES (Post and Pastor, 1996), FORMAN (Chen and Twilley, 1998), EDS (Ngugi et al., 2011) and FORCLIM (Bugmann and Solomon, 2000). (4) Spatially explicit forest models: for example, SORTIE (Pacala et al., 1993), MANGRO (Berger et al., 2008) and TROLL (Maréchaux and Chave, 2017). (5) Landscape models (linking gap models): for example, ZELIG (Miller and Urban, 1999), LANDIS (Mladenoff, 2004), FORMIND (Kohler and Huth, 1998), TREEGRASS (Simioni et al., 2000) and PSS (Fennel et al., 2012). (6) Regional models: for example, SEIB-DDVM (Sato et al., 2007) and ED (Moorcroft et al., 2001). Downloaded from https://academic.oup.com/aob/advance-article-abstract/doi/10.1093/aob/mcaa043/5805513 by guest on 16 June 2020
Agent-based modelling used to address species and/or applied ecology questions (published since 2006).
Agent-based modelling used to address theoretical ecology questions (published since 2006).
An Overview of Agent-Based Models in Plant Biology and Ecology

March 2020

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325 Reads

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52 Citations

Annals of Botany

Agent-based modeling (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 modeling 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 modeling, 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 scale 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.


Citations (15)


... Presently, there are several lake water ecological models available, each with distinct advantages [31][32][33]. These models help assess changes in water nutrients and pollutants [34], eutrophication and risk assessments [35], and the identification of direct or indirect impact factors on lake ecology [36]. Among these models, AQUATOX, which was developed by the United States Environmental Protection Agency (US EPA), stands out as highly effective and features a flexible structure and user-friendly interface [37]. ...

Reference:

Lake Water Ecological Simulation for a Typical Alpine Lake on the Tibetan Plateau
A generically parameterized model of Lake eutrophication: The impact of Stoichiometric ratios and constraints on the abundance of natural phytoplankton communities (GPLake-S)
  • Citing Article
  • November 2022

Ecological Modelling

... For instance, habitat specialists, species with large body sizes, species at higher trophic levels, and species that do not rely heavily on mutualist species are expected to go extinct first when habitat occurrence decreases (Didham, 2010). However, understudied traits important for understanding and estimating fragmentation effects in the field are dispersal and locomotion strategies, which are fundamental features of life (Nathan, 2008;Zhang et al., 2022). We used locomotion and dispersion as generic synonyms to describe an organism's ability to move from one location to another and considered that a relatively higher rate of locomotion corresponds to a relatively greater area traveled in a landscape. ...

Directed movement changes coexistence outcomes in heterogeneous environments

Ecology Letters

... In addition to their resources, the obligatory mutualistic populations need the presence of another population for their growth. Examples of such mutualism are given in [3,10]. In a obligatory mutualism the authors (see [3]) used the Holling type II function for the mutualistic interaction and showed the coexistence or extinction of the two heterotrophs by numerical simulations. ...

Periodic oscillation and tri-stability in mutualism systems with two consumers
  • Citing Article
  • February 2022

Journal of Mathematical Analysis and Applications

... A failure to incorporate dispersal rate into models of vegetation dynamics greatly compromises their predictive capability, leading to substantial modeling uncertainty [40]. In mathematical models of species invasion, invasive species have been widely parameterized with faster dispersal rates than native ones, given that invasive species are expanding to new habitats, but native ones tend to be stable in their habitats [21]. However, the variation in the comparison of dispersal rate between invasive and native species are largely unknown, and the variation may be driven by plant life forms (herbaceous vs. woody plants), disturbance levels (low vs. high disturbance levels), and measurement methods. ...

Integrating mechanical treatment and biological control to improve field treatment efficiency on invasions

... The savannahs of Southern Africa have two distinct seasons: a dry season from April to September and a wet season from October to March (Bourlière and Hadley, 1970). These seasons markedly influence Loxodonta africana, African savannah elephant, movements as elephants require large amounts of food and water daily and can travel considerable distances to obtain them (Chamaillé-Jammes et al., 2013;Diaz et al., 2021). Elephants are more nomadic and will travel larger distances in the wet season when seasonal waterholes and ephemeral streams are widely available (Loarie et al., 2009a(Loarie et al., , 2009bYoung et al., 2009;Chamaillé-Jammes et al., 2013; van Aarde, 2017;Tshipa et al., 2017;Diaz et al., 2021). ...

Development and validation of a spatially-explicit agent-based model for space utilization by African savanna elephants (Loxodonta africana) based on determinants of movement
  • Citing Article
  • May 2021

Ecological Modelling

... The synthesis approach overcomes limitations associated with accessing real data, such as privacy concerns, insufficient resolution, missing attributes, especially in survey and census data [2]. Synthetic populations are particularly useful to study the interplay of individual components [3], especially in fields including economics [4], sociology [5], ecology [6], and transportation [7]. The process of creating synthetic populations typically involves (1) generating sociodemographic attributes for individuals and households, (2) assigning ...

An Overview of Agent-Based Models in Plant Biology and Ecology

Annals of Botany

... It also allows us to distinguish between different dynamical mechanisms resulting in long transient dynamics such as ghost attractors, saddles (including chaotic saddles), slow-fast systems, etc. [6,7]. While our review [7] contributes towards the development of a unifying description of ecological transients, possibly with applications in life sciences more generally, given the complexity of the subject more work is needed before it becomes a comprehensive theory and a standard part of mainstream ecology [13,14]. The latter will require a joint effort of mathematicians and ecologists, in particular in the development of protocols for long-term monitoring and also to identify the key variables to monitor [13], some of which can be counter-intuitive and obscure. ...

Mathematical ecologists describe apparently long-stable dynamics that undergo sudden change to a different regime
  • Citing Article
  • November 2019

Physics of Life Reviews

... A highly related study is that Gao and Lou [15] analyzed the impact of dispersal asymmetry on the total biomass of a single species in a two-patch environment. See also Wu et al. [38] for analysis on a source-sink system. The current work is more challenging in that the population size in each patch varies with dispersal asymmetry. ...

Dispersal asymmetry in a two-patch system with source–sink populations
  • Citing Article
  • November 2019

Theoretical Population Biology

... The predator-prey relationship is fundamental in nature, making predator-prey models one of the most basic and widely studied biological models. Due to increasingly frequent human activities and spatial heterogeneity, the habitats of many species have been fragmented into separate patches [1][2][3][4][5]. Understanding how species interact across these fragmented habitats has become crucial for ecological management and conservation efforts, as well as for predicting the long-term persistence of species in altered environments. ...

Asymptotic population abundance of a two-patch system with asymmetric diffusion
  • Citing Article
  • January 2019

Discrete and Continuous Dynamical Systems

... Nonetheless, intricate biochemical processes could introduce uncertainties in predictions. Therefore, the prerequisite for conducting precise analyses entails acquiring sufficient data from a multitude of sources Chang et al., 2019;Dibs et al., 2023). To address the paucity of research on potential mitigating effects of IBWD amid climate change, three datasets were linked to enhance our understanding of the role of IBWD projects in shaping the mechanisms of P fate and transport, in the shallow YQR. ...

A Generically Parameterized model of Lake eutrophication (GPLake) that links field-, lab- and model-based knowledge

The Science of The Total Environment