October 2023
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16 Reads
SIAM Journal on Applied Mathematics
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October 2023
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16 Reads
SIAM Journal on Applied Mathematics
November 2022
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83 Reads
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4 Citations
Ecological Modelling
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.
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.
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.
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.
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.
April 2021
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37 Reads
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10 Citations
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.
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.
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.
... 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]. ...
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. ...
November 2021
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. ...
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. ...
June 2021
... 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). ...
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 ...
March 2020
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. ...
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. ...
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. ...
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. ...
August 2019
The Science of The Total Environment