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Bull Math Biol 2021 Nov 27;84(1):10. Epub 2021 Nov 27.

Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV, 89154, USA.

This article studies a multi-strain epidemic model with diffusion and environmental heterogeneity. We address the question of a control strategy for multiple strains of the infectious disease by investigating how the local distributions of the transmission and recovery rates affect the dynamics of the disease. Our study covers both full model (in which case the diffusion rates for all subgroups of the population are positive) and the ODE-PDE case (in which case we require a total lock-down of the susceptible subgroup and allow the infected subgroups to have positive diffusion rates). In each case, a basic reproduction number of the epidemic model is defined and it is shown that if this reproduction number is less than one then the disease will be eradicated in the long run. On the other hand, if the reproduction number is greater than one, then the disease will become permanent. Moreover, we show that when the disease is permanent, creating a common safety area against all strains and lowering the diffusion rate of the susceptible subgroup will result in reducing the number of infected populations. Numerical simulations are presented to support our theoretical findings.

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http://dx.doi.org/10.1007/s11538-021-00957-6 | DOI Listing |

November 2021

Ecol Lett 2021 Nov 24. Epub 2021 Nov 24.

Department of Environmental Science and Policy, University of California, Davis, Davis, California, USA.

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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http://dx.doi.org/10.1111/ele.13925 | DOI Listing |

November 2021

Bull Math Biol 2021 Sep 15;83(10):109. Epub 2021 Sep 15.

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China.

We study the evolution of dispersal in advective three-patch models with distinct network topologies. Organisms can move between connected patches freely and they are also subject to the passive, directed drift. The carrying capacity is assumed to be the same in all patches, while the drift rates could vary. We first show that if all drift rates are the same, the faster dispersal rate is selected for all three models. For general drift rates, we show that the infinite diffusion rate is a local Convergence Stable Strategy (CvSS) for all three models. However, there are notable differences for three models: For Model I, the faster dispersal is always favored, irrespective of the drift rates, and thus the infinity dispersal rate is a global CvSS. In contrast, for Models II and III a singular strategy will exist for some ranges of drift rates and bi-stability phenomenon happens, i.e., both infinity and zero diffusion rates are local CvSSs. Furthermore, for both Models II and III, it is possible for two competing populations to coexist by varying drift and diffusion rates. Some predictions on the dynamics of n-patch models in advective environments are given along with some numerical evidence.

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http://dx.doi.org/10.1007/s11538-021-00939-8 | DOI Listing |

September 2021

J Nonlinear Sci 2021 3;31(5):73. Epub 2021 Jul 3.

School of Mathematical Sciences, Shanghai Jiaotong University, Shanghai, 200240 China.

Based on a susceptible-infected-susceptible patch model, we study the influence of dispersal on the disease prevalence of an individual patch and all patches at the endemic equilibrium. Specifically, we estimate the disease prevalence of each patch and obtain a weak order-preserving result that correlated the patch reproduction number with the patch disease prevalence. Then we assume that dispersal rates of the susceptible and infected populations are proportional and derive the overall disease prevalence, or equivalently, the total infection size at no dispersal or infinite dispersal as well as the right derivative of the total infection size at no dispersal. Furthermore, for the two-patch submodel, two complete classifications of the model parameter space are given: one addressing when dispersal leads to higher or lower overall disease prevalence than no dispersal, and the other concerning how the overall disease prevalence varies with dispersal rate. Numerical simulations are performed to further investigate the effect of movement on disease prevalence.

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http://dx.doi.org/10.1007/s00332-021-09731-3 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8254459 | PMC |

July 2021

J Math Biol 2021 03 15;82(5):36. Epub 2021 Mar 15.

CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, Université PSL, 75775, Paris cedex 16, France.

We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these probabilities as dispersal strategies. We show that the evolutionarily stable strategies are to move in one direction only. Our results predict that it is more beneficial for the species to choose the direction with smaller variation in the resource distribution. This finding seems to be in agreement with the classical results of Hastings (1983) and Dockery et al. (1998) for the evolution of slow dispersal, i.e. random diffusion is selected against in spatially heterogeneous environments. These conclusions also suggest that broader dispersal strategies should be considered regarding the movement in heterogeneous habitats.

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http://dx.doi.org/10.1007/s00285-021-01579-1 | DOI Listing |

March 2021

J Math Biol 2021 01 19;82(1-2). Epub 2021 Jan 19.

Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo, 152-8551, Japan.

This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the population of a single species with logistic growth residing in a patchy environment and study the effects of dispersal and spatial heterogeneity of patches on the total population at equilibrium. Our objective is to maximize the total population by redistributing the resources among the patches under the constraint that the total amount of resources is limited. It is shown that the global maximizer can be characterized for any number of patches when the diffusion rate is either sufficiently small or large. To show this, we compute the first variation of the total population with respect to resources in the two patches case. In the case of three or more patches, we compute the asymptotic expansion of all patches by using the Taylor expansion with respect to the diffusion rate. To characterize the shape of the global maximizer, we use a recurrence relation to determine all coefficients of all patches.

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http://dx.doi.org/10.1007/s00285-021-01565-7 | DOI Listing |

January 2021

Bull Math Biol 2020 10 6;82(10):131. Epub 2020 Oct 6.

Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA.

We study the dynamics of two competing species in three-patch models and illustrate how the topology of directed river network modules may affect the evolution of dispersal. Each model assumes that patch 1 is at the upstream end, patch 3 is at the downstream end, but patch 2 could be upstream, or middle stream, or downstream, depending on the specific topology of the modules. We posit that individuals are subject to both unbiased dispersal between patches and passive drift from one patch to another, depending upon the connectivity of patches. When the drift rate is small, we show that for all models, the mutant species can invade when rare if and only if it is the slower disperser. However, when the drift rate is large, most models predict that the faster disperser wins, while some predict that there exists one evolutionarily singular strategy. The intermediate range of drift is much more complex: most models predict the existence of one singular strategy, but it may or may not be evolutionarily stable, again depending upon the topology of modules, while one model even predicts that for some intermediate drift rate, singular strategy does not exist and the faster disperser wins the competition.

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http://dx.doi.org/10.1007/s11538-020-00803-1 | DOI Listing |

October 2020

J Math Biol 2019 05 2;78(6):1605-1636. Epub 2019 Jan 2.

Chinese University of Hong Kong - Shenzhen, Shenzhen, China.

We study the dynamics of a consumer-resource reaction-diffusion model, proposed recently by Zhang et al. (Ecol Lett 20(9):1118-1128, 2017), in both homogeneous and heterogeneous environments. For homogeneous environments we establish the global stability of constant steady states. For heterogeneous environments we study the existence and stability of positive steady states and the persistence of time-dependent solutions. Our results illustrate that for heterogeneous environments there are some parameter regions in which the resources are only partially limited in space, a unique feature which does not occur in homogeneous environments. Such difference between homogeneous and heterogeneous environments seems to be closely connected with a recent finding by Zhang et al. (2017), which says that in consumer-resource models, homogeneously distributed resources could support higher population abundance than heterogeneously distributed resources. This is opposite to the prediction by Lou (J Differ Equ 223(2):400-426, 2006. https://doi.org/10.1016/j.jde.2005.05.010 ) for logistic-type models. For both small and high yield rates, we also show that when a consumer exists in a region with a heterogeneously distributed input of exploitable renewed limiting resources, the total population abundance at equilibrium can reach a greater abundance when it diffuses than when it does not. In contrast, such phenomenon may fail for intermediate yield rates.

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http://dx.doi.org/10.1007/s00285-018-1321-z | DOI Listing |

May 2019

J Math Biol 2020 01 3;80(1-2):3-37. Epub 2018 Nov 3.

Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, People's Republic of China.

We study the evolutionary stability of dispersal strategies, including but not limited to those that can produce ideal free population distributions (that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium). The environment is assumed to be variable in space but constant in time. We assume that there is a separation of times scales, so that dispersal occurs on a fast timescale, evolution occurs on a slow timescale, and population dynamics and interactions occur on an intermediate timescale. Starting with advection-diffusion models for dispersal without population dynamics, we use the large time limits of profiles for population distributions together with the distribution of resources in the environment to calculate growth and interaction coefficients in logistic and Lotka-Volterra ordinary differential equations describing population dynamics. We then use a pairwise invasibility analysis approach motivated by adaptive dynamics to study the evolutionary and/or convergence stability of strategies determined by various assumptions about the advection and diffusion terms in the original advection-diffusion dispersal models. Among other results we find that those strategies which can produce an ideal free distribution are evolutionarily stable.

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http://dx.doi.org/10.1007/s00285-018-1302-2 | DOI Listing |

January 2020

Math Biosci 2018 12 16;306:10-19. Epub 2018 Oct 16.

School of Computer Science, Shaanxi Normal University, Xi'an, Shaanxi 710119, China.

The community composition in open advective environments, where individuals are exposed to unidirectional flow, is formed by the complex interplays of hydrological and biological factors. We investigate the coexistence mechanism of species by a reaction-diffusion-advection competition model proposed by Lutscher et al. in [19]. It turns out that the locations of two critical curves, which separate the stable region of the semi-trivial solutions from the unstable one, determines whether coexistence or bistability happens. Furthermore, the analytical and numerical results suggest a tradeoff driven coexistence mechanism. More precisely, there is a tradeoff between the dispersal strategy and growth competence which allows the transition of competition outcomes, including competition exclusion, coexistence and bistability. This shifting may have an effect on the community composition in aquatic habitat.

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http://dx.doi.org/10.1016/j.mbs.2018.09.013 | DOI Listing |

December 2018

Ying Yong Sheng Tai Xue Bao 2017 Jul;28(7):2155-2163

Ministry of Education Key Laboratory of Soil and Water Conversation and Desertification Combating, College of Soil and Water Conservation, Beijing Forestry University, Beijing 100083, China.

This study aimed to qualify the potential water sources and their responses to seasonal precipitations for the system of Platycladus orientalis and Vitex negundo var. heterophylla by IsoSource model based on stable hydrogen and oxygen isotopic analysis in Jiufeng Mountain area of Beijing. The results showed that the O of water from 0-20 cm soil layer was enriched, whereas that was depleted as the soil layer deepened. P. orientalis used water mainly from 0-30 cm soil la-yer, being composed of rainwater 2-3 days before at the beginning of dry season. The water absorbed by P. orientalis and V. negundo sourced from 0-10 cm and 10-30 cm soil layer, which was fed on recent rainwater at the end of dry season. In wet season P. orientalis mainly accessed the soil water (from 0-40 cm layer, 59.3%) and recent rainwater (12.5%), while V. negundo drank the water from 0-30 cm soil layer derived from recent heavy rain. P. orientalis actively uptook the deeper soil water with time, until the end of growing season (November), its available water was from 60-80 cm soil layer and sourced from the rainwater happened 2-3 days before. Meanwhile, V. negundo completed its growing cycle and was on the brink of death. This system faced less competition for water use, stating its vertical water availability for climate adaptation in this region, which could reduce water and soil loss and minimize the instantaneous damage under heavy rainstorm attack.

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http://dx.doi.org/10.13287/j.1001-9332.201707.011 | DOI Listing |

July 2017

Bull Math Biol 2017 05 29;79(5):1051-1069. Epub 2017 Mar 29.

Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.

Geritz, Gyllenberg, Jacobs, and Parvinen show that two similar species can coexist only if their strategies are in a sector of parameter space near a nondegenerate evolutionarily singular strategy. We show that the dimorphism region can be more general by using the unfolding theory of Wang and Golubitsky near a degenerate evolutionarily singular strategy. Specifically, we use a PDE model of river species as an example of this approach. Our finding shows that the dimorphism region can exhibit various different forms that are strikingly different from previously known results in adaptive dynamics.

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http://dx.doi.org/10.1007/s11538-017-0268-3 | DOI Listing |

May 2017

Math Biosci 2017 01 10;283:136-144. Epub 2016 Nov 10.

Department of Evolution and Ecology, University of California at Davis, Davis, California 95616, United States. Electronic address:

Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results in an ideal free distribution, is evolutionary stable in spatially varying but temporally constant environments. Many species, however, primarily disperse prior to reproduction (natal dispersal) and less commonly between reproductive events (breeding dispersal). These species include territorial species such as birds and reef fish, and sessile species such as plants, and mollusks. As demographic and dispersal terms combine in a multiplicative way for models of natal dispersal, rather than the additive way for the previously studied models, we develop new mathematical methods to study the evolution of natal dispersal for continuous-time and discrete-time models. A fundamental ecological dichotomy is identified for the non-trivial equilibrium of these models: (i) the per-capita growth rates for individuals in all patches are equal to zero, or (ii) individuals in some patches experience negative per-capita growth rates, while individuals in other patches experience positive per-capita growth rates. The first possibility corresponds to an ideal-free distribution, while the second possibility corresponds to a "source-sink" spatial structure. We prove that populations with a dispersal strategy leading to an ideal-free distribution displace populations with dispersal strategy leading to a source-sink spatial structure. When there are patches which cannot sustain a population, ideal-free strategies can be achieved by sedentary populations, and we show that these populations can displace populations with any irreducible dispersal strategy. Collectively, these results support that evolution selects for natal or breeding dispersal strategies which lead to ideal-free distributions in spatially heterogenous, but temporally homogenous, environments.

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http://dx.doi.org/10.1016/j.mbs.2016.11.003 | DOI Listing |

January 2017

Arch Med Sci 2016 Oct 20;12(5):950-958. Epub 2016 Jul 20.

Department of Cardiology, Second Affiliated Hospital of Dalian Medical University, Dalian, Liaoning, China.

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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5016581 | PMC |

http://dx.doi.org/10.5114/aoms.2016.61356 | DOI Listing |

October 2016

J Biol Dyn 2015 21;9 Suppl 1:188-212. Epub 2014 Oct 21.

a Department of Mathematics , The Ohio State University , Columbus , OH 43210 , USA.

We study a two-species competition model in a closed advective environment, where individuals are exposed to unidirectional flow (advection) but no individuals are lost through the boundary. The two species have the same growth and advection rates but different random dispersal rates. The linear stability analysis of the semi-trivial steady state suggests that, in contrast to the case without advection, slow dispersal is generally selected against in closed advective environments. We investigate the invasion exponent for various types of resource functions, and our analysis suggests that there might exist some intermediate dispersal rate that will be selected. When the diffusion and advection rates are small and comparable, we determine criteria for the existence and multiplicity of singular strategies and evolutionarily stable strategies. We further show that every singular strategy is convergent stable.

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http://dx.doi.org/10.1080/17513758.2014.969336 | DOI Listing |

March 2016

Bull Math Biol 2014 Feb 16;76(2):261-91. Epub 2014 Jan 16.

Mathematical Biosciences Institute, Ohio State University, Columbus, OH, 43210, USA,

We consider a mathematical model of two competing species for the evolution of conditional dispersal in a spatially varying, but temporally constant environment. Two species are different only in their dispersal strategies, which are a combination of random dispersal and biased movement upward along the resource gradient. In the absence of biased movement or advection, Hastings showed that the mutant can invade when rare if and only if it has smaller random dispersal rate than the resident. When there is a small amount of biased movement or advection, we show that there is a positive random dispersal rate that is both locally evolutionarily stable and convergent stable. Our analysis of the model suggests that a balanced combination of random and biased movement might be a better habitat selection strategy for populations.

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http://dx.doi.org/10.1007/s11538-013-9901-y | DOI Listing |

February 2014

Bull Math Biol 2014 Feb 3;76(2):335-76. Epub 2013 Dec 3.

Mathematical Biosciences Institute, The Ohio State University, Ohio, 43210, USA,

We consider a two-patch model for a single species with dispersal and time delay. For some explicit range of dispersal rates, we show that there exists a critical value τc for the time delay τ such that the unique positive equilibrium of the system is locally asymptotically stable for τ ∈[0,τc) and unstable for τ > τc .

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http://dx.doi.org/10.1007/s11538-013-9921-7 | DOI Listing |

February 2014

J Math Biol 2014 Dec 17;69(6-7):1319-42. Epub 2013 Oct 17.

Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA.

We consider a two-species competition model in a one-dimensional advective environment, where individuals are exposed to unidirectional flow. The two species follow the same population dynamics but have different random dispersal rates and are subject to a net loss of individuals from the habitat at the downstream end. In the case of non-advective environments, it is well known that lower diffusion rates are favored by selection in spatially varying but temporally constant environments, with or without net loss at the boundary. We consider several different biological scenarios that give rise to different boundary conditions, in particular hostile and "free-flow" conditions. We establish the existence of a critical advection speed for the persistence of a single species. We derive a formula for the invasion exponent and perform a linear stability analysis of the semi-trivial steady state under free-flow boundary conditions for constant and linear growth rate. For homogeneous advective environments with free-flow boundary conditions, we show that populations with higher dispersal rate will always displace populations with slower dispersal rate. In contrast, our analysis of a spatially implicit model suggest that for hostile boundary conditions, there is a unique dispersal rate that is evolutionarily stable. Nevertheless, both scenarios show that unidirectional flow can put slow dispersers at a disadvantage and higher dispersal rate can evolve.

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http://dx.doi.org/10.1007/s00285-013-0730-2 | DOI Listing |

December 2014

Annu Int Conf IEEE Eng Med Biol Soc 2013 ;2013:834-7

This paper describes the design of an 8-channel high voltage stimulator chip for rehabilitation of stroke patients through surface stimulation, which requires high stimulation currents and high compliance voltage. The chip gets stimulation control data through its Serial Peripheral Interface (SPI), and can accordingly generate biphasic stimulation currents with different amplitudes, duration, frequencies and polarities independently for each channel. The current driver is implemented with thick oxide devices with a supply voltage up to 90V. The chip is designed in a 0.35εm X-FAB high voltage process.

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http://dx.doi.org/10.1109/EMBC.2013.6609630 | DOI Listing |

June 2014

J Math Biol 2014 Mar 15;68(4):851-77. Epub 2013 Feb 15.

Mathematical Biosciences Institute, Ohio State University, Columbus, OH, 43210, USA,

We consider a two-species competition model in which the species have the same population dynamics but different dispersal strategies. Both species disperse by a combination of random diffusion and advection along environmental gradients, with the same random dispersal rates but different advection coefficients. Regarding these advection coefficients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we find that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be three or more evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of conditional dispersal of organisms depends upon the spatial heterogeneity of the environment in a subtle way.

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http://dx.doi.org/10.1007/s00285-013-0650-1 | DOI Listing |

March 2014

J Biol Dyn 2012 24;6:117-30. Epub 2011 Jun 24.

Department of Mathematics, Ohio State University, Columbus, OH 43210, USA.

We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17-36 [ 9 ]] concerning the dynamics of a diffusion-advection-competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [ 9 ]. It was shown in [ 9 ] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [ 9 ] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [ 9 ], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.

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http://dx.doi.org/10.1080/17513758.2010.529169 | DOI Listing |

December 2012

Proc Biol Sci 2012 Aug 2;279(1741):3209-16. Epub 2012 May 2.

Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA.

In many non-monogamous systems, males invest less in progeny than do females. This leaves males with higher potential rates of reproduction, and a likelihood of sexual conflict, including, in some systems, coercive matings. If coercive matings are costly, the best female strategy may be to avoid male interaction. We present a model that demonstrates female movement in response to male harassment as a mechanism to lower the costs associated with male coercion, and the effect that female movement has on selection in males for male harassment. We found that, when females can move from a habitat patch to a refuge to which males do not have access, there may be a selection for either high, or low harassment male phenotype, or both, depending on the relationship between the harassment level of male types in the population and a threshold level of male harassment. This threshold harassment level depends on the relative number of males and females in the population, and the relative resource values of the habitat; the threshold increases as the sex ratio favours females, and decreases with the value of the refuge patch or total population. Our model predicts that selection will favour the harassment level that lies closest to this threshold level of harassment, and differing harassment levels will coexist within the population only if they lie on the opposite sides of the threshold harassment. Our model is consistent with empirical results suggesting that an intermediate harassment level provides maximum reproductive fitness to males when females are mobile.

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http://dx.doi.org/10.1098/rspb.2012.0246 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3385715 | PMC |

August 2012

J Math Biol 2012 Nov 3;65(5):943-65. Epub 2011 Nov 3.

Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA.

A central question in the study of the evolution of dispersal is what kind of dispersal strategies are evolutionarily stable. Hastings (Theor Pop Biol 24:244-251, 1983) showed that among unconditional dispersal strategies in a spatially heterogeneous but temporally constant environment, the dispersal strategy with no movement is convergent stable. McPeek and Holt's (Am Nat 140:1010-1027, 1992) work suggested that among conditional dispersal strategies in a spatially heterogeneous but temporally constant environment, an ideal free dispersal strategy, which results in the ideal free distribution for a single species at equilibrium, is evolutionarily stable. We use continuous-time and discrete-space models to determine when the dispersal strategy with no movement is evolutionarily stable and when an ideal free dispersal strategy is evolutionarily stable, both in a spatially heterogeneous but temporally constant environment.

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http://dx.doi.org/10.1007/s00285-011-0486-5 | DOI Listing |

November 2012

Am Nat 2011 Jul;178(1):15-29

U.S. Geological Survey, Department of Biology, University of Miami, Coral Gables, Florida USA, 33124.

A key assumption of the ideal free distribution (IFD) is that there are no costs in moving between habitat patches. However, because many populations exhibit more or less continuous population movement between patches and traveling cost is a frequent factor, it is important to determine the effects of costs on expected population movement patterns and spatial distributions. We consider a food chain (tritrophic or bitrophic) in which one species moves between patches, with energy cost or mortality risk in movement. In the two-patch case, assuming forced movement in one direction, an evolutionarily stable strategy requires bidirectional movement, even if costs during movement are high. In the N-patch case, assuming that at least one patch is linked bidirectionally to all other patches, optimal movement rates can lead to source-sink dynamics where patches with negative growth rates are maintained by other patches with positive growth rates. As well, dispersal between patches is not balanced (even in the two-patch case), leading to a deviation from the IFD. Our results indicate that cost-associated forced movement can have important consequences for spatial metapopulation dynamics. Relevance to marine reserve design and the study of stream communities subject to drift is discussed.

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http://dx.doi.org/10.1086/660280 | DOI Listing |

July 2011

Bull Math Biol 2012 Feb 10;74(2):257-99. Epub 2011 May 10.

Mathematical Bioscience Institute, Ohio State University, Columbus, OH 43210, USA.

We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For nonmonotone resource functions, our findings suggest that there may exist some dispersal strategies which are not ideal free, but could be locally evolutionarily stable and/or convergent stable, and allow for the coexistence of more than one species.

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http://dx.doi.org/10.1007/s11538-011-9662-4 | DOI Listing |

February 2012

Biol Trace Elem Res 2011 Sep 3;142(3):693-703. Epub 2010 Aug 3.

Burns Institute, The First Affiliated Hospital, Nanchang University, Nanchang, China.

Lanthanide ions have been proven to have various biologic effects. Lanthanum with extremely active physical and chemical property was evidenced to possess antibacterial and immune adjustment effects. In the present study, the anti-inflammatory effects of lanthanum chloride (LaCl(3)) on lipopolysaccharide (LPS)-challenged mice were examined in vivo and in vitro. The results indicated that LaCl(3) can greatly decrease the secretion of tumor necrosis factor alpha (TNF-α) and interleukin (IL)-1β as well as TNF-α mRNA expression in the mice challenged with LPS. To clarify the mechanism involved, the effects of LaCl(3) on the activation of nuclear factor (NF)-κB were examined both in liver and in peritoneal macrophages. The LPS-induced activation of NF-κB was significantly blocked by LaCl(3). These findings demonstrate that the inhibition of the LPS-induced inflammatory media, such as TNF-α and IL-1β, by LaCl(3), is due to the inhibition of NF-κ B activation.

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http://dx.doi.org/10.1007/s12011-010-8792-0 | DOI Listing |

September 2011

Math Biosci Eng 2010 Jan;7(1):17-36

Department of Mathematics, University of Miami, P. O . Box 249085, Coral Gables, FL 33124-4250, United States.

A general question in the study of the evolution of dispersal is what kind of dispersal strategies can convey competitive advantages and thus will evolve. We consider a two species competition model in which the species are assumed to have the same population dynamics but different dispersal strategies. Both species disperse by random diffusion and advection along certain gradients, with the same random dispersal rates but different advection coefficients. We found a conditional dispersal strategy which results in the ideal free distribution of species, and show that it is a local evolutionarily stable strategy. We further show that this strategy is also a global convergent stable strategy under suitable assumptions, and our results illustrate how the evolution of conditional dispersal can lead to an ideal free distribution. The underlying biological reason is that the species with this particular dispersal strategy can perfectly match the environmental resource, which leads to its fitness being equilibrated across the habitats.

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http://dx.doi.org/10.3934/mbe.2010.7.17 | DOI Listing |

January 2010

J Biol Dyn 2009 Jul;3(4):410-29

Department of Mathematics, Ohio State University, Columbus, OH, USA.

This article is concerned with the evolution of certain types of density-dependent dispersal strategy in the context of two competing species with identical population dynamics and same random dispersal rates. Such density-dependent movement, often referred to as cross-diffusion and self-diffusion, assumes that the movement rate of each species depends on the density of both species and that the transition probability from one place to its neighbourhood depends solely on the arrival spot (independent of the departure spot). Our results suggest that for a one-dimensional homogeneous habitat, if the gradients of two cross- and self-diffusion coefficients have the same direction, the species with the smaller gradient will win, i.e. the dispersal strategy with the smaller gradient of cross- and self-diffusion coefficient will evolve. In particular, it suggests that the species with constant cross- and self-diffusion coefficients may have competitive advantage over species with non-constant cross- and self-diffusion coefficients. However, if the two gradients have opposite directions, neither of the two dispersal strategies wins as these two species can coexist.

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http://dx.doi.org/10.1080/17513750802491849 | DOI Listing |

July 2009

J Theor Biol 2009 Jan 9;256(2):187-200. Epub 2008 Oct 9.

Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA.

We synthesize previous theory on ideal free habitat selection to develop a model of predator movement mechanisms, when both predators and prey are mobile. We consider a continuous environment with an arbitrary distribution of resources, randomly diffusing prey that consume the resources, and predators that consume the prey. Our model introduces a very general class of movement rules in which the overall direction of a predator's movement is determined by a variable combination of (i) random diffusion, (ii) movement in the direction of higher prey density, and/or (iii) movement in the direction of higher density of the prey's resource. With this model, we apply an adaptive dynamics approach to two main questions. First, can it be adaptive for predators to base their movement solely on the density of the prey's resource (which the predators do not consume)? Second, should predator movements be exclusively biased toward higher densities of prey/resources, or is there an optimal balance between random and biased movements? We find that, for some resource distributions, predators that track the gradient of the prey's resource have an advantage compared to predators that track the gradient of prey directly. Additionally, we show that matching (consumers distributed in proportion to resources), overmatching (consumers strongly aggregated in areas of high resource density), and undermatching (consumers distributed more uniformly than resources) distributions can all be explained by the same general habitat selection mechanism. Our results provide important groundwork for future investigations of predator-prey dynamics.

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http://dx.doi.org/10.1016/j.jtbi.2008.09.024 | DOI Listing |

January 2009

Math Biosci Eng 2008 Apr;5(2):315-35

Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, USA.

This paper is concerned with an indefinite weight linear eigenvalue problem in cylindrical domains. We investigate the minimization of the positive principal eigenvalue under the constraint that the weight is bounded by a positive and a negative constant and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. Both our analysis and numerical simulations for rectangular domains indicate that there exists a threshold value such that if the total weight is below this threshold value, then the optimal favorable region is a circular-type domain at one of the four corners, and a strip at the one end with shorter edge otherwise.

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http://dx.doi.org/10.3934/mbe.2008.5.315 | DOI Listing |

April 2008

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