Pub Date : 2015-01-01DOI: 10.1080/23737867.2015.1035571
Jonathan T. Rowell, J. Rychtář
The US National Science Foundation has promoted the early integration of undergraduate students into academic research environments by funding activities such as the Research Experiences for Undergraduates (REU) programs. Here, we discuss the operation of the first year for one REU site held on the campus of the University of North Carolina at Greensboro. Eight students from across the country were brought together for a 10-week summer programme in mathematical biology to work on research topics related to the establishment of cooperative behaviour. The students were paired in four teams, which approached the dynamic tension between cooperation and defection from a variety of mathematical and contextual perspectives. Two projects employed agent-based models on lattice environments: the first consisting of sparse populations of mobile individuals and the second featuring age-structured populations, history-dependent fitness, and the possibility of kinship recognition. A third project looked at the evolutionary dynamics of behavioural frequencies in a model of society comprised of three social strata. The final project focused on the ecological range distribution of non-cooperative, cooperative and kleptoparasitic populations in heterogeneous resource environments. We describe both the general results of the students’ research efforts and our observations on the efficacy of several enrichment activities provided to the students over the course of the REU summer.
{"title":"Cooperative behaviour in theory and practice: leading undergraduate research in behaviour mathematical biology","authors":"Jonathan T. Rowell, J. Rychtář","doi":"10.1080/23737867.2015.1035571","DOIUrl":"https://doi.org/10.1080/23737867.2015.1035571","url":null,"abstract":"The US National Science Foundation has promoted the early integration of undergraduate students into academic research environments by funding activities such as the Research Experiences for Undergraduates (REU) programs. Here, we discuss the operation of the first year for one REU site held on the campus of the University of North Carolina at Greensboro. Eight students from across the country were brought together for a 10-week summer programme in mathematical biology to work on research topics related to the establishment of cooperative behaviour. The students were paired in four teams, which approached the dynamic tension between cooperation and defection from a variety of mathematical and contextual perspectives. Two projects employed agent-based models on lattice environments: the first consisting of sparse populations of mobile individuals and the second featuring age-structured populations, history-dependent fitness, and the possibility of kinship recognition. A third project looked at the evolutionary dynamics of behavioural frequencies in a model of society comprised of three social strata. The final project focused on the ecological range distribution of non-cooperative, cooperative and kleptoparasitic populations in heterogeneous resource environments. We describe both the general results of the students’ research efforts and our observations on the efficacy of several enrichment activities provided to the students over the course of the REU summer.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"2 1","pages":"29 - 45"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2015.1035571","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1080/23737867.2015.1049969
S. Donovan, C. Eaton, S. Gower, P. Kristin, Jenkins, M. D. LaMar, DorothyBelle Poli, R. R. Sheehy, J. Wojdak
This letter provides an overview of the Quantitative Undergraduate Biology Education and Synthesis (QUBES) Project funded through the National Science Foundation. The project has five distinct, but interdependent, initiatives which work together to support faculty and students in the teaching and learning of quantitative biology (QB). QUBES has adopted an integrated strategy to improving the frequency and effectiveness of QB instruction that includes coordinating a broad consortium of professional stakeholders, supporting faculty development and the implementation of new teaching practices, providing an infrastructure for collaboration and access to high quality materials, establishing new metrics for faculty teaching scholarship and documenting the project outcomes.
{"title":"QUBES: a community focused on supporting teaching and learning in quantitative biology","authors":"S. Donovan, C. Eaton, S. Gower, P. Kristin, Jenkins, M. D. LaMar, DorothyBelle Poli, R. R. Sheehy, J. Wojdak","doi":"10.1080/23737867.2015.1049969","DOIUrl":"https://doi.org/10.1080/23737867.2015.1049969","url":null,"abstract":"This letter provides an overview of the Quantitative Undergraduate Biology Education and Synthesis (QUBES) Project funded through the National Science Foundation. The project has five distinct, but interdependent, initiatives which work together to support faculty and students in the teaching and learning of quantitative biology (QB). QUBES has adopted an integrated strategy to improving the frequency and effectiveness of QB instruction that includes coordinating a broad consortium of professional stakeholders, supporting faculty development and the implementation of new teaching practices, providing an infrastructure for collaboration and access to high quality materials, establishing new metrics for faculty teaching scholarship and documenting the project outcomes.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"2 1","pages":"46 - 55"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2015.1049969","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60102060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1080/23737867.2015.1111777
K. Crawford, A. Lancaster, Hyunju Oh, J. Rychtář
African sleeping sickness is a vector-borne disease caused by the parasite Trypanosoma brucei. It is transmitted by tsetse flies and one of the most effective strategies to combat the disease is the use of insecticide-treated cattle (ITC). In this paper, we present a game-theoretical model, in which individual farmers choose their own level of ITC in order to maximize their own benefits, effectively balancing the cost of ITC and the risk of their cows contracting the disease. We find that even when the usage of ITC is strictly voluntary, the optimal ITC usage will eliminate the disease when the cost of ITC is not prohibitively large. This is in a sharp contrast with similar scenarios of vaccination games where a voluntary vaccination never eliminates a disease entirely.
{"title":"A voluntary use of insecticide-treated cattle can eliminate African sleeping sickness","authors":"K. Crawford, A. Lancaster, Hyunju Oh, J. Rychtář","doi":"10.1080/23737867.2015.1111777","DOIUrl":"https://doi.org/10.1080/23737867.2015.1111777","url":null,"abstract":"African sleeping sickness is a vector-borne disease caused by the parasite Trypanosoma brucei. It is transmitted by tsetse flies and one of the most effective strategies to combat the disease is the use of insecticide-treated cattle (ITC). In this paper, we present a game-theoretical model, in which individual farmers choose their own level of ITC in order to maximize their own benefits, effectively balancing the cost of ITC and the risk of their cows contracting the disease. We find that even when the usage of ITC is strictly voluntary, the optimal ITC usage will eliminate the disease when the cost of ITC is not prohibitively large. This is in a sharp contrast with similar scenarios of vaccination games where a voluntary vaccination never eliminates a disease entirely.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"73 1","pages":"101 - 91"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2015.1111777","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60102127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1080/23737867.2015.1048316
M. De Silva, S. Jang
We propose a Lotka–Volterra competition model of two populations where one population is subject to Allee effects and is also under stocking to investigate competition outcomes. The resulting model is analysed by studying its global asymptotic dynamics. In some cases, the endangered population can drive the other population to extinction, while in other cases, the endangered population cannot survive. Coexistence of both competing populations is possible in some parameter regimes. It is concluded that considerable care must be taken before implanting the population that is subject to Allee effects.
{"title":"Competitive exclusion and coexistence in a Lotka–Volterra competition model with Allee effects and stocking","authors":"M. De Silva, S. Jang","doi":"10.1080/23737867.2015.1048316","DOIUrl":"https://doi.org/10.1080/23737867.2015.1048316","url":null,"abstract":"We propose a Lotka–Volterra competition model of two populations where one population is subject to Allee effects and is also under stocking to investigate competition outcomes. The resulting model is analysed by studying its global asymptotic dynamics. In some cases, the endangered population can drive the other population to extinction, while in other cases, the endangered population cannot survive. Coexistence of both competing populations is possible in some parameter regimes. It is concluded that considerable care must be taken before implanting the population that is subject to Allee effects.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"2 1","pages":"56 - 66"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2015.1048316","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-01-01DOI: 10.1080/23737867.2014.11414465
E. Board
Abstract Here the editorial board provides additional information about Letters in Biomathematics and outlines benefits of publishing in the journal.
在这里，编辑委员会提供了关于《生物数学快报》的额外信息，并概述了在该期刊上发表的好处。
{"title":"Why Publish in Letters in Biomathematics","authors":"E. Board","doi":"10.1080/23737867.2014.11414465","DOIUrl":"https://doi.org/10.1080/23737867.2014.11414465","url":null,"abstract":"Abstract Here the editorial board provides additional information about Letters in Biomathematics and outlines benefits of publishing in the journal.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"1 1","pages":"1 - 1"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2014.11414465","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-01-01DOI: 10.1080/23737867.2014.11414471
Liang Sun
Abstract A diffusion equation can be used to estimate the oxygen concentration profiles for a highly-regular capillary bed of skeletal muscle. In reality, the capillaries may be arranged more or less randomly in normal tissues. The oxygen concentration, along with its time-wise distribution, may be uneven. Heterogeneity in the tissue bed is much more commonly considered. This article presents a mathematical analysis of the capillary-tissue exchange of substrate in microcirculation in rectangular regions where multiple capillaries are embedded with arbitrary characteristics. A matching technique is used to help solve the associated governing equations.
{"title":"Substrate Diffusion and Consumption in Rectangular Capillary-Tissue Bed","authors":"Liang Sun","doi":"10.1080/23737867.2014.11414471","DOIUrl":"https://doi.org/10.1080/23737867.2014.11414471","url":null,"abstract":"Abstract A diffusion equation can be used to estimate the oxygen concentration profiles for a highly-regular capillary bed of skeletal muscle. In reality, the capillaries may be arranged more or less randomly in normal tissues. The oxygen concentration, along with its time-wise distribution, may be uneven. Heterogeneity in the tissue bed is much more commonly considered. This article presents a mathematical analysis of the capillary-tissue exchange of substrate in microcirculation in rectangular regions where multiple capillaries are embedded with arbitrary characteristics. A matching technique is used to help solve the associated governing equations.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"1 1","pages":"67 - 76"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2014.11414471","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-01-01DOI: 10.1080/23737867.2014.11414477
R. Erickson, W. Thogmartin, R. Russell, J. Diffendorfer, Jennifer A. Szymanski
Abstract Bats are ecologically and economically important species because they consume insects, transport nutrients, and pollinate flowers. Many species of bats, including those in the Myotis genus, are facing population decline and increased extinction risk. Despite these conservation concerns, few models exist for providing insight into the population dynamics of bats in a spatially explicit context. We developed a model for bats by considering the stage-structured colonial life history of Myotis bats with their annual migration behavior. This model provided insight into network dynamics. We specifically focused on two Myotis species living in the eastern United States: the Indiana bat (M. sodalis), which is a Federally listed endangered species, and the little brown bat (M. lucifugus), which is under consideration for listing as an endangered species. We found that multiple equilibria exist for the local, migratory subpopulations even though the total population was constant. These equilibria suggest the location and magnitude of stressors such as White-nose Syndrome, meteorological phenomena, or impacts of wind turbines on survival influence system dynamics and risk of population extirpation in difficult to predict ways.
{"title":"A Stage-Structured, Spatially Explicit Migration Model for Myotis Bats: Mortality location affects system dynamics","authors":"R. Erickson, W. Thogmartin, R. Russell, J. Diffendorfer, Jennifer A. Szymanski","doi":"10.1080/23737867.2014.11414477","DOIUrl":"https://doi.org/10.1080/23737867.2014.11414477","url":null,"abstract":"Abstract Bats are ecologically and economically important species because they consume insects, transport nutrients, and pollinate flowers. Many species of bats, including those in the Myotis genus, are facing population decline and increased extinction risk. Despite these conservation concerns, few models exist for providing insight into the population dynamics of bats in a spatially explicit context. We developed a model for bats by considering the stage-structured colonial life history of Myotis bats with their annual migration behavior. This model provided insight into network dynamics. We specifically focused on two Myotis species living in the eastern United States: the Indiana bat (M. sodalis), which is a Federally listed endangered species, and the little brown bat (M. lucifugus), which is under consideration for listing as an endangered species. We found that multiple equilibria exist for the local, migratory subpopulations even though the total population was constant. These equilibria suggest the location and magnitude of stressors such as White-nose Syndrome, meteorological phenomena, or impacts of wind turbines on survival influence system dynamics and risk of population extirpation in difficult to predict ways.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"1 1","pages":"157 - 172"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2014.11414477","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-01-01DOI: 10.1080/23737867.2014.11414469
M. Yahdi, C. Sulyok, Karissa Smith, Alison Bugenis
Abstract The paper provides a mathematical framework for cost-effective and environmentally safe strategies to minimize alfalfa damage from pests in alfalfa agroecosystems with optimal biodiversity levels and to predict outcomes for scenarios not covered by field experiments. Alfalfa is the most important forage legume world-wide and is a valuable source of nutrition for farm animals. The potato leafhopper (PLH) pest damages the alfalfa plant leading to a reduction of the productivity, a loss in nutritional value, and a decrease in milk production. The PLH pest outbreaks are also prone in monocultures. New mathematical models are shown to accurately fit results from field experiments utilizing plant diversity and enemies (pest-predator) hypotheses. The focus is on polyculture as a farming technique and the damsel bug, Nabis, a natural predator of the PLH. Mathematical methods include the Shannon diversity index, differential equations, scramble competition approaches, and sensitivity analysis to determine critical parameters.
{"title":"Modeling and Sensitivity Analysis of the Role of Biodiversity to Control Pest Damage in Agroecosystems","authors":"M. Yahdi, C. Sulyok, Karissa Smith, Alison Bugenis","doi":"10.1080/23737867.2014.11414469","DOIUrl":"https://doi.org/10.1080/23737867.2014.11414469","url":null,"abstract":"Abstract The paper provides a mathematical framework for cost-effective and environmentally safe strategies to minimize alfalfa damage from pests in alfalfa agroecosystems with optimal biodiversity levels and to predict outcomes for scenarios not covered by field experiments. Alfalfa is the most important forage legume world-wide and is a valuable source of nutrition for farm animals. The potato leafhopper (PLH) pest damages the alfalfa plant leading to a reduction of the productivity, a loss in nutritional value, and a decrease in milk production. The PLH pest outbreaks are also prone in monocultures. New mathematical models are shown to accurately fit results from field experiments utilizing plant diversity and enemies (pest-predator) hypotheses. The focus is on polyculture as a farming technique and the damsel bug, Nabis, a natural predator of the PLH. Mathematical methods include the Shannon diversity index, differential equations, scramble competition approaches, and sensitivity analysis to determine critical parameters.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"1 1","pages":"41 - 50"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2014.11414469","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-01-01DOI: 10.1080/23737867.2014.11414470
Timothy D. Comar, M. Hegazy, M. Henderson, Daniel Hrozencik
Abstract We investigate the dynamics of three-gene regulatory networks with one feedback circuit using the Boolean and continuous models put forth by Gehrmann and Drossel [4]. We establish the existence of Hopf bifurcations in the continuous models and use these bifurcations to compare the models more closely. With this analysis we are able to establish the regions in the parameter space where the dynamical behavior of the models agree and where they disagree.
{"title":"A Comparison of the Boolean and Continuous Dynamics of Three-Gene Regulatory Networks","authors":"Timothy D. Comar, M. Hegazy, M. Henderson, Daniel Hrozencik","doi":"10.1080/23737867.2014.11414470","DOIUrl":"https://doi.org/10.1080/23737867.2014.11414470","url":null,"abstract":"Abstract We investigate the dynamics of three-gene regulatory networks with one feedback circuit using the Boolean and continuous models put forth by Gehrmann and Drossel [4]. We establish the existence of Hopf bifurcations in the continuous models and use these bifurcations to compare the models more closely. With this analysis we are able to establish the regions in the parameter space where the dynamical behavior of the models agree and where they disagree.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"1 1","pages":"51 - 65"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2014.11414470","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-01-01DOI: 10.1080/23737867.2014.11432419
Olcay Akman, Dan Cairns, Timothy D. Comar, Daniel Hrozencik
Abstract X. Song and Z. Xiang [7] develop an impulsive differential equations model for a two-prey, one-predator model with stage structure for the predator. They demon-strate the conditions on the impulsive period for which a globally asymptotically stable pest-eradication periodic solution exists, as well as conditions on the im-pulsive period for which the prey species is permanently maintained under an economically acceptable threshold. We extend their model by including stage structure for both predator and prey and also by adding stochastic elements in the birth rate of the prey. As in [7], we find the conditions under which a globally asymptotically stable pest-eradication periodic solution exists.
{"title":"Integrated Pest Management with a Mixed Birth Rate for Prey Species","authors":"Olcay Akman, Dan Cairns, Timothy D. Comar, Daniel Hrozencik","doi":"10.1080/23737867.2014.11432419","DOIUrl":"https://doi.org/10.1080/23737867.2014.11432419","url":null,"abstract":"Abstract X. Song and Z. Xiang [7] develop an impulsive differential equations model for a two-prey, one-predator model with stage structure for the predator. They demon-strate the conditions on the impulsive period for which a globally asymptotically stable pest-eradication periodic solution exists, as well as conditions on the im-pulsive period for which the prey species is permanently maintained under an economically acceptable threshold. We extend their model by including stage structure for both predator and prey and also by adding stochastic elements in the birth rate of the prey. As in [7], we find the conditions under which a globally asymptotically stable pest-eradication periodic solution exists.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"1 1","pages":"87 - 95"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2014.11432419","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60101417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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