PeerJ Preprints: Mathematical Biologyhttps://peerj.com/preprints/index.atom?journal=peerj&subject=1900Mathematical Biology articles published in PeerJ PreprintsDiscrete stochastic marine metapopulation disease modelhttps://peerj.com/preprints/264542019-11-282019-11-28Gorka BidegainTal Ben-Horin
Some marine microparasitic pathogens can survive several months in the water column to make contact with or to be absorbed or filtered by hosts. Once inside, pathogens invade the host if they find suitable conditions for reproduction. This transmission from the environment occurs via pathogens released from infected and dead infected animals. Some recent modeling studies concentrated on the disease dynamic imposed by this complex interaction between population and water column at the host-pathogen level in single populations. However, only when a marine disease can be understood at the metapopulation scale effective approaches to management will become routinely achievable. The discrete-time disease model in this paper investigates both spatial and temporal dynamics of hosts and waterborne pathogens in a metapopulation system of three patches. This system with a patch providing infective particles and susceptible and infected individuals by dispersal tries to imitate the effect of current forces in the ocean on the passive dispersal of organisms. The model detects behaviours that are not present in single population continuous-time and deterministic models.
Some marine microparasitic pathogens can survive several months in the water column to make contact with or to be absorbed or filtered by hosts. Once inside, pathogens invade the host if they find suitable conditions for reproduction. This transmission from the environment occurs via pathogens released from infected and dead infected animals. Some recent modeling studies concentrated on the disease dynamic imposed by this complex interaction between population and water column at the host-pathogen level in single populations. However, only when a marine disease can be understood at the metapopulation scale effective approaches to management will become routinely achievable. The discrete-time disease model in this paper investigates both spatial and temporal dynamics of hosts and waterborne pathogens in a metapopulation system of three patches. This system with a patch providing infective particles and susceptible and infected individuals by dispersal tries to imitate the effect of current forces in the ocean on the passive dispersal of organisms. The model detects behaviours that are not present in single population continuous-time and deterministic models.Seasonality in ecology: Progress and prospects in theoryhttps://peerj.com/preprints/272352019-10-112019-10-11Easton R WhiteAlan Hastings
Seasonality is an important feature of essentially all natural systems but the consequences of seasonality have been vastly underappreciated. Early work emphasized the role of seasonality in driving cyclic population dynamics, but the consequences of seasonality for ecological processes are far broader. Yet, seasonality is often not explicitly included in either empirical or theoretical studies. Many aspects of ecological dynamics can only be understood when seasonality is included, ranging from the oscillations in the incidence of childhood diseases to the coexistence of species. Through several case studies, we outline what is now known about seasonality in an ecological context and set the stage for future efforts. We discuss approaches for incorporating seasonality in mathematical models, including Floquet theory. We argue, however, that these tools are still limited in scope and more approaches need to be developed.
Seasonality is an important feature of essentially all natural systems but the consequences of seasonality have been vastly underappreciated. Early work emphasized the role of seasonality in driving cyclic population dynamics, but the consequences of seasonality for ecological processes are far broader. Yet, seasonality is often not explicitly included in either empirical or theoretical studies. Many aspects of ecological dynamics can only be understood when seasonality is included, ranging from the oscillations in the incidence of childhood diseases to the coexistence of species. Through several case studies, we outline what is now known about seasonality in an ecological context and set the stage for future efforts. We discuss approaches for incorporating seasonality in mathematical models, including Floquet theory. We argue, however, that these tools are still limited in scope and more approaches need to be developed.ImageJ and 3D Slicer: open source 2/3D morphometric softwarehttps://peerj.com/preprints/279982019-10-022019-10-02Fiona PyeNussaȉbah B RajaBryan ShirleyÁdám T KocsisNiklas HohmannDuncan J E MurdockEmilia Jarochowska
In a world where an increasing number of resources are hidden behind paywalls and monthly subscriptions, it is becoming crucial for the scientific community to invest energy into freely available, community-maintained systems. Open-source software projects offer a solution, with freely available code which users can utilise and modify, under an open source licence. In addition to software accessibility and methodological repeatability, this also enables and encourages the development of new tools.
As palaeontology moves towards data driven methodologies, it is becoming more important to acquire and provide high quality data through reproducible systematic procedures. Within the field of morphometrics, it is vital to adopt digital methods that help mitigate human bias from data collection. In addition, mathematically founded approaches can reduce subjective decisions which plague classical data. This can be further developed through automation, which increases the efficiency of data collection and analysis.
With these concepts in mind, we introduce two open-source shape analysis software, that arose from projects within the medical imaging field. These are ImageJ, an image processing program with batch processing features, and 3D Slicer which focuses on 3D informatics and visualisation. They are easily extensible using common programming languages, with 3D Slicer containing an internal python interactor, and ImageJ allowing the incorporation of several programming languages within its interface alongside its own simplified macro language. Additional features created by other users are readily available, on GitHub or through the software itself.
In the examples presented, an ImageJ plugin “FossilJ” has been developed which provides semi-automated morphometric bivalve data collection. 3D Slicer is used with the extension SPHARM-PDM, applied to synchrotron scans of coniform conodonts for comparative morphometrics, for which small assistant tools have been created in Python.
In a world where an increasing number of resources are hidden behind paywalls and monthly subscriptions, it is becoming crucial for the scientific community to invest energy into freely available, community-maintained systems. Open-source software projects offer a solution, with freely available code which users can utilise and modify, under an open source licence. In addition to software accessibility and methodological repeatability, this also enables and encourages the development of new tools.As palaeontology moves towards data driven methodologies, it is becoming more important to acquire and provide high quality data through reproducible systematic procedures. Within the field of morphometrics, it is vital to adopt digital methods that help mitigate human bias from data collection. In addition, mathematically founded approaches can reduce subjective decisions which plague classical data. This can be further developed through automation, which increases the efficiency of data collection and analysis.With these concepts in mind, we introduce two open-source shape analysis software, that arose from projects within the medical imaging field. These are ImageJ, an image processing program with batch processing features, and 3D Slicer which focuses on 3D informatics and visualisation. They are easily extensible using common programming languages, with 3D Slicer containing an internal python interactor, and ImageJ allowing the incorporation of several programming languages within its interface alongside its own simplified macro language. Additional features created by other users are readily available, on GitHub or through the software itself.In the examples presented, an ImageJ plugin “FossilJ” has been developed which provides semi-automated morphometric bivalve data collection. 3D Slicer is used with the extension SPHARM-PDM, applied to synchrotron scans of coniform conodonts for comparative morphometrics, for which small assistant tools have been created in Python.Human influence on predator-prey relationship: Red Panda and Snow Leopardhttps://peerj.com/preprints/278962019-08-132019-08-13Jagat Kafle
This paper is a mathematical model based upon the human influence on the predator-prey relationship between Red Panda and Snow Leopard, which are the major species in the mountain ecosystem. It explores if these species get extinct in a certain area due to imbalance in their interaction. First, simple model of the species is discussed with no interaction between the species. Interactive model is then introduced to simulate their population when they interact with each other. The human influence is then introduced to the interactive model to observe if the species get extinct. The data in this paper are approximated for a certain area based upon the population density and habitat of the two species. All the models are simulated in python programs using Euler's method.
This paper is a mathematical model based upon the human influence on the predator-prey relationship between Red Panda and Snow Leopard, which are the major species in the mountain ecosystem. It explores if these species get extinct in a certain area due to imbalance in their interaction. First, simple model of the species is discussed with no interaction between the species. Interactive model is then introduced to simulate their population when they interact with each other. The human influence is then introduced to the interactive model to observe if the species get extinct. The data in this paper are approximated for a certain area based upon the population density and habitat of the two species. All the models are simulated in python programs using Euler's method.Interdisciplinary summer bridge programs to improve student outcomeshttps://peerj.com/preprints/278162019-06-232019-06-23Easton R White
The Biology Undergraduate Scholars Program (BUSP) at UC Davis provides additional academic support and advising for a small (<40 students) cohort in the biological sciences each year. Students come from historically underrepresented racial or ethnic groups, the educational opportunity program, or have a disability. As part of the program, students participate in a two-week biology bridge program to prepare them for introductory ecology and evolution. The bridge program involves active learning assignments and team-based learning with a focus on the connection between biology and mathematics. We found that BUSP participants improved their biology knowledge through the summer bridge program. However, math confidence, SAT scores, Grit measures, and performance in the bridge program were not predictive of success in their biology course. We also found that BUSP students were more likely to remain in Life Science major and graduate.
The Biology Undergraduate Scholars Program (BUSP) at UC Davis provides additional academic support and advising for a small (<40 students) cohort in the biological sciences each year. Students come from historically underrepresented racial or ethnic groups, the educational opportunity program, or have a disability. As part of the program, students participate in a two-week biology bridge program to prepare them for introductory ecology and evolution. The bridge program involves active learning assignments and team-based learning with a focus on the connection between biology and mathematics. We found that BUSP participants improved their biology knowledge through the summer bridge program. However, math confidence, SAT scores, Grit measures, and performance in the bridge program were not predictive of success in their biology course. We also found that BUSP students were more likely to remain in Life Science major and graduate.Ecosystem antifragility: Beyond integrity and resiliencehttps://peerj.com/preprints/278132019-06-212019-06-21Miguel Equihua ZamoraMariana EspinosaCarlos GershensonOliver López-CoronaMariana MunguiaOctavio Pérez-MaqueoElvia Ramírez-Carrillo
We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.
We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.The geometric formulas of the Lewis’s law and Aboav-Weaire’s law in two dimensions based on ellipse packinghttps://peerj.com/preprints/277972019-06-182019-06-18Kai Xu
The two-dimensional (2D) Lewis’s law and Aboav-Weaire’s law are two simple formulas derived from empirical observations. Numerous attempts have been made to improve the empirical formulas. In this study, we simulated a series of Voronoi diagrams by randomly disordered the seed locations of a regular hexagonal 2D Voronoi diagram, and analyzed the cell topology based on ellipse packing. Then, we derived and verified the improved formulas for Lewis’s law and Aboav-Weaire’s law. Specifically, we found that the upper limit of the second moment of edge number is 3. In addition, we derived the geometric formula of the von Neumann-Mullins’s law based on the new formula of the Aboav-Weaire’s law. Our results suggested that the cell area, local neighbor relationship, and cell growth rate are closely linked to each other, and mainly shaped by the effect of deformation from circle to ellipse and less influenced by the global edge distribution.
The two-dimensional (2D) Lewis’s law and Aboav-Weaire’s law are two simple formulas derived from empirical observations. Numerous attempts have been made to improve the empirical formulas. In this study, we simulated a series of Voronoi diagrams by randomly disordered the seed locations of a regular hexagonal 2D Voronoi diagram, and analyzed the cell topology based on ellipse packing.Then, we derived and verified the improved formulas for Lewis’s law and Aboav-Weaire’s law. Specifically, we found that the upper limit of the second moment of edge number is 3. In addition, we derived the geometric formula of the von Neumann-Mullins’s law based on the new formula of the Aboav-Weaire’s law. Our results suggested that the cell area, local neighbor relationship, and cell growth rate are closely linked to each other, and mainly shaped by the effect of deformation from circle to ellipse and less influenced by the global edge distribution.Ellipse packing in two-dimensional celltessellation: A theoretical explanation for Lewis’s law and Aboav-Weaire’s lawhttps://peerj.com/preprints/274212019-02-012019-02-01Kai Xu
Background: Lewis’s law and Aboav-Weaire’s law are two fundamental laws used to describe the topology of two-dimensional (2D) structures; however, their theoretical bases remain unclear.
Methods: We used R package Conicfit software to fit ellipses based on the geometric parameters of polygonal cells with ten different kinds of natural and artificial 2D structures.
Results: Our results indicated that the cells could be classified as ellipse’s inscribed polygon (EIP) and that they tended to form ellipse’s maximal inscribed polygon (EMIP). This phenomenon was named as ellipse packing. On the basis of the number of cell edges, cell area, and semi-axes of fitted ellipses, we derived and verified new relations of Lewis’s law and Aboav-Weaire’s law .
Conclusions: Ellipse packing is a short-range order that places restrictions on the cell topology and growth pattern. Lewis’s law and Aboav-Weaire’s law mainly reflect the effect of deformation from circle to ellipse on cell area and the edge number of neighboring cells, respectively. The results of this study could be used to simulate the dynamics of cell topology during growth.
Background: Lewis’s law and Aboav-Weaire’s law are two fundamental laws used to describe the topology of two-dimensional (2D) structures; however, theirtheoretical bases remain unclear. Methods: We used R package Conicfit software to fit ellipses based on the geometric parameters of polygonal cells with ten different kinds of natural and artificial 2D structures. Results: Our results indicated that the cells could be classified as ellipse’s inscribed polygon (EIP) and that they tended to form ellipse’s maximal inscribed polygon (EMIP). This phenomenon was named as ellipse packing. On the basis of the number of cell edges, cell area, and semi-axes of fitted ellipses, we derived and verified new relations of Lewis’s law and Aboav-Weaire’s law . Conclusions: Ellipse packing is a short-range order that places restrictions on the cell topology and growth pattern. Lewis’s law and Aboav-Weaire’s law mainly reflect the effect of deformation from circle to ellipse on cell area and the edge number of neighboring cells, respectively. The results of this study could be used to simulate the dynamics of cell topology during growth.Synergy between assortative mating and allopatry favor speciation in endemic Galapagos birdshttps://peerj.com/preprints/275122019-02-012019-02-01Klaus JaffeCarlos Bosque
Integrating new data with older reports on the behavior of small land-birds in the Galapagos archipelago reveal that geographic isolation of population together with behavioral segregation of populations produce a synergy that is more likely to produce speciation than any of those factors on its own. This result expands our understanding of assortative mating, based on computer experiments of biological evolution, showing that assortation favors speciation in both sympatric and allopatric populations.
Integrating new data with older reports on the behavior of small land-birds in the Galapagos archipelago reveal that geographic isolation of population together with behavioral segregation of populations produce a synergy that is more likely to produce speciation than any of those factors on its own. This result expands our understanding of assortative mating, based on computer experiments of biological evolution, showing that assortation favors speciation in both sympatric and allopatric populations.Multi-scale models and data for infectious diseases: A systematic reviewhttps://peerj.com/preprints/274852019-01-142019-01-14Lauren M ChildsFadoua El MoustaidZachary GajewskiSarah KadelkaRyan Nikin-BeersJohn W. Smith, Jr.Melody WalkerLeah R. Johnson
The observed dynamics of infectious diseases are driven by processes across multiple scales. First is within-host, that is how an infection progresses inside a single individual (for instance viral and immune dynamics). Second is how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a wholistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 19 of 139 qualifying papers across 30 years that include both linked models at the within and between host levels and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.
The observed dynamics of infectious diseases are driven by processes across multiple scales. First is within-host, that is how an infection progresses inside a single individual (for instance viral and immune dynamics). Second is how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a wholistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 19 of 139 qualifying papers across 30 years that include both linked models at the within and between host levels and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.