Fluctuations in the Abundance of a Species considered Mathematically

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WITH regard to Prof. Volterra's interesting article, “Fluctuations in the Abundance of a Species considered Mathematically,” in NATURE of October 16, page 558, I may be permitted to point to certain prior publications on the subject, of which Prof. Volterra seems to be unaware. The general theory as well as a number of special cases have been set forth in “Elements of Physical Biology” (published by Williams and Wilkins, Baltimore, 1925), in which work a considerable number of references to the journal literature are given. Among other things Prof. Volterra's diagram “Fig. 2” will be found on page go of the book cited; the expression for the period of isochronous small oscillations in the case of two species is also found on the same page. Prof. Volterra refers to certain applications of his analysis to problems of sea fisheries, to a passage in Darwin's “Origin of Species,” to extinction of species, to pathogenic germs, and to parasitology. An application to sea fisheries is found in the book cited on page 95; to a passage in Herbert Spencer on page 61; to the extinction of species on pages 94, 95; to pathogenic germs on pages 77, 79, 147 et seq.; to parasitology on page 83.

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  • Research Article
  • 10.3934/dcdsb.2025066
Pattern formation of a Beddington-DeAngelis predator-prey model with prey-taxis and nonlocal competition
  • Jan 1, 2025
  • Discrete and Continuous Dynamical Systems - B
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Pattern formation of a Beddington-DeAngelis predator-prey model with prey-taxis and nonlocal competition

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  • 10.3934/era.2023337
On the contribution of qualitative analysis in mathematical modeling of plasmid-mediated ceftiofur resistance
  • Jan 1, 2023
  • Electronic Research Archive
  • Eduardo Ibargüen-Mondragón + 2 more

<abstract><p>The acquisition of antibiotic resistance due to the consumption of food contaminated with resistant strains is a public health problem that has been increasing in the last decades. Mathematical modeling is contributing to the solution of this problem. In this article we performed the qualitative analysis of a mathematical model that explores the competition dynamics <italic>in vivo</italic> of ceftiofur-resistant and sensitive commensal enteric <italic>Escherichia coli</italic> (E. coli) in the absence and during parenteral ceftiofur therapy within the gut of cattle, considering the therapeutic effects (<italic>pharmacokinetics</italic> (PK)/<italic>pharmacodynamics</italic> (PD)) in the outcome of infection. Through this analysis, empirical properties obtained through <italic>in vivo</italic> experimentation were verified, and it also evidenced other properties of bacterial dynamics that had not been previously shown. In addition, the impact of PD and PK has been evaluated.</p></abstract>

  • Conference Article
  • Cite Count Icon 1
  • 10.1109/cec.2003.1299383
Critical biodiversity and connectivity
  • Dec 8, 2003
  • P.A Whigham

This article explores the concept of connectivity and biodiversity by using a simple model of an ecosystem. The model is different from standard artificial life systems since there is no attempt to solve a particular problem, nor is there competition between individuals that drives a coevolution and fitness. Fitness gradually increases throughout the simulation, and mutation rate varies based on population size. Additionally, the system is run with a low mutation rate aiming to produce steady-state behaviour. A simple niche structure at every site allows concepts such as keystone species to be defined, and allows an exploration of diversity and extinction. The article addresses two main issues with this model: does altering the connectivity of neighbourhoods affect the critical point and stability of an ecosystem, and are species-area relationships determined by connectivity?.

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  • 10.1007/978-3-030-01989-1_10
Population Dynamics in Space
  • Jan 1, 2018
  • Robert Fletcher + 1 more

Over the past several decades, the role of space in population dynamics and trends has been illuminated, and spatially structured population dynamics have been emphasized in conservation and management strategies. We use the term spatially structured population as a broad umbrella term for a population that includes some amount of spatial heterogeneity. This term captures many spatially focused concepts in population biology. Our general goal is to provide an overview of the role of space on populations, with an eye toward conservation-relevant issues. To do so, we first discuss some common frameworks for understanding and conserving spatially structured populations, including the metapopulation paradigm that focuses on colonization–extinction dynamics and the spatial demography (or landscape demography) paradigm that focuses on demographic vital rates. Both of these paradigms have provided major insights to ecology and conservation, including the concept of source–sink dynamics, spatial synchrony, metapopulation capacity, and how the roles of immigration and emigration can vary with spatial scale. We then illustrate some of these concepts with data on spatiotemporal variation in abundance and colonization–extinction dynamics in the wind-dispersed orchid, Lepanthes rupestris, in Puerto Rico. This example provides insight into understanding spatial synchrony in populations, and shows how factors driving occupancy can be similar to those driving colonization–extinction dynamics. We end by outlining other common approaches to understanding spatially structured populations and their viability for conservation.

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  • Research Article
  • Cite Count Icon 20
  • 10.1016/j.tpb.2017.04.003
Unlimited niche packing in a Lotka–Volterra competition game
  • May 8, 2017
  • Theoretical Population Biology
  • Ross Cressman + 5 more

A central question in the study of ecology and evolution is: “Why are there so many species?” It has been shown that certain forms of the Lotka–Volterra (L–V) competition equations lead to an unlimited number of species. Furthermore, these authors note how any change in the nature of competition (the competition kernel) leads to a finite or small number of coexisting species. Here we build upon these works by further investigating the L–V model of unlimited niche packing as a reference model and evolutionary game for understanding the environmental factors restricting biodiversity. We also examine the combined eco-evolutionary dynamics leading up to the species diversity and traits of the ESS community in both unlimited and finite niche-packing versions of the model. As an L–V game with symmetric competition, we let the strategies of individuals determine the strength of the competitive interaction (like competes most with like) and also the carrying capacity of the population. We use a mixture of analytic proofs (for one and two species systems) and numerical simulations. For the model of unlimited niche packing, we show that a finite number of species will evolve to specific convergent stable minima of the adaptive landscape (also known as species archetypes). Starting with a single species, faunal buildup can proceed either through species doubling as each diversity-specific set of minima are reached, or through the addition of species one-by-one by randomly assigning a speciation event to one of the species. Either way it is possible for an unlimited number or species to evolve and coexist. We examine two simple and biologically likely ways for breaking the unlimited niche-packing: (1) some minimum level of competition among species, and (2) constrain the fundamental niche of the trait space to a finite interval. When examined under both ecological and evolutionary dynamics, both modifications result in convergent stable ESSs with a finite number of species. When the number of species is held below the number of species in an ESS coalition, we see a diverse array of convergent stable niche archetypes that consist of some species at maxima and some at minima of the adaptive landscape. Our results support those of others and suggest that instead of focusing on why there are so many species we might just as usefully ask, why are there so few species?

  • Research Article
  • Cite Count Icon 28
  • 10.1007/s12190-023-01842-2
Strong resonance bifurcations for a discrete-time prey–predator model
  • Jan 30, 2023
  • Journal of Applied Mathematics and Computing
  • Bo Li + 2 more

Strong resonance bifurcations for a discrete-time prey–predator model

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  • 10.1007/978-3-319-58163-7_11
Quantifying Information Flow in Chemical Reaction Networks
  • Jan 1, 2017
  • Ozan Kahramanoğulları

We introduce an efficient algorithm for stochastic flux analysis of chemical reaction networks (CRN) that improves our previously published method for this task. The flux analysis algorithm extends Gillespie’s direct method, commonly used for stochastically simulating CRNs with respect to mass action kinetics. The extension to the direct method involves only book-keeping constructs, and does not require any labeling of network species. We provide implementations, and illustrate on examples that our algorithm for stochastic flux analysis provides a means for quantifying information flow in CRNs. We conclude our discussion with a case study of the biochemical mechanism of gemcitabine, a prodrug widely used for treating various carcinomas.

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  • Preprint Article
  • Cite Count Icon 2
  • 10.1101/2021.09.27.461947
Intraspecific variation stabilizes classic predator-prey dynamics
  • Sep 28, 2021
  • Stefano Allesina + 2 more

ABSTRACTIn 1920, Alfred J. Lotka found that, to his “considerable surprise”, the dynamics of a simple predatorprey model he had devised led “to undamped, and hence indefinitely continued, oscillations”1,2— which he thought epitomized the “rhythm of Nature” dear to the Victorians. In 1926, the same model was proposed independently by mathematician Vito Volterra3,4, who was inspired by the work of his son-in-law, fish biologist Umberto D’Ancona5. For over a century, the equations that now bear their names have served as a template for the development of sophisticated models for population dynamics6–10. Coexistence in this classic predator-prey model is fragile—stochasticity or temporal variability in parameter values result in extinctions. The dynamics can be stabilized by intraspecific competition or other forms of self-regulation, but the prevalence of these processes in large food webs has been questioned11,12. Here we show that when we consider populations characterized by intraspecific variability, dynamics are stable—despite the absence of any direct self-regulation. Our results can be generalized further, defining a new class of consumer-resource models8,13. By accounting for intraspecific variation, which is manifest in all biological populations, we obtain dynamics that differ qualitatively and quantitatively from those found for homogeneous populations—challenging a central assumption of many ecological models.

  • Research Article
  • Cite Count Icon 22
  • 10.1023/a:1008913219660
Modelling processes that generate and maintain coral community diversity
  • Sep 1, 2000
  • Biodiversity & Conservation
  • R Van Woesik

This study addresses why adjacent sites on coral reefs are different, why some places support so few coral species, and how human impacts are affecting coral community dynamics and ultimately diversity. The paper includes a brief review outlining what theory tells us and how that theory relates to empirical data. A metapopulation and a metacommunity model are introduced. The metapopulation model can be used to predict a species' probability of site occupancy and the metacommunity model can be used to predict the number of species supported at any one site. The models identify the primary mechanisms that generate and maintain local (10s m2–10s km2) coral diversity based on a regional (100s km2) perspective. Local diversity appears regulated by differential post-settlement mortality that in turn leads to local extinction of some species. Indeed, harsh local environments cause high levels of local extinction and these environments support few coral species.

  • Research Article
  • Cite Count Icon 30
  • 10.1080/08948550214054
Processes Regulating Coral Communities
  • Jul 1, 2002
  • Comments� on Theoretical Biology
  • R Van Woesik

Processes Regulating Coral Communities

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  • Animals : an Open Access Journal from MDPI
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essential to maintaining balance in a community acutely vulnerable to outer pressures and inner conflicts. Christine Eber has written a striking novel that reflects these challenges as well as underscoring the wisdom of Maya culture, which has allowed its people to survive thousands of years under difficult conditions. Her compelling narrative not only shows why these people deserve our respect but moves the reader greatly. Brenda Rosenbaum Mayan Hands Foundation Aline Kominsky-Crumb Love That Bunch Montreal. Drawn & Quarterly. 2018. 211 pages. The reservoir of material for comedy, either stand-up or on the page, is often autobiographical , and this is certainly the case for Aline Kominsky-Crumb (yes, she is married to the R. Crumb, who has his own autobiographical comic reservoir). KominskyCrumb first hit the comics scene in San Books in Review Anna Laestadius Larsson Hilma: En roman om gåtan Hilma af Klint Stockholm. Piratförlaget. 2017. 323 pages. SEEING TO BELIEVING: it could be the motto for this book. Hilma, “A novel about the enigma that was Hilma af Klint,” is a captivating, intelligently fictionalized “life” of a painter who has only recently become internationally famous, but it seems hard to engage with the character Hilma af Klint. Her fervent—and, yes, enigmatic—psychic beliefs dominate her story, increasingly taking over from what we instinctively warm to as “normal” preoccupations. But, seeing her paintings, manifestations of another world perceived by her alone, is not only an overwhelming experience but also imparts meaning to her as a character and as a person. Hilma af Klint was born in 1862 into a comfortable upper-middle-class family. She was well educated for a girl of that time and class; her father had enchanted her with mathematical games and stories of scientific advances ever since she was a clever, fey child. She read On the Origin of Species while still a schoolgirl, partly because she found Darwin’s theories a good way to stop the spirit of her dead older sister, Anna, from spooking her. For the rest of Hilma’s life, her art was inspired by the tensions between our biological existence and the spiritual messages flowing into her mind, mostly in a quasireligious flow of hightoned moral instruction. A young woman at a time when the barriers against women doing anything other than getting and being married were breaking down, Hilma was eventually allowed to study art seriously. During a period as a struggling painter of landscapes and portraits , she became part of The Five, a group of women with similar interests and backgrounds . The group served as an emotional hothouse that encouraged Hilma’s few love affairs—all with other women—as well as her growing fascination with esoteric knowledge. The most extraordinary part of her life as an artist followed from a gradual , instinctive rejection of the demands of bodily pleasures, from food to love, until she had eschewed just about everything but contemplation of nature (late in life, she studied mosses and flowers with a botanist’s focus on detail) and painting. af Klint would have understood what her contemporary and potential soulmate Kandinsky meant by seeking “to symbolize the innerer Klang or inner need of the artist.” Spiritual guidance drove her to express transcendent truths in abstract shapes and glowing colors on very large canvases—the extraordinary Temple series alone contains almost two hundred of these. Text, including spirit “words,” as well as elements of mathematics and biology are included in the images. Anna Laestadius Larsson deals ingeniously with the challenge of portraying the woman as well as her work by creating a frame story: eighty-two-year-old Hilma tells her grown-up nephew Erik about her life. We gain insights into her steadiness of purpose and personal magnetism; Erik is deeply impressed both by his aunt and her art, but—like so many of us—confused by the talk of spirits. Hilma’s storytelling explains a great deal about her, including her fundamental lack of interest in other people. ANNA LAESTADIUS LARSSON 104 WLT WINTER 2019 Francisco in 1972 with Goldie, published by the Wimmen’s Comix Collective. Goldie, a clear precursor to Bunch, is neurotic, selfdeprecating , and striving. Bunch followed...

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  • International Journal of Technological Learning, Innovation and Development
  • Philip Cooke

This paper concerns the brief history of the Regional Innovation Systems (RIS) concept. It shows that the success of the concept in academic and policy circles is because, unlike most regional economic policy instruments, it is flexible and eschews 'one-size-fits-all' type thinking by analysing and advocating different instruments according to the characteristics of the region. There are three sources of influence upon the concept. The first one is general systems theory, especially as it evolved in the late 1960s as the systems planning perspective. Second, the innovation systems approach was influenced by an emergent regional innovation policy and practice literature in the 1980s. Finally, it drew on ideas of 'network regions' which themselves have origins in industrial district theory, milieu research, and finally, innovation systems studies. The whole has made for one of the fastest growing research literatures in innovation studies generally. At the policy level, RIS strategies have in recent years been adopted by countries such as South Korea, China, Norway and Sweden.

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