Evolution of physical processes in models of population dynamics

Neste texto apresentamos e discutimos um breve panorama cronológico para a dinâmica de populações, observando o ponto de vista dos autores, bem como a evolução dos principais modelos matemáticos e sua importância histórica. Com foco na predição temporal e espacial da variação do número de indivíduos de uma população, analisamos como modelar matematicamente os processos físicos como crescimento, interação, difusão e fluxo de um coletivo de indivíduos. Partimos do bem conhecido modelo de Fibonacci e discutimos como modelos que o sucederam, a saber, o modelo Malthusiano, Lotka-Volterra e Fisher-Kolmogorov, foram capazes de ampliar o entendimento do comportamento de uma população. Apresentamos, nesta linha temporal sinuosa, como as interações entre uma mesma espécie e entre espécies podem ser explicadas e modeladas. Mostramos como funciona o processo de extinção de uma espécie predadora, o fenômeno de difusão de um coletivo devido as mais diversas exigências espaciais, as migrações e invasões de territórios por meio de uma dinâmica convectiva nos modelos de dinâmica de uma população e também como a não-localidade nas interações e no crescimento ampliam enormemente nosso entendimento sobre os padrões na natureza.In this paper we present and discuss a brief overview chronological for the population dynamics, observing the point of view of the authors, as well as the evolution of the main mathematical models and its historical importance. Focusing on temporal and spatial prediction of the variation in the number of individuals in a population, we analyze how to mathematically model the physical processes such as growth, interaction, dissemination and flow of a collective of individuals. We start from the well-known model of Fibonacci and discussed how models who succeeded him, namely the Malthusian model, Lotka-Volterra and Fisher-Kolmogorov were able to expand the understanding of the behavior of a population. Here, in this winding timeline as the interactions between species and between species can be explained and modeled. We show how the process of extinguishing a predatory species works, the diffusion phenomenon of a collective because the most diverse space requirements, migration and invasions of territories by means of convective momentum in dynamic models of a population as well as non-locality in interactions and growth greatly expand our understanding of the patterns in nature

Self-organization and pattern formation in physical and biological systems

Neste trabalho apresentamos uma breve discussão sobre a descrição matemática do fenômeno formação de padrão em sistemas biológicos, observando os modelos matemáticos de dinâmica de populações. Listamos vários exemplos de sistemas físicos, químicos e biológicos que exibem este fenômeno enfatizando, em cada um, os parâmetros principais envolvidos em seu entendimento. Mostramos que, no caso das populações, o fenômeno padrão pode ser modelado ao modificarmos a equação de Fisher-Kolmogorov, considerando uma interação não-local para o termo de competição. Apresentamos um estudo analítico e numérico da equação de Fisher-Kolmogorov com difusão e analisamos o papel dos termos de crescimento, difusão e competição na formação dos padrões.In this work we present a brief discussion of the mathematical description of pattern formation phenomena in biological systems through the mathematical models of population dynamics. We present some examples of physical, chemical and biological systems which exhibit this phenomena. For each system we show the main parameters that describe the patterns. We show that in the case of population, patterns can be described when we modify the Fisher-Kolmogorov equation, considering a non-local interaction for the competition term. We present an analytical and numerical study of the Fisher-Kolmogorov equation with diffusion and we analyze the role of growth, diffusion and competition term in the pattern formation

Pattern formation and coexistence domains for a nonlocal population dynamics

In this communication we propose a most general equation to study pattern formation for one-species population and their limit domains in systems of length L. To accomplish this we include non-locality in the growth and competition terms where the integral kernels are now depend on characteristic length parameters alpha and beta. Therefore, we derived a parameter space (alpha,beta) where it is possible to analyze a coexistence curve alpha*=alpha*(\beta) which delimits domains for the existence (or not) of pattern formation in population dynamics systems. We show that this curve has an analogy with coexistence curve in classical thermodynamics and critical phenomena physics. We have successfully compared this model with experimental data for diffusion of Escherichia coli populations

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear un derstanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5–7 vast areas of the tropics remain understudied.8–11 In the American tropics, Amazonia stands out as the world’s most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepre sented in biodiversity databases.13–15 To worsen this situation, human-induced modifications16,17 may elim inate pieces of the Amazon’s biodiversity puzzle before we can use them to understand how ecological com munities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple or ganism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region’s vulnerability to environmental change. 15%–18% of the most ne glected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lostinfo:eu-repo/semantics/publishedVersio

Catálogo Taxonômico da Fauna do Brasil: setting the baseline knowledge on the animal diversity in Brazil

The limited temporal completeness and taxonomic accuracy of species lists, made available in a traditional manner in scientific publications, has always represented a problem. These lists are invariably limited to a few taxonomic groups and do not represent up-to-date knowledge of all species and classifications. In this context, the Brazilian megadiverse fauna is no exception, and the Catálogo Taxonômico da Fauna do Brasil (CTFB) (http://fauna.jbrj.gov.br/), made public in 2015, represents a database on biodiversity anchored on a list of valid and expertly recognized scientific names of animals in Brazil. The CTFB is updated in near real time by a team of more than 800 specialists. By January 1, 2024, the CTFB compiled 133,691 nominal species, with 125,138 that were considered valid. Most of the valid species were arthropods (82.3%, with more than 102,000 species) and chordates (7.69%, with over 11,000 species). These taxa were followed by a cluster composed of Mollusca (3,567 species), Platyhelminthes (2,292 species), Annelida (1,833 species), and Nematoda (1,447 species). All remaining groups had less than 1,000 species reported in Brazil, with Cnidaria (831 species), Porifera (628 species), Rotifera (606 species), and Bryozoa (520 species) representing those with more than 500 species. Analysis of the CTFB database can facilitate and direct efforts towards the discovery of new species in Brazil, but it is also fundamental in providing the best available list of valid nominal species to users, including those in science, health, conservation efforts, and any initiative involving animals. The importance of the CTFB is evidenced by the elevated number of citations in the scientific literature in diverse areas of biology, law, anthropology, education, forensic science, and veterinary science, among others

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost