Limiting Similarity
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Limiting Similarity
Limiting similarity (informally "limsim") is a concept in theoretical ecology and community ecology that proposes the existence of a maximum level of niche overlap between two given species that will allow continued coexistence. This concept is a corollary of the competitive exclusion principle, which states that, controlling for all else, two species competing for exactly the same resources cannot stably coexist. It assumes normally-distributed resource utilization curves ordered linearly along a resource axis, and as such, it is often considered to be an oversimplified model of species interactions. Moreover, it has theoretical weakness, and it is poor at generating real-world predictions or falsifiable hypotheses. Thus, the concept has fallen somewhat out of favor except in didactic settings (where it is commonly referenced), and has largely been replaced by more complex and inclusive theories. History In 1932, Georgii Gause created the competitive exclusion principle based ...
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Theoretical Ecology
Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world. The field is broad and includes foundations in appli ...
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Competitive Lotka–Volterra Equations
The competitive Lotka–Volterra equations are a simple model of the population dynamics of species competing for some common resource. They can be further generalised to the Generalized Lotka–Volterra equation to include trophic interactions. Overview The form is similar to the Lotka–Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. In the equations for predation, the base population model is exponential. For the competition equations, the logistic equation is the basis. The logistic population model, when used by ecologists often takes the following form: = rx\left(1-\right). Here is the size of the population at a given time, is inherent per-capita growth rate, and is the carrying capacity. Two species Given two populations, and , with logistic dynamics, the Lotka–Volterra formulation adds an additional term to account for the species' interactions. Th ...
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Ecology
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and it is not synonymous with environmentalism. Among other things, ecology is the study of: * The abundance, biomass, and distribution of organisms in the context of the environment * Life processes, antifragility, interactions, and adaptations * The movement of materials and energy through living communities * The successional development of ecosystems * Cooperation, competition, and predation within and between species * Patterns of biodiversity and its effect on ecosystem processes Ecology has practical applications in conservation biology, wetland management, natural resource managemen ...
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Competitive Exclusion Principle
In ecology, the competitive exclusion principle, sometimes referred to as Gause's law, is a proposition that two species which compete for the same limited resource cannot coexist at constant population values. When one species has even the slightest advantage over another, the one with the advantage will dominate in the long term. This leads either to the extinction of the weaker competitor or to an evolutionary or behavioral shift toward a different ecological niche. The principle has been paraphrased in the maxim "complete competitors can not coexist". History The competitive exclusion principle is classically attributed to Georgy Gause, although he actually never formulated it. The principle is already present in Darwin's theory of natural selection. Throughout its history, the status of the principle has oscillated between ''a priori'' ('two species coexisting ''must'' have different niches') and experimental truth ('we find that species coexisting do have different niches' ...
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Quaternary
The Quaternary ( ) is the current and most recent of the three periods of the Cenozoic Era in the geologic time scale of the International Commission on Stratigraphy (ICS). It follows the Neogene Period and spans from 2.58 million years ago to the present. The Quaternary Period is divided into two epochs: the Pleistocene (2.58 million years ago to 11.7 thousand years ago) and the Holocene (11.7 thousand years ago to today, although a third epoch, the Anthropocene, has been proposed but is not yet officially recognised by the ICS). The Quaternary Period is typically defined by the cyclic growth and decay of continental ice sheets related to the Milankovitch cycles and the associated climate and environmental changes that they caused. Research history In 1759 Giovanni Arduino proposed that the geological strata of northern Italy could be divided into four successive formations or "orders" ( it, quattro ordini). The term "quaternary" was introduced by Jules Desnoye ...
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Gastropod
The gastropods (), commonly known as snails and slugs, belong to a large taxonomic class of invertebrates within the phylum Mollusca called Gastropoda (). This class comprises snails and slugs from saltwater, from freshwater, and from land. There are many thousands of species of sea snails and slugs, as well as freshwater snails, freshwater limpets, and land snails and slugs. The class Gastropoda contains a vast total of named species, second only to the insects in overall number. The fossil history of this class goes back to the Late Cambrian. , 721 families of gastropods are known, of which 245 are extinct and appear only in the fossil record, while 476 are currently extant with or without a fossil record. Gastropoda (previously known as univalves and sometimes spelled "Gasteropoda") are a major part of the phylum Mollusca, and are the most highly diversified class in the phylum, with 65,000 to 80,000 living snail and slug species. The anatomy, behavior, feeding, and re ...
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Fossil
A fossil (from Classical Latin , ) is any preserved remains, impression, or trace of any once-living thing from a past geological age. Examples include bones, shells, exoskeletons, stone imprints of animals or microbes, objects preserved in amber, hair, petrified wood and DNA remnants. The totality of fossils is known as the ''fossil record''. Paleontology is the study of fossils: their age, method of formation, and evolutionary significance. Specimens are usually considered to be fossils if they are over 10,000 years old. The oldest fossils are around 3.48 billion years old to 4.1 billion years old. Early edition, published online before print. The observation in the 19th century that certain fossils were associated with certain rock strata led to the recognition of a geological timescale and the relative ages of different fossils. The development of radiometric dating techniques in the early 20th century allowed scientists to quantitatively measure the ...
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Paleoecology
Paleoecology (also spelled palaeoecology) is the study of interactions between organisms and/or interactions between organisms and their environments across geologic timescales. As a discipline, paleoecology interacts with, depends on and informs a variety of fields including paleontology, ecology, climatology and biology. Paleoecology emerged from the field of paleontology in the 1950s, though paleontologists have conducted paleoecological studies since the creation of paleontology in the 1700s and 1800s. Combining the investigative approach of searching for fossils with the theoretical approach of Charles Darwin and Alexander von Humboldt, paleoecology began as paleontologists began examining both the ancient organisms they discovered and the reconstructed environments in which they lived. Visual depictions of past marine and terrestrial communities have been considered an early form of paleoecology. Overview of paleoecological approaches * Classic paleoecology uses data from ...
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Character Displacement
Character displacement is the phenomenon where differences among similar species whose distributions overlap geographically are accentuated in regions where the species co-occur, but are minimized or lost where the species' distributions do not overlap. This pattern results from evolutionary change driven by biological competition among species for a limited resource (e.g. food). The rationale for character displacement stems from the competitive exclusion principle, also called Gause's Law, which contends that to coexist in a stable environment two competing species must differ in their respective ecological niche; without differentiation, one species will eliminate or exclude the other through competition. Character displacement was first explicitly explained by William L. Brown Jr. and E. O. Wilson in 1956: "Two closely related species have overlapping ranges. In the parts of the ranges where one species occurs alone, the populations of that species are similar to the other ...
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Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ...
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Community Ecology
In ecology, a community is a group or association of populations of two or more different species occupying the same geographical area at the same time, also known as a biocoenosis, biotic community, biological community, ecological community, or life assemblage. The term community has a variety of uses. In its simplest form it refers to groups of organisms in a specific place or time, for example, "the fish community of Lake Ontario before industrialization". Community ecology or synecology is the study of the interactions between species in communities on many spatial and temporal scales, including the distribution, structure, abundance, demography, and interactions between coexisting populations. The primary focus of community ecology is on the interactions between populations as determined by specific genotypic and phenotypic characteristics. Community ecology also takes into account abiotic factors that influence species distributions or interactions (e.g. annual temperat ...
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