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In evolutionary game theory, complete mixing refers to an assumption about the type of interactions that occur between individual organisms. Interactions between individuals in a population attains complete mixing if and only if the probably individual x interacts with individual y is equal for all y.
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.
This assumption is implicit in the replicator equation a system of differential equations that represents one model in evolutionary game theory. This assumption usually does not hold for most organismic populations, since usually interactions occur in some spatial setting where individuals are more likely to interact with those around them. Although the assumption is empirically violated, it represents a certain sort of scientific idealization which may or may not be harmful to the conclusions reached by that model. This question has led individuals to investigate a series of other models where there is not complete mixing (e.g. Cellular automata models).
In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness function to incorporate the distribution of the population types rather than setting the fitness of a particular type constant. This important property allows the replicator equation to capture the essence of selection. Unlike the quasispecies equation, the replicator equation does not incorporate mutation and so is not able to innovate new types or pure strategies.
Idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false but make models easier to understand or solve. That is, it is determined whether the phenomenon approximates an "ideal case," then the model is applied to make a prediction based on that ideal case.
Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.
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.
This glossary of ecology is a list of definitions of terms and topics in ecology and related fields. For more specific definitions from other glossaries related to ecology, see Glossary of biology and Glossary of environmental science.
Group selection is a proposed mechanism of evolution in which natural selection acts at the level of the group, instead of at the more conventional level of the individual.
In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable. Although commonly thought of in terms of causal relationships, the concept of an interaction can also describe non-causal associations. Interactions are often considered in the context of regression analyses or factorial experiments.
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:
Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them. Example scenarios are ageing populations, population growth, or population decline.
Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic and help inform public health interventions. Models use some basic assumptions and mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programmes. The modelling can help in deciding which intervention/s to avoid and which to trial.
Evolutionary ecology lies at the intersection of ecology and evolutionary biology. It approaches the study of ecology in a way that explicitly considers the evolutionary histories of species and the interactions between them. Conversely, it can be seen as an approach to the study of evolution that incorporates an understanding of the interactions between the species under consideration. The main subfields of evolutionary ecology are life history evolution, sociobiology, the evolution of inter specific relations and the evolution of biodiversity and of communities.
Human behavioral ecology (HBE) or human evolutionary ecology applies the principles of evolutionary theory and optimization to the study of human behavioral and cultural diversity. HBE examines the adaptive design of traits, behaviors, and life histories of humans in an ecological context. One aim of modern human behavioral ecology is to determine how ecological and social factors influence and shape behavioral flexibility within and between human populations. Among other things, HBE attempts to explain variation in human behavior as adaptive solutions to the competing life-history demands of growth, development, reproduction, parental care, and mate acquisition.
Life history theory is an analytical framework designed to study the diversity of life history strategies used by different organisms throughout the world, as well as the causes and results of the variation in their life cycles. It is a theory of biological evolution that seeks to explain aspects of organisms' anatomy and behavior by reference to the way that their life histories—including their reproductive development and behaviors, life span and post-reproductive behavior—have been shaped by natural selection. A life history strategy is the "age- and stage-specific patterns" and timing of events that make up an organism's life, such as birth, weaning, maturation, death, etc. These events, notably juvenile development, age of sexual maturity, first reproduction, number of offspring and level of parental investment, senescence and death, depend on the physical and ecological environment of the organism.
Competition is an interaction between organisms or species in which both the organisms or species are harmed. Limited supply of at least one resource used by both can be a factor. Competition both within and between species is an important topic in ecology, especially community ecology. Competition is one of many interacting biotic and abiotic factors that affect community structure. Competition among members of the same species is known as intraspecific competition, while competition between individuals of different species is known as interspecific competition. Competition is not always straightforward, and can occur in both a direct and indirect fashion.
The following outline is provided as an overview of and topical guide to ecology:
In ecology, a community is a group or association of populations of two or more different species occupying the same geographical area and in a particular time, also known as a biocoenosis. 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".
Wagner's gene network model is a computational model of artificial gene networks, which explicitly modeled the developmental and evolutionary process of genetic regulatory networks. A population with multiple organisms can be created and evolved from generation to generation. It was first developed by Andreas Wagner in 1996 and has been investigated by other groups to study the evolution of gene networks, gene expression, robustness, plasticity and epistasis.
Evolving digital ecological networks are webs of interacting, self-replicating, and evolving computer programs that experience the same major ecological interactions as biological organisms. Despite being computational, these programs evolve quickly in an open-ended way, and starting from only one or two ancestral organisms, the formation of ecological networks can be observed in real-time by tracking interactions between the constantly evolving organism phenotypes. These phenotypes may be defined by combinations of logical computations that digital organisms perform and by expressed behaviors that have evolved. The types and outcomes of interactions between phenotypes are determined by task overlap for logic-defined phenotypes and by responses to encounters in the case of behavioral phenotypes. Biologists use these evolving networks to study active and fundamental topics within evolutionary ecology.
The following outline is provided as an overview of and topical guide to evolution: