Discrete and continuous state population models in a noisy world. 2004

Gábor Domokos, and István Scheuring
Department of Mechanics, Materials and Structures, Center for Applied Mathematics and Computational Physics, Budapest University of Technology and Economics, Budapest, H-1111, Muegyetem rkp.3, Hungary.

Simple ecological models operate mostly with population densities using continuous variables. However, in reality densities could not change continuously, since the population itself consists of integer numbers of individuals. At first sight this discrepancy appears to be irrelevant, nevertheless, it can cause large deviations between the actual statistical behaviour of biological populations and that predicted by the corresponding models. We investigate the conditions under which simple models, operating with continuous numbers of individuals can be used to approximate the dynamics of populations consisting of integer numbers of individuals. Based on our definition for the (statistical) distance between the two models we show that the continuous approach is acceptable as long as sufficiently high biological noise is present, or, the dynamical behaviour is regular (non-chaotic). The concepts are illustrated with the Ricker model and tested on the Tribolium castaneum data series. Further, we demonstrate with the help of T. castaneum's model that if time series are not much larger than the possible population states (as in this practical case) the noisy discrete and continuous models can behave temporarily differently, almost independently of the noise level. In this case the noisy, discrete model is more accurate [OR has to be applied].

UI MeSH Term Description Entries
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D011156 Population Density Number of individuals in a population relative to space. Overpopulation,Population Size,Underpopulation,Densities, Population,Density, Population,Population Densities,Population Sizes
D011157 Population Dynamics The pattern of any process, or the interrelationship of phenomena, which affects growth or change within a population. Malthusianism,Neomalthusianism,Demographic Aging,Demographic Transition,Optimum Population,Population Decrease,Population Pressure,Population Replacement,Population Theory,Residential Mobility,Rural-Urban Migration,Stable Population,Stationary Population,Aging, Demographic,Decrease, Population,Decreases, Population,Demographic Transitions,Dynamics, Population,Migration, Rural-Urban,Migrations, Rural-Urban,Mobilities, Residential,Mobility, Residential,Optimum Populations,Population Decreases,Population Pressures,Population Replacements,Population Theories,Population, Optimum,Population, Stable,Population, Stationary,Populations, Optimum,Populations, Stable,Populations, Stationary,Pressure, Population,Pressures, Population,Replacement, Population,Replacements, Population,Residential Mobilities,Rural Urban Migration,Rural-Urban Migrations,Stable Populations,Stationary Populations,Theories, Population,Theory, Population,Transition, Demographic,Transitions, Demographic
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D013269 Stochastic Processes Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables. Process, Stochastic,Stochastic Process,Processes, Stochastic
D014231 Tribolium A genus of small beetles of the family Tenebrionidae; T. confusum is the "confused flour beetle". Triboliums
D017711 Nonlinear Dynamics The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos. Chaos Theory,Models, Nonlinear,Non-linear Dynamics,Non-linear Models,Chaos Theories,Dynamics, Non-linear,Dynamics, Nonlinear,Model, Non-linear,Model, Nonlinear,Models, Non-linear,Non linear Dynamics,Non linear Models,Non-linear Dynamic,Non-linear Model,Nonlinear Dynamic,Nonlinear Model,Nonlinear Models,Theories, Chaos,Theory, Chaos

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