Abstract
We examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelford. The ensuing paradigm sets natality and mortality rates to express through extreme values of population growth determining factor. Dynamics through time occur over different growth phases. Transition points are interpreted as thresholds of viability, starvation, and intraspecific competition. In this delivery, we focus on the qualitative study of the global trajectory expressed on continuous time and on exploring the feasibility of analytical results against data on populations growing under experimental or natural conditions. All study cases sustained fittings of high reproducibility both at empirical and interpretative slants. Possible phase configurations include regimes with multiple stable equilibria, sigmoidal growth, extinction, or stationarity. Here, we also outline that the associating discrete-time piecewise model composes the logistic map applied over a particular region of the phase configuration. Preliminary exploratory analysis suggests that the logistic map’s chaos onset could surpass once the orbit enters a contiguous phase region.
Highlights
As a rule, mathematical models that attempt to describe the dynamics of two or more populations, subject to a specific type of interaction in an ecosystem, are formulated based on too rigid hypotheses, resulting in poor concordance of the model’s predictions with the natural process. e high degree of complexity of biological phenomena and their significant spatial-temporal variations do not assimilate by single-rule models, which are incapable of presenting the functional diversity required by levels of reliable prediction
An ad hoc logical system that could sustain such an enterprise is what we comprehend as a principle of limiting factors (PLF) for population growth. is paradigm entailed the derivation of a population model (PPM) as a collection of submodels called growth phases that continuously compose the global trend of population size
Each growth phase describes the dynamics over a specific time interval. e naming composite further refers to the principle of limiting factors-driven piecewise population model, which represents utilizing the PLFPPM acronym
Summary
Mathematical models that attempt to describe the dynamics of two or more populations, subject to a specific type of interaction in an ecosystem, are formulated based on too rigid hypotheses, resulting in poor concordance of the model’s predictions with the natural process. e high degree of complexity of biological phenomena and their significant spatial-temporal variations do not assimilate by single-rule models, which are incapable of presenting the functional diversity required by levels of reliable prediction. Mathematical models that attempt to describe the dynamics of two or more populations, subject to a specific type of interaction in an ecosystem, are formulated based on too rigid hypotheses, resulting in poor concordance of the model’s predictions with the natural process. Complexity between opposing influences such as birth generating and growth inhibitory processes. Each of these effects depends on a series of factors inherent to population growth. An alternative approach is considering a horizontal integration of complexity through a piecewise modeling strategy. While embracing this approach to gain interpretative strength, it would be desirable to imbue the construct of a mechanistic profile. We include several study cases that show the empirical and interpretative adequacy of the present paradigm. e Appendix presents a qualitative study of associating continuous-time global trajectory
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