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Register a new userSpecies Population Dynamics with Competition and Random Events
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Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is shown that random events cause the population mean of each specie to make smooth transition from far above to far below of its growth rate threshold. At the same time, the population mean of the weaker specie never reaches the extinction point. It is also shown that, as a result of competition, the relative population fluctuations do not die out as the growth rates of both species are raised far above their respective thresholds. This behavior is most remarkable at the maximum competition point where the weaker species population statistics becomes completely chaotic regardless of how far its growth rate in raised.
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We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are characterized with predation efficiency and death rates, to which Darwinian evolutionary adaptation is introduced. Competition for limited prey abundance drives the populations optimization with respect to predation efficiency and death rates. We study the influence of various ecological elements on the final state, finding that both indirect competition and evolutionary adaptation are insufficient to yield a stable ecosystem. However, stable three-species coexistence is observed when direct interaction between the two predator species is implemented.
The analysis of eight molecular datasets involving human and teleost examples along with morphological samples from several groups of Neotropical electric fish (Order: Gymnotiformes) were used in this thesis to test the dynamics of both intraspecific variation and interspecific diversity. In terms of investigating molecular interspecific diversity among humans, two experimental exercises were performed. A cladistic exchange experiment tested for the extent of discontinuity and interbreeding between H. sapiens and neanderthal populations. As part of the same question, another experimental exercise tested the amount of molecular variance resulting from simulations which treated neanderthals as being either a local population of modern humans or as a distinct subspecies. Finally, comparisons of hominid populations over time with fish species helped to define what constitutes taxonomically relevant differences between morphological populations as expressed among both trait size ranges and through growth patterns that begin during ontogeny. Compared to the subdivision found within selected teleost species, H. sapiens molecular data exhibited little variation and discontinuity between geographical regions. Results of the two experimental exercises concluded that neanderthals exhibit taxonomic distance from modern H. sapiens. However, this distance was not so great as to exclude the possibility of interbreeding between the two subspecific groups. Finally, a series of characters were analyzed among species of Neotropical electric fish. These analyses were compared with hominid examples to determine what constituted taxonomically relevant differences between populations as expressed among specific morphometric traits that develop during the juvenile phase.
Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC) concept: $x$ causes $y$ if $x$ improves the prediction of $y$ in a dynamic model. However, the entangled nature of nonlinear ecological systems has led to question the appropriateness of Granger causality, especially in its classical linear Multivariate AutoRegressive (MAR) model form. Convergent-cross mapping (CCM), a nonparametric method developed for deterministic dynamical systems, has been suggested as an alternative. Here, we show that linear GC and CCM are able to uncover interactions with surprisingly similar performance, for predator-prey cycles, 2-species deterministic (chaotic) or stochastic competition, as well as 10- and 20-species interaction networks. There is no correspondence between the degree of nonlinearity of the dynamics and which method performs best. Our results therefore imply that Granger causality, even in its linear MAR($p$) formulation, is a valid method for inferring interactions in nonlinear ecological networks; using GC or CCM (or both) can instead be decided based on the aims and specifics of the analysis.
Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even though the derivation of the adaptive dynamics from a given invasion fitness function is general and model-independent, the derivation of the invasion fitness function itself requires specification of an underlying ecological model. Therefore, evolutionary insights gained from adaptive dynamics models are generally model-dependent. Logistic models for symmetric, frequency-dependent competition are widely used in this context. Such models have the property that the selection gradients derived from them are gradients of scalar functions, which reflects a certain gradient property of the corresponding invasion fitness function. We show that any adaptive dynamics model that is based on an invasion fitness functions with this gradient property can be transformed into a generalized symmetric competition model. This provides a precise delineation of the generality of results derived from competition models. Roughly speaking, to understand the adaptive dynamics of the class of models satisfying a certain gradient condition, one only needs a complete understanding of the adaptive dynamics of symmetric, frequency-dependent competition. We show how this result can be applied to number of basic issues in evolutionary theory.
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent models for coalescence (with or without recombination) can be described in terms of the so-called phase-type theory, where complicated and tedious calculations are circumvented by the use of matrices. The application of phase-type theory consists of describing the stochastic model as a Markov model by appropriately setting up a state space and calculating the corresponding intensity and reward matrices. Formulae of interest are then expressed in terms of these aforementioned matrices. We illustrate this by a few examples calculating the mean, variance and even higher order moments of the site frequency spectrum in the multiple merger coalescent models, and by analysing the mean and variance for the number of segregating sites for multiple samples in the two-locus ancestral recombination graph. We believe that phase-type theory has great potential as a tool for analysing probability models in population genetics. The compact matrix notation is useful for clarification of current models, in particular their formal manipulation (calculation), but also for further development or extensions.
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