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R F Costantino

Publications and source records attributed to R F Costantino.

16 recordsLinked to original sources
PubMed2006

Experimental support of the scaling rule for demographic stochasticity.

A scaling rule of ecological theory, accepted but lacking experimental confirmation, is that the magnitude of fluctuations in population densities due to demographic stochasticity scales inversely with the square root of population numbers. This supposition is based on analyses of models exhibiting exponential growth or stable equilibria. Using two quantitative measures, we extend the scaling rule to situations in which population densities fluctuate due to nonlinear deterministic dynamics. These measures are applied to populations of the flour beetle Tribolium castaneum that display chaotic dynamics in both 20-g and 60-g habitats. Populations cultured in the larger habitat exhibit a clarification of the deterministic dynamics, which follows the inverse square root rule. Lattice effects, a deterministic phenomenon caused by the discrete nature of individuals, can cause deviations from the scaling rule when population numbers are small. The scaling rule is robust to the probability distribution used to model demographic variation among individuals.

Animals↗
PubMed2003

Anatomy of a chaotic attractor: subtle model-predicted patterns revealed in population data.

Mathematically, chaotic dynamics are not devoid of order but display episodes of near-cyclic temporal patterns. This is illustrated, in interesting ways, in the case of chaotic biological populations. Despite the individual nature of organisms and the noisy nature of biological time series, subtle temporal patterns have been detected. By using data drawn from chaotic insect populations, we show quantitatively that chaos manifests itself as a tapestry of identifiable and predictable patterns woven together by stochasticity. We show too that the mixture of patterns an experimentalist can expect to see depends on the scale of the system under study.

Animals↗
PubMed2003

Explaining and predicting patterns in stochastic population systems.

Lattice effects in ecological time-series are patterns that arise because of the inherent discreteness of animal numbers. In this paper, we suggest a systematic approach for predicting lattice effects. We also show that an explanation of all the patterns in a population time-series may require more than one deterministic model, especially when the dynamics are complex.

Animals↗
PubMed2001

Lattice effects observed in chaotic dynamics of experimental populations.

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete-state models. We suggest that such lattice effects could be an important component of natural population fluctuations.

Animals↗
PubMed1998

Resonant population cycles in temporally fluctuating habitats.

Experiments with the flour beetle Tribolium have revealed that animal numbers were larger in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volume of the same average size. In this paper we derive and analyze a discrete stage-structured mathematical model that explains this phenomenon as a kind of resonance effect. Habitat volume is incorporated into the model by the assumption that all rates of cannibalism (larvae on eggs, adults on eggs and pupae) are inversely proportional to the volume of the culture medium. We tested this modeling assumption by conducting and statistically analyzing laboratory experiments. For parameter estimates derived from experimental data, our model indeed predicts, under certain circumstances, a larger (cycle-average) total population abundance when the habitat volume periodically fluctuates than when the habitat volume is held constant at the average volume. The model also correctly predicts certain phase relationships and transient dynamics observed in data. The analyses involve a thorough integration of mathematics, statistical methods, biological details and experimental data.

Animals↗
PubMed1975

Genetic analysis of a population of Tribolium. V. Viability of the unsaturated fatty acid sensitive mutant.

The viability pattern of the unsaturated fatty acid sensitive mutant (cos/cos) of Tribolium castaneum was examined with reference to the normal genotype from egg hatching through adult emergence. The beetles were cultured on diets with 0, 3, or 5% corn oil in growth chambers maintained at 33 +/- 1 degree C and either 42 +/- 6% or 75 +/- 3% relative humidity. The pattern of the mutant was altered during the larval stage and was dependent on both the concentration of dietary fatty acid and the relative humidity of the culture chamber. Values of the viability component of fitness were assigned to the cos/cos, +/-/cos and +/-/+/- genotypes for multiple environments based on the number of eggs surviving to pupation. In large, random mating populations segregating at this locus, a stable genetic polymorphism is forecast. Predicted rates of change of allele frequency are dependent upon the culture conditions.

Animals↗