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.

Multiple attractors, saddles, and population dynamics in periodic habitats.

Mathematical models predict that a population which oscillates in the absence of time-dependent factors can develop multiple attracting final states in the advent of periodic forcing. A periodically-forced, stage-structured mathematical model predicted the transient and asymptotic behaviors of Tribolium (flour beetle) populations cultured in periodic habitats of fluctuating flour volume. Predictions included multiple (2-cycle) attractors, resonance and attenuation phenomena, and saddle influences. Stochasticity, combined with the deterministic effects of an unstable 'saddle cycle' separating the two stable cycles, is used to explain the observed transients and final states of the experimental cultures. In experimental regimes containing multiple attractors, the presence of unstable invariant sets, as well as stochasticity and the nature, location, and size of basins of attraction, are all central to the interpretation of data.

Hypercholesterolemia screening. Does knowledge of blood cholesterol level affect dietary fat intake?

OBJECTIVE: To assess whether knowing blood cholesterol test results influences people's intention to lower their dietary fat intake and to assess changes in diet after 3 months. DESIGN: Randomized clinical study. SETTING: Two hospital-based family medicine centres. PARTICIPANTS: A total of 526 patients aged 18 to 65, without prior knowledge of their blood cholesterol levels, were recruited. Seventy did not appear for their appointments, and 37 did not meet study criteria, leaving 419 participants. From that group, 391 completed the study. INTERVENTIONS: Patients submitted to cholesterol screening were randomly assigned to one of two groups, completing the study questionnaires either before (control group) or after (experimental group) being informed of their screening test results. All participants were called 3 months after transmission of test results to assess their dietary fat intake at that time. MAIN OUTCOME MEASURES: Differences in intention to adopt a low-fat diet reported between the experimental and control groups and differences in dietary fat intake modification after 3 months between patients with normal and abnormal blood cholesterol test results. RESULTS: Knowledge of test results influenced patients' intentions to adopt low-fat diets (F1,417 = 5.4, P = .02). Patients reported lower mean dietary fat intake after 3 months than at baseline (P < .0001). The reduction was greater in patients with abnormal screening results (F2,388 = 3.6, P = .03). CONCLUSIONS: Being informed of personal blood cholesterol levels effects an immediate change in eating habits that translates into reduced dietary fat intake.

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.

Aerobic exercise and the placebo effect: a controlled study.

An experiment was conducted with 48 healthy young adults engaged in a supervised 10-week exercise program to determine whether a placebo effect is involved within the exercise-psychological enhancement connection. Based on an expectancy modification procedure, one-half of the subjects were led to believe that their program was specifically designed to improve psychological well-being (experimental condition) whereas no such intervention was made with the second half (control condition). Expectations for psychological benefits and aerobic capacity (VO2max) were measured before and after completion of the program. Self-esteem, as the indicator of psychological well-being, was measured on four specific occasions: at the beginning, after the fourth and seventh weeks, and upon completion of the training program. The results showed similar significant increases in fitness levels in both conditions. Moreover, self-esteem was significantly improved over time in the experimental but not in the control condition. These findings provide evidence to support the notion that exercise may enhance psychological well-being via a strong placebo effect. Implications of the results with regard to exercise prescription are discussed.

Predictors of smoking behaviour: an application of Ajzen's theory of planned behaviour.

The aim of the present paper was to verify the basic assumptions underlying the theory of planned behaviour for the prediction of cigarette smoking intentions and behaviour among adults of the general population (study 1) and a group of pregnant women (study 2). Each study was developed based upon Ajzen's theory of planned behaviour. In both studies, baseline data was collected at home with trained interviewers and with the use of paper and pencil questionnaires. The self-report on behaviour was obtained 6 months (study 1) and between 8 and 9 months (study 2) after baseline data collection. In study 1, for smokers, perceived behavioural control, attitudes and subjective norm were explaining intention, whereas perceived behavioural control and habit were the most important predictors of behaviour. In study 2, smoker's intentions was mainly under the influence of perceived behavioural control and attitude, whereas behaviour was predicted by perceived behavioural control only. The present studies suggest that promotional programmes should help smokers to know and develop their will-power regarding non-smoking of cigarettes and should be informed of the effort required in order to modify smoking behaviour.

Erroneous perceptions and arousal among regular and occasional video poker players.

This study investigated the relationship between the level of arousal (Heart Rate) and the number of erroneous perceptions among video poker players. Twelve regular and twelve occasional gamblers participated in a gambling session conducted in a natural environment. It was hypothesised that 1) a significant positive correlation would be observed between arousal and the number of erroneous verbalizations, 2) regular players would show a higher level of arousal than occasional players, and 3) they would emit more erroneous verbalizations. Results showed that hypotheses one and three were confirmed. Theoretical and practical implications of these results for the psychology of gambling are discussed.

Optimism and health-relevant cognitions after a myocardial infarction.

The relationship between dispositional optimism (LOT) and health-relevant cognitions after a myocardial infarction was examined with 158 patients (mean age = 52.7 +/- 8.1 yr.). Patients above the median on optimism (i.e., optimists) scored significantly lower on perceived susceptibility, perceived severity, and experienced fear than did pessimists. However, no difference on perceived self-efficacy was reported between optimists and pessimists. It is concluded that these results provide further evidence for the LOT's construct validity.

Quantitative in situ hybridization to measure single-cell changes in vasopressin and oxytocin mRNA levels after osmotic stimulation.

1. The measurement of cellular mRNA content by quantitative in situ hybridization is a valuable approach to the study of gene expression in brain since this tissue exhibits a high degree of phenotypic heterogeneity. 2. The cellular content of vasopressin and oxytocin mRNA in hypothalamo-neurohypophysial system neurons was altered by maintaining rats for 24 hr on 2% sodium chloride water. 3. Statistical and graphical techniques were then used to analyze cell by cell how mRNA levels were altered as a result of osmotic stimulation. We propose that the negative binomial probability distribution is a suitable model to describe how mRNA content varies across a defined cell population. For both measures of oxytocin and vasopressin mRNA levels, maximum-likelihood estimation indicated that this model adequately described empirical findings obtained from rats drinking tap water or salt water. 4. Both graphical and statistical analyses suggested how the defined neural system responds to osmotic stimulation: mRNA content was altered as a multiplicative function of "initial state." The utility and limitations of the quantitative approach are discussed.

Graphical and statistical approaches to data analysis for in situ hybridization.

Quantification of gene expression in a morphological context is an invaluable tool for neurobiological investigation. The ability to measure the quantity of specific mRNA molecules at the level of the single neuron permits one to monitor the modulation of complex cell synthetic activity of intact neuron populations. The cells of interest can be contiguous or dispersed in functionally significant patterns throughout a broad anatomical region of the brain. The application of quantitative in situ hybridization is technically difficult and labor intensive. Nevertheless, it has great utility for investigating gene expression from a structural perspective. (1) In situ hybridization permits one to ask questions concerning the anatomical pattern of neuronal gene expression. (2) It permits analyses concerning the initiation of expression, cell location, cell type, and alterations of level of expression within a spatial and temporal context. (3) In cases where blotting methods suggest a message exists at low copy, in situ hybridization permits queries at the single-cell level. For example, in situ hybridization can determine if very few cells are expressing the gene product or if many neurons dispersed throughout a brain region exhibit low mRNA copy number/cell. Quantitative analyses also allow detailed investigation of cell response to physiologically meaningful stimulation. Our application of statistical and numerical methods is a demonstration of the utility of probabilistic models; the mixture distribution accounted for data from both labeled and unlabeled sources. In agreement with many previous investigations, grain density over an unlabeled uniform source (oxytocinergic cells) was suitably described by the Poisson distribution. The population of labeled vasopressinergic cells, however, was best described by the negative binomial distribution. Previous investigations from different fields of biology show that the negative binomial can be used to describe many biological phenomena, and this distribution was considered in at least two previous investigations to evaluate autoradiographic data which did not fit the Poisson function. From a theoretical perspective, the probabilistic relationship between beta-particle decay (a Poisson function) and the distribution of message levels among individual neurons in a cell group (gamma distribution) prompts consideration of the negative binomial. For both data sets the observed variances were larger than the mean, and the labeled portion of the data sets exhibited positive skewness.(ABSTRACT TRUNCATED AT 400 WORDS)

A comparison of the Fishbein and Ajzen and the Triandis attitudinal models for the prediction of exercise intention and behavior.

The main purpose of the study was to compare the efficiency of the Fishbein and Ajzen and the Triandis models to predict (1) the intention to participate regularly in some physical activities during free time within a 3-week period and (2) the exercise behavior within these 3 weeks among a group of 166 subjects, aged 22 to 65 years. Our results show that the Triandis model was as efficient as the Fishbein and Ajzen model in predicting the exercise behavior. However, the results obtained from the Triandis model demonstrate the importance of the habit of exercising in predicting the exercise behavior. Moreover, the Triandis model was superior to the Fishbein and Ajzen model in explaining behavioral intention. Of particular interest was the salience of the affective, social, and personal belief components of the Triandis model. In addition, from a practical perspective, this comparative study showed that (1) to exercise regularly is perceived as hard work, and (2) individuals believe that it is their own responsibility to exercise or not to exercise.

The impact of physical fitness and health-age appraisal upon exercise intentions and behavior.

This study investigated the relative and combined effectiveness of the Canadian Home Fitness Test (CHFT) and Health Hazard Appraisal (HHA) to modify (1) intention to exercise with and without knowledge of the results and (2) intention and behavior to exercise over 3 months. The 200 subjects were randomly attributed to groups, either (1) physical-fitness evaluation (PF), (2) appraised health age (HA), (3) physical-fitness evaluation and health-hazard appraisal (PF-HA), or (4) control (C). The immediate impact on the intention to exercise of passing one and/or the other tests, without knowledge of the results, was not significant. With knowledge of the results, the intentions of the PF and PF-HA groups differed from those of the C group. This effect disappeared after 3 months. There was no significant impact on exercise behavior over 3 months. The results indicated a short-term motivational effect from being informed of CHFT results. Maintaining this effect might require intervention on a long-term basis.

Prediction of leisure-time exercise behavior: a path analysis (LISREL V) model.

In an attempt to understand the inherent process underlying the regular practice of physical activity, the relationships among subjective norm, attitude, habit, intention, and future behaviors have been investigated in a random sample of 136 University of Toronto employees. For this purpose, leisure-time exercise behavior was measured on two occasions after a statement of intentions had been obtained: 3 weeks later (proximal behavior) and 2 months later (distal behavior). The results of a path analysis (LISREL) suggest that intention is directly influenced by habit and attitude, proximal behavior is the result of habit only, and distal behavior can be explained by a combination of intention and proximal behavior. Subjective norm was not a significant predictor of intention, proximal behavior, or distal behavior. This modeling approach offers a clearer understanding of the dynamics of exercise intention and behavior, strongly supporting the role of habit as a determinant of exercise behavior.

Natural selection, fitness entropy, and the dynamics of coevolution.

The coevolutionary dynamics of interacting populations were studied by combining continuous time Lotka-Volterra models of population growth with single-locus genetic models of weak selection. The effects of natural selection on population growth were evaluated using Ginzburg's fitness entropy function as a measure of the deviation of a population's initial allele frequencies from their polymorphic equilibrium values. This entropy measure was used to relate the dynamics of a community composed of evolving populations to the dynamics of a "reference community" whose populations are initially in genetic equilibrium. Specifically, a quantity called the "selective difference area" was defined as the total difference between the population size trajectories of a reference and evolving population. The selective difference area represents the amount of extra life a species would realize if the entire community were at genetic equilibrium. It was shown that this selective difference area is a simple linear function of the initial fitness entropies of each species. This prediction is independent of the strength of selection and holds for any arbitrary set of initial population densities. Numerical examples were presented to illustrate the results. Under the assumption of weak selection, a generalization for arbitrary population growth models was outlined.

Life not lived due to disequilibrium in heterogeneous age-structured populations.

Three models of age-structured populations with demographically heterogeneous subpopulations are analyzed. In the first model, each subpopulation has its own age-specific vital rates which are fixed in time. In the second model, the vital rates of each subpopulation are uniformly inhibited by increasing total numbers of individuals. In the third, the vital rates of groups of subpopulations are inhibited by the total numbers of individuals in other groups of subpopulations with an intensity that depends on the interacting pair of groups. Three functions are defined to measure disequilibrium in the subpopulation frequencies, subpopulation age structures, and total population size. For the first model, we show that disequilibrium will shift the trajectory of the total numbers of individuals forward or backward in time by an asymptotic constant that is proportional to the sum of the disequilibrium measures. For the second model, we establish sufficient conditions for the existence of a globally stable equilibrium and we show that disequilibrium will result in a finite loss or gain in life which is proportional to the sum of the disequilibrium measures. For the last model, we show that the loss or gain in life for each group of subpopulations is a linear combination over all groups of the sums of the three disequilibrium measures. We illustrate these results with numerical examples and give possible biological interpretations of the models. We relate these new results to previous work on the cost of natural selection and measures of demographic disequilibrium.

Natural selection and density-dependent population growth.

Natural selection was studied in the context of density-dependent population growth using a single locus, continuous time model for the rates of change of population size and allele frequency. The maximization principle of density-dependent selection was applied to a class of fitness expressions with explicit recruitment and mortality terms. Three general results were obtained: First, at low population densities, the genetic basis of selection is the difference between the mean recruitment rate and the mean mortality rate. Second, at densities much higher than the equilibrium population size, selection is expected to act to minimize the mean mortality rate. Third, as the population approaches its equilibrium density, selection is predicted to maximize the ratio of the mean recruitment rate to the mean mortality rate.

Natural selection and fitness entropy in a density-regulated population.

The entropy H(p(o),p*) of a population with the initial allele frequency p(o) given the equilibrium polymorphic frequency p* has been proposed as a measure of natural selection. In the present paper, we have extended this concept to include a particular aspect of density-dependent selection. We compared size trajectory of a population initially at genetic equilibrium, N(t), with the size trajectories of populations not initially at p*,N(t), but which do eventually converge to a common equilibrium allele frequency and equilibrium density, N*. The following experimentally testable hyopthesis was established. The total area defined by the difference between the trajectories of N(t) and N(t) as they converge to N* is directly proportional to the fitness entropy when population size is transformed using the density-dependent fitness value. Two properties of this relationship were noted. First, it is independent of the magnitude of natural selection and, secondly, it does not depend upon the initial population density as long as the equilibrium and nonequilibrium populations have the same initial numbers. This hypothesis was evaluated with experimental data on the flour beetle Tribolium castaneum.