Estimating transition probabilities of singly and doubly stochastic matrices

Vector quadratic programming techniques, based on the classical theory of vector quadratic forms, subjected to linear restrictions, minimization techniques are applied to the estimation of the transition probabilities of singly and doubly stochastic matrices.     

Alternative life-history pathways and the elasticity of stochastic matrix models

Loop analysis is a powerful tool for analyzing matrix population models. This note shows that the results of loop analysis, which have been proved for constant matrices only, apply to stochastic matrices as well if elasticity is defined as the effect of a proportional perturbation of both mean and variance. Using the ideas of loop analysis, it is shown that the structure of the stochastic matrix in terms of alternative life-history pathways has important consequences for the effect of stochasticity on elasticities. If the life cycle contains nonoverlapping, alternative life-history pathways, the ranking in terms of elasticity of the most critical vital rates may be reversed in stochastic and the corresponding average environments. This has obvious and important consequences for population management because focusing on a deterministic model would lead to an ineffective or counterproductive management strategy.     

Convergence to stationary distributions in two-species stochastic competition models

Two sets of sufficient conditions are given for convergence to stationary distributions, for some general models of two species competing in a randomly varying environment. The models are nonlinear stochastic difference equations which define Markov chains. One set of sufficient conditions involves strong continuity and -irreducibility of the transition probability for the chain. The second set has a much weaker irreducibility condition, but is only applicable to monotonic models. The results are applied to a stochastic two-species Ricker model, and to Chesson's lottery model with vacant space, to illustrate how the assumptions can be checked in specific models.     

Dose-effect correlations in a stochastic function of cell reactivity

A random reactivity function involving a correlation between "refusal" probabilities in cells irradiated with various doses was estimated. The dose-effect curves were obtained for this reactivity function and their behaviour in the simplest correlation functions was analyzed.     

Variability and correlations in muskmelon in relation to the cultivation method

Summary Six fruit characters have been measured in 23 cultivars of Cucumis melo, representing a wide geographical range. Plants were grown both in the greenhouse and in the field. When the 23 cultivars were analyzed together, the largest component of variance was found between cultivars under both growth conditions, suggesting the existence of large genetic diversity for all the characters studied. Generally, variance between plants within cultivars was less than or equal to variance between fruits within plant. This indicates that environmental variation is the most important part of the variation within cultivars. Correlations between pairs of characters at cultivar, plant and fruit levels were calculated from the variance-covariance components. In the majority of paired traits, the correlation values indicated that genetic and environmental factors may act in the same direction.     

Deterministic limits to stochastic spatial models of natural enemies

Stochastic spatial models are becoming an increasingly popular tool for understanding ecological and epidemiological problems. However, due to the complexities inherent in such models, it has been difficult to obtain any analytical insights. Here, we consider individual-based, stochastic models of both the continuous-time Lotka-Volterra system and the discrete-time Nicholson-Bailey model. The stability of these two stochastic models of natural enemies is assessed by constructing moment equations. The inclusion of these moments, which mimic the effects of spatial aggregation, can produce either stabilizing or destabilizing influences on the population dynamics. Throughout, the theoretical results are compared to numerical models for the full distribution of populations, as well as stochastic simulations.     

Fitting parameters of stochastic birth-death models to metapopulation data

Populations that are structured into small local patches are a common feature of ecological and epidemiological systems. Models describing this structure are often referred to as metapopulation models in ecology or household models in epidemiology. Small local populations are subject to demographic stochasticity. Theoretical studies of household disease models without resistant stages (SIS models) have shown that local stochasticity can be ignored for between patch disease transmission if the number of connected patches is large. In that case the distribution of the number of infected individuals per household reaches a stationary distribution described by a birth-death process with a constant immigration term. Here we show how this result, in conjunction with the balancing condition for birth-death processes, provides a framework to estimate demographic parameters from a frequency distribution of local population sizes. The parameter estimation framework is applicable to estimate parameters of disease transmission models as well as metapopulation models.     

Importance of morpho-clinical correlations in the diagnosis of congestive cardiomyopathies

A morphologic score was performed in 17 myocardial biopsy specimens proceeding from patients with congestive cardiomyopathies. The electron microscopic changes were estimated according to their frequency and severity. According to this score, the morphological findings were compared with the clinical data and some echographic indexes of the myocardial contractility. These correlations turned out to be of great value in estimating the prognosis of these patients and allowed to set up three different stages of evolution in the congestive cardiomyopathies.     

Hemoglobin transition in relation to metamorphosis in normal and isogenicXenopus

Summary Electrophoretic separation of hemoglobins of normalXenopus laevis and of isogenic animals derived from female hybrids ofXenopus laevis×Xenopus gilli revealed 5–9 components in premetamorphic larvae, and 3–4 components in adult toads. InXenopus laevis the number of larval hemoglobin components showed considerable variation, but this variation was absent in isogenic tadpoles, suggesting a genetic basis for hemoglobin polymorphism in larvae.Electrophoretic separation of larval and adult hemoglobins at different concentrations of acrylamide and treatment of these solutions with mercaptoethanol revealed that larval hemoglobin components are charge isomers, whereas adult hemoglobin was found to contain a minor dimeric component.Estimation of hemoglobin components showed that the main increase in adult hemoglobin, i.e from 30–90% of total hemoglobin, occurs within 4 weeks after completion of metamorphosis. By incroporation of³H amino acids in vivo a switch to preferential synthesis of adult hemoglobin and a corresponding decrease in larval hemoglobin production could be demonstrated during early climax stages. This suggests that thyroid hormones are involved in the hemoglobin transition. Yet chemical inhibition of the larval thyroid by thiourea resulted in a delayed but complete hemoglobin transition without morphological transformation. It is concluded that hemoglobin transition and morphological transformation of theXenopus tadpole require different concentrations of thyroid hormones.Abbreviations Hb hemoglobin - Hb_A adult hemoglobin - Hb_L larval hemoglobin     

Division of labour and social insect colony performance in relation to task and mating number under two alternative response threshold models

Some social insects exhibit an exceptionally high degree of polyandry. Alternative hypotheses exist to explain the benefits of multiple mating through enhanced colony performance. This study critically extends theoretical analyses of the hypothesis that enhanced division of labour confers fitness benefits to the queen that are sufficient to explain the observed mating frequencies of social insects. The effects of widely varying numbers of tasks and matings were systematically investigated in two alternative computer simulation models. One model was based on tasks that have to be performed to maintain an optimal trait value, while the other model was based on tasks that only have to be sufficiently performed to exceed a minimum trait value to confer full fitness returns. Both model versions were evaluated assuming a broad and a narrow response threshold distribution. The results consistently suggest a beneficial effect of multiple mating on colony performance, albeit with quickly diminishing returns. An increasing number of tasks decreased performance of colonies with few patrilines but not of more genetically diverse colonies. Instead, a performance maximum was found for intermediate task numbers. The results from the two model versions and two response threshold distributions did not fundamentally differ, suggesting that the type of tasks and the breadth of response thresholds do not affect the benefit of multiple mating. In general, our results corroborate previous models that have evaluated simpler task/patriline scenarios. Furthermore, selection for an intermediate number of tasks is indicated that could constrain the degree of division of labour. We conclude that enhanced division of labour may have favoured the evolution of multiple mating but is insufficient to explain the extreme mating numbers observed in some social insects, even in complex task scenarios.     

The use of Markovian metapopulation models: a comparison of three methods reducing the dimensionality of transition matrices

The use of Markovian models is an established way for deriving the complete distribution of the size of a population and the probability of extinction. However, computationally impractical transition matrices frequently result if this mathematical approach is applied to natural populations. Binning, or aggregating population sizes, has been used to permit a reduction in the dimensionality of matrices. Here, we present three deterministic binning methods and study the errors due to binning for a metapopulation model. Our results indicate that estimation errors of the investigated methods are not consistent and one cannot make generalizations about the quality of a method. For some compared output variables of populations studied, binning methods that caused a strong reduction in dimensionality of matrices resulted in better estimations than methods that produced a weaker reduction. The main problem with deterministic binning methods is that they do not properly take into account the stochastic population process itself. Straightforward usage of binning methods may lead to substantial errors in population-dynamical predictions.     

Importance of Photobacterium phosphoreum in relation to spoilage of modified atmosphere-packed fish products

Occurrence and growth of Photobacterium phosphoreum were studied in 20 experiments with fresh fish from Denmark, Iceland and Greece. The organism was detected in all marine fish species but not in fish from fresh water. Growth of P. phosphoreum to high levels (>10⁷ cfu g⁻¹) was observed in most products and the organism is likely to be of importance for spoilage of several modified atmosphere-packed (MAP) marine fish species when stored at chill temperatures. Some microbiological methods recommended for control of fish products by national and international authorities are inappropriate for detection of psychrotolerant and heat-labile micro-organisms like P. phosphoreum . These methods have been used in many previous studies of MAP fish and this could explain why, contrary to the findings in the present study, P. phosphoreum in general was not detected previously in spoiled MAP fish.     

Behavioral models of the relation of animals to alcohol

Worked out on the outbred white male rats the behavioural models allow to pick out animals with initial alcohol motivation from the intact rats' group and to pick out animals with alcohol dependency and withdrawal syndrome from chronically alcoholized rats' group.