Limit theorems for the population size of a birth and death process allowing catastrophes

The linear birth and death process with catastrophes is formulated as a right continuous random walk on the non-negative integers which evolves in continuous time with an instantaneous jump rate proportional to the current value of the process. It is shown that distributions of the population size can be represented in terms of those of a certain Markov branching process. The ergodic theory of Markov branching process transition probabilities is then used to develop a fairly complete understanding of the behaviour of the population size of the birth-death-catastrophe process.Research done while on leave at Colorado State University from the University of Western Australia and partially supported by N.S.F. grant DMS-8501763     

A stationary distribution for the growth of a population subject to random catastrophes

The problem of the existence of a stationary distribution and the convergence towards it in a certain semistochastic model for the growth of a population is considered. It is assumed that the population grows according to a deterministic equation, but at certain times there are catastrophes, which lead to a decrease in the population level. The hazard function for the occurrence of catastrophes is a function of the population level only. The size of these jumps have a distribution that depends on the population size immediately before the catastrophe. A constructive method for finding the stationary distribution is given.     

Plankton population dynamics: food web interactions and abiotic constraints

1. In this introduction, I try to follow some developments in plankton ecology, how they have led to current research topics, and how the contributions in this issue of Freshwater Biology are related to these fields of research.
2. Due to several favourable features, such as small size, short generation time and a relatively homogeneous habitat, planktonic organisms remain ideal subjects for theoretical and experimental population ecology.
3. Important current research topics involve: (1) the control of plankton communities by external abiotic factors; (2) bottom-up (limitation by resources) and top-down (control by predators) effects in the food web; (3) the importance of dormant resting stages and benthic–pelagic coupling in plankton dynamics; (4) costs and benefits of the mixotrophic strategy, i.e. the ability to combine a phototrophic and a phagotrophic mode of nutrition.     

Variation and seasonal changes in hoverfly species: interactions between temperature, age and genotype

Eristalis tenax L. and E. intricarius L. are two hoverflies which vary considerably in colour pattern. Whilst much of the phenotypic variation in both species is due to genetic variation at major gene loci, there are interactions with pupal temperature and with age of adult. Low pupal temperatures produce, on average, darker abdominal patterns in E. tenax , although the effect is hard to pick out in natural populations. Changes of pattern with age convert a bimodal autumn population to a unimodal post-hibernation population in the following spring. Hair colour is also made darker by cold treatment. Pupal treatments have a strong effect on hair colouration in E. intricarius. High temperatures inhibit the production of black hairs on the thorax, but not all the genotypes are equally sensitive to temperature. Seasonal fluctuations in colour pattern frequencies are detectable in E. intricarius. In three Eristalis species that have been studied so far, the interactions between genotype, age and temperature operate in quite different ways. The temperature responses may be relevant to theories of thermal melanism, although the colour pattern polymorphisms are, more obviously, examples of Batesian mimicry.     

Variation of 15 autosomal microsatellite DNA loci in the Russian population

The allele frequencies of 15 autosomal STR loci (D3S1358, vWA, FGA, TH01, TPOX, CSF1PO, D5S818, D13S317, D7S820, D16S539, D2S1338, D8S1179, D21S11, D18S51, and D19S433) used in forensic medicine were determined for the Russian population of European Russia (N = 176). The power of discrimination (PD) and power of exclusion (PE) of the system of the 15 STR loci were 0.999 999 999 999 999 986 and 0.999 999 331 310 171 000, respectively. The allele and genotype frequency distributions in the Russian population corresponded to the Hardy-Weinberg equilibrium. The D2S1338, D18S51, D21S11, and FGA loci were identified as the most informative markers for the Russian population and proposed as a reference for forensic studies in the Russian Federation.     

Quantifying the outcome of plant–granivore interactions

In many interspecific interactions, the balance of costs and benefits varies with ecological circumstances. As a prominent example, seed‐caching granivores may act as seed predators and reduce plant recruitment or as seed dispersers and increase recruitment, making it difficult to interpret whether differences in seed removal by granivores would harm or benefit plant populations. We used a heuristic model to evaluate the outcome of plant‐granivore interactions, using commonly measured field data: probability of seedling emergence when granivores are excluded, and emergence of cached and uneaten seeds. Published studies to date suggest that the outcome of plant‐rodent interactions tends weakly towards mutualism, but differs among particular plant–granivore pairs and ecological conditions, supporting the notion of context‐dependence. A modeling framework also allowed us to distinguish parameters that affect the qualitative outcome of plant–granivore interactions from those that do not. Similar approaches would facilitate more efficient and cost‐effective evaluation of complex species interactions.     

Variation in the airborne fungal spore population of the Tuscarawas Valley II

For years the medical profession has recognized a relationship between fungal airspora and the incitement of respiratory allergies. An evaluation of outdoor fungal airspora on an eastern Ohio campus during June 1988 revealed significant differences in quality and quantity with respect to microenvironments. Type of vegetation, diurnal periodicities, and daily weather conditions affected the airspora at each site. Shaded lawns within groves and windbreaks, unshaded lawns, and asphalt-covered parking lots presented varying dynamics for fungal spore liberation. Unshaded lawns produced airspora most abundantly during morning and least abundantly during afternoon. Arboreal sites produced airspora most prolifically at midday. A deciduous sycamore grove produced fewer afternoon airspora than evergreen pine and arborvitae stands. Evening airspora at all vegetated sites increased after experiencing afternoon troughs. Frequently encountered molds included Cladosporium spp., brightly pigmented sterile mycelia, and Alternaria spp.     

Variation in plant quality and the population dynamics of herbivores: there is nothing average about aphids

In the attempt to use results from small-scale studies to make large-scale predictions, it is critical that we take into account the greater spatial heterogeneity encountered at larger spatial scales. An important component of this heterogeneity is variation in plant quality, which can have a profound influence on herbivore population dynamics. This influence is particularly relevant when we consider that the strength of density dependence can vary among host plants and that the strength of density dependence determines the difference between exponential and density- dependent growth. Here, we present some simple models and analyses designed to examine the impact of variable plant quality on the dynamics of insect herbivore populations, and specifically the consequences of variation in the strength of density dependence among host plants. We show that average values of herbivore population growth parameters, calculated from plants that vary in quality, do not predict overall population growth. Furthermore, we illustrate that the quality of a few individual plants within a larger plant population can dominate herbivore population growth. Our results demonstrate that ignoring spatial heterogeneity that exists in herbivore population growth on plants that differ in quality can lead to a misunderstanding of the mechanisms that underlie population dynamics.     

Variation in microbial population during composting of agro-industrial waste

Two compost piles were prepared, using two ventilation systems: forced ventilation and ventilation through mechanical turning. The material to compost was a mixture of orange waste, olive pomace, and grass clippings (2:1:1 v/v). During the composting period (375 days), samples were periodically taken from both piles, and the enumeration of fungi, actinomycetes, and heterotrophic bacteria was carried out. All studied microorganisms were incubated at 25 and 55 °C after inoculation in appropriate growth media. Fungi were dominant in the early stages of both composting processes; heterotrophic bacteria proliferated mainly during the thermophilic stage, and actinomycetes were more abundant in the final stage of the composting process. Our results showed that the physical and chemical parameters: temperature, pH, moisture, and aeration influenced the variation of the microbial population along the composting process. This study demonstrated that composting of these types of wastes, despite the prolonged mesophilic stage, provided an expected microbial variation.     

Trophic interactions and population growth rates: describing patterns and identifying mechanisms

While the concept of population growth rate has been of central importance in the development of the theory of population dynamics, few empirical studies consider the intrinsic growth rate in detail, let alone how it may vary within and between populations of the same species. In an attempt to link theory with data we take two approaches. First, we address the question ''what growth rate patterns does theory predict we should see in time-series?'' The models make a number of predictions, which in general are supported by a comparative study between time-series of harvesting data from 352 red grouse populations. Variations in growth rate between grouse populations were associated with factors that reflected the quality and availability of the main food plant of the grouse. However, while these results support predictions from theory, they provide no clear insight into the mechanisms influencing reductions in population growth rate and regulation. In the second part of the paper, we consider the results of experiments, first at the individual level and then at the population level, to identify the important mechanisms influencing changes in individual productivity and population growth rate. The parasitic nematode Trichostrongylus tenuis is found to have an important influence on productivity, and when incorporated into models with their patterns of distribution between individuals has a destabilizing effect and generates negative growth rates. The hypothesis that negative growth rates at the population level were caused by parasites was demonstrated by a replicated population level experiment. With a sound and tested model framework we then explore the interaction with other natural enemies and show that in general they tend to stabilize variations in growth rate. Interestingly, the models show selective predators that remove heavily infected individuals can release the grouse from parasite-induced regulation and allow equilibrium populations to rise. By contrast, a tick-borne virus that killed chicks simply leads to a reduction in the equilibrium. When humans take grouse they do not appear to stabilize populations and this may be because many of the infective stages are available for infection before harvesting commences. In our opinion, an understanding of growth rates and population dynamics is best achieved through a mechanistic approach that includes a sound experimental approach with the development of models. Models can be tested further to explore how the community of predators and others interact with their prey.     

Variation of reproductive traits in a population of the lizard Lacerta vivipara

Variation in reproductive traits (sexual maturity, clutch size, clutch weight, mean egg mass, newborn weight) was studied during a four year period in a population of the live-bearing lizard Lacerta vivipara . Sexual maturity was associated with attaining a minimum body size. Clutch size increased with female body length and litter weight increased with clutch size. A major component of the within year variation in these reproductive traits was attributable to female size. Analysis of successive clutches in individual females indicated that a significant fraction of the variation in litter size, adjusted for female length, was due to consistent differences between individuals. Newborn weight varied within and among litters, but no relations between hatchling mass or mean egg mass in a litter and other traits were detected.
Size-adjusted reproductive performances remained constant during the course of this study, even though environmental conditions (weather factors, food availability) varied annually. Observed among year variations in reproductive characteristics were attributable to differences in the body size distributions of the adult females.     

Hopf bifurcations in multiple-parameter space of the Hodgkin-Huxley equations II. Singularity theoretic approach and highly degenerate bifurcations

In the Hodgkin-Huxley equations (HH), we have identified the parameter regions in which either two stable periodic solutions with different amplitudes and periods and an equilibrium point or two stable periodic solutions coexist. The global structure of bifurcations in the multiple-parameter space in the HH suggested that the bistabilities of the periodic solutions are associated with the degenerate Hopf bifurcation points by which several qualitatively different behaviors are organized. In this paper, we clarify this by analyzing the details of the degenerate Hopf bifurcations using the singularity theory approach which deals with local bifurcations near a highly degenerate fixed point. Received: 23 April 1999 / Accepted in revised form: 24 September 1999