Second-order analysis of spatial clustering for inhomogeneous populations.

Motivated by recent interest in the possible spatial clustering of rare diseases, the paper develops an approach to the assessment of spatial clustering based on the second-moment properties of a labelled point process. The concept of no spatial clustering is identified with the hypothesis that in a realisation of a stationary spatial point process consisting of events of two qualitatively different types, the type 1 events are a random sample from the superposition of type 1 and type 2 events. A diagnostic plot for estimating the nature and physical scale of clustering effects is proposed. The availability of Monte Carlo tests of significance is noted. An application to published data on the spatial distribution of childhood leukaemia and lymphoma in North Humberside is described.     

The regulation of gastrointestinal helminth populations

One quarter of the world's human population suffers infection with helminth parasites. The population dynamics of the ten or so species, which cause disease of clinical significance have been well characterized by epidemiological field survey. The parasites are in general highly aggregated between hosts, and their populations seem to be temporally stable and to recover rapidly from perturbation, including interventions designed to alleviate disease. This paper reviews current understanding of the population regulation of helminth species of medical significance. Both empirical (field and laboratory) and theoretical results are included, and we attempt to interpret the findings in the broader context of the population ecology of free-living species. We begin by considering the evidence for regulation from field data concerning the temporal stability of helminth populations within communities and from the results of perturbation experiments. The detection of regulatory processes is then discussed (with regard to statistical and logistical considerations), and the evidence from both the field and laboratory studies reviewed. Deterministic models are described to investigate the possible consequences of regulation imposed at different points in the parasite life-cycle. The causes and consequences of parasite aggregation are considered, and a stochastic model used to investigate the impact of different combination of regulatory processes and heterogeneity generating mechanisms.     

The regulation of the dynamics of human populations

The important aspects of population dynamics are shown in a model along with the changes of population structure, the reasons for these changes and the conditions under which such changes take place. Subsequently, the reasons for these population dynamic processes which can be arranged in a three step scale are shown. Here, it must be differentiated between endogenous processes, due to factors inherent in the population, and exogenous ones caused by external forces effecting structural changes. The population political trends has to be incorporated as a part of the exogenous factors. The questions of regularities in the population dynamics are shown in the examples of important population theories in history. At the same time the theoretically possible borders are described, within which, due to purely physiological reasons, a population dynamic process has to occur. However, these borders will never be reached. Examination of the inertia of the population dynamic processes suggests an examination of the questions about the probability of the self-destructive processes in population dynamics. Considering the strong self-regulatory processes within a population the hypothesis of a population extinction is refuted.     

The natural regulation of Giant tortoise populations on Aldabra Atoll. Reproduction

A two-year reproduction study of three isolated populations of different densities of the Aldabra Giant tortoise ( Geochelone gigantea Schweigger) showed dissimilarity in gonadal parameters; (i) as population density increased age at sexual maturity was delayed in males and females; (ii) although the mean number of mature follicles was similar in all populations, preovulatory follicular atresia was only found in the high density population; (iii) annual variation in preovulatory follicular atresia was dependent on rainfall and food availability; (iv) the number of clutches laid/♀/year decreased with increasing population density as did clutch size; in the high density population (and depending on rainfall) only 30–80% of the mature females bred. The discussion considered the importance of movement in determining survival/reproduction.     

Localization and extinction of bacterial populations under inhomogeneous growth conditions

The transition from localized to systemic spreading of bacteria, viruses, and other agents is a fundamental problem that spans medicine, ecology, biology, and agriculture science. We have conducted experiments and simulations in a simple one-dimensional system to determine the spreading of bacterial populations that occurs for an inhomogeneous environment under the influence of external convection. Our system consists of a long channel with growth inhibited by uniform ultraviolet (UV) illumination except in a small "oasis", which is shielded from the UV light. To mimic blood flow or other flow past a localized infection, the oasis is moved with a constant velocity through the UV-illuminated "desert". The experiments are modeled with a convective reaction-diffusion equation. In both the experiment and model, localized or extinct populations are found to develop, depending on conditions, from an initially localized population. The model also yields states where the population grows everywhere. Further, the model reveals that the transitions between localized, extended, and extinct states are continuous and nonhysteretic. However, it does not capture the oscillations of the localized population that are observed in the experiment.     

Disease regulation of age-structured host populations

A lethal, contagious disease can generate a density-dependent regulation of its host, provided the hosts' contact rate grows with population size. The condition for disease-induced population control is that the expected number of offspring of an infected newborn be less than one. In vertebrates that acquired immunity if they survive infection, the disease changes the age structure of its host population. The steady-state age structure of a disease-regulated host with age-dependent fecundity is computed. Local stability analysis indicates that the equilibrium age structure is always stable. However, when the usual exponentially distributed duration of the disease is replaced by a constant duration, the population can exhibit oscillations with a long period.     

Cytokine-modulated regulation of helper T cell populations

Helper T (Th) cells are a crucial component of the adaptive immune system and are of fundamental importance in orchestrating the appropriate response to pathogenic challenge. They fall into two broad categories defined by the cytokines each produces. Th1 cells produce interferon- gamma and are required for effective immunity to intracellular bacteria, viruses and protozoa whereas Th2 produce IL-4 and are required for optimal antibody production to T-dependent antigens. A great deal of experimental data on the regulation of Th1 and Th2 differentiation have been obtained but many essential features of this complex system are still not understood. Here we present a mathematical model of Th1/Th2 differentiation and cross regulation. We model Fas-mediated activation-induced cell death (AICD) as this process has been identified as an important mechanism for limiting clonal expansion and resolving T cell responses. We conclude that Th2 susceptibility to AICD is important for stabilizing the two polarized arms of the T helper response, and that cell-cell killing, not suicide, is the dominant mechanism for Fas-mediated death of Th1 effectors. We find that the combination of the anti-proliferative effect of the cytokine TGF- beta and the inhibiting influence of IL-10 on T cell activation are crucial controls for Th2 populations. We see that the strengths of the activation signals for each T helper cell subset, which are dependent on the antigen dose, co-stimulatory signals and the cytokine environment, critically determine the dominant helper subset. Switches from Th1- to Th2-dominance may be important in chronic infection and we show that this phenomenon can arise from differential AICD susceptibility of T helper subsets, and asymmetries in the nature of the cross-suppressive cytokine interactions. Our model suggests that in some senses a predominantly type 2 reaction may well be the "default" pathway for an antigen-specific immune response, due to these asymmetries.     

The natural regulation of buffalo populations in East Africa: III. Population trends and mortality*

Analysis is carried out on the population data obtained from censuses and estimates of fertility and recruitment for the years 1965–1972, From the analysis, adult mortality is the only detectable reduction which acts as a negative feedback on the population, and is the only one needed to regulate the population in a way similar to the observed population trends. From a frequency distribution of ages at death, an approximate composite life table is constructed. This shows that males and females have similar age-specific mortalities until old age, but then males survive relatively better. Information on the causes of mortality indicate that the regulating adult mortality is caused in part by undernutrition, which in turn is due to food limitation rather than to social and physiological factors. Predation causes only a small part of the annual adult mortality, and its effect is swamped by other factors. Diseases play an important part as a primary factor in juvenile mortality but not in adult mortality because of the development of immunity. However, both disease and predation are important as secondary agents killing adults already weakened by moderate undernutrition. It is suggested that they play an essential role by hastening the population's response to changes in the food supply, and hence dampening oscillations that might develop in population and resource.     

Density-dependent regulation of natural and laboratory rotifer populations

Density-dependent regulation of abundance is fundamentally important in the dynamics of most animal populations. Density effects, however, have rarely been quantified in natural populations, so population models typically have a large uncertainty in their predictions. We used models generated from time series analysis to explore the form and strength of density-dependence in several natural rotifer populations. Population growth rate (r) decreased linearly or non-linearly with increased population density, depending on the rotifer species. Density effects in natural populations reduced r to 0 at densities of 1–10 l^–1 for 8 of the 9 rotifer species investigated. The sensitivities of these species to density effects appeared normally distributed, with a mean r=0 density of 2.3 l^–1 and a standard deviation of 1.9. Brachionus rotundiformis was the outlier with 10–100× higher density tolerance. Density effects in laboratory rotifer populations reduced r to 0 at population densities of 10–100 ml^–1, which is 10⁴ higher than densities in natural populations. Density effects in laboratory populations are due to food limitation, autotoxicity or to their combined effects. Experiments with B. rotundiformis demonstrated the absence of autotoxicity at densities as high as 865 ml^–1, a much higher density than observed in natural populations. It is, therefore, likely that food limitation rather than autotoxicity plays a major role in regulating natural rotifer populations.     

The natural regulation of buffalo populations in East Africa: II. Reproduction,recruitment and growth*

Aspects of the seasonality of breeding, age-specific fertility, and growth were studied in a sample of animals collected from the Serengeti buffalo population, and compared with two populations in Uganda. Fluctuations in fertility and recruitment were studied by the use of regular aerial photographic samples of herds in the Serengeti. The fluctuations in fertility rate were not related to density and hence could not have regulated the population. Buffalo show a pronounced seasonality in births which is correlated with the quality of ingested food and with rainfall. Since the female has a considerably higher food requirement during late pregnancy and lactation, nutrition is probably an important factor determining this seasonality. Conception does not appear to be influenced by nutrition, for the quality of food remains high throughout the rainy season prior to and during the period of conception. Growth rate, age of first ovulation, and age of sexual maturity do not appear to differ between the Serengeti and Uganda populations. Although there is little difference in fertility between these populations, as measured from the collected samples, little weight can be placed on this evidence, for large fluctuations in fertility can take place from year to year within a population. The fluctuations in the Serengeti population do not appear to be correlated with rainfall, and it is possible that they are random. Fluctuations in recruitment from year to year are also observed. Two sample areas over 100 km apart but within the same population show parallel fluctuations suggesting a similar external influence on the size of the recruitment. This recruitment is not correlated with population size but it may be related to rainfall. Underweight calves at birth have been recorded and this may have been caused by the undernutrition of pregnant females during the dry season through a combination of poor food supply and the demands of the previous lactation.     

Hormonal regulation of proliferation in two populations of rabbit endometrial cells in culture.

We have previously described a technique to culture rabbit primary endometrium epithelial cells in chemically defined medium, whose proliferation was determined to respond to estrogens and progesterone. The cultures were found to be made up of two cell populations: quiescent and dividing cells. We describe here techniques to select for these two cell populations using ³H-thymidine and cytosine arabinoside or Colcemid. The quiescent cells were found to be the only target for the growth-promoting effect of estrogens. Epidermal growth factor and prostaglandin F-2α stimulated the proliferation of both cell populations. Progesterone was found not to antagonize the effect of estrogen on the quiescent cells unless the hormone was incubated previously with a mixed cell culture. This finding suggests the existence of a progesterone putative factor (PPF) resulting from the interaction of progesterone and dividing cells which is involved in the inhibition of the estrogenic effect on endometrial cell proliferation. Two other progestins were not found to have the same effect as progesterone, showing the specificity of this ovarian hormone action.     

Fluctuations and regulation of wheat-bulb fly populations at Rothamsted

Four populations of the wheat-bulb fly studied at Rothamsted incurred substantial and regulatory losses of larvae caused by food shortage. The following hypothesis is proposed to explain population changes of the fly. Fluctuations caused by weather are stabilized by density-dependent larval mortality caused by food shortage. The effect of weather is, however, pervasive as it also affects food shortage by influencing the number of shoots available to larvae.     

Moose-wolf dynamics and the natural regulation of moose populations

Summary In southwestern Québec, non-harvested moose populations stabilize at a density of 0.40 animal·km^-2. In an attempt to test whether or not moose were regulated by predators, we investigated wolf predation near this equilibrium density (0.37) and at 2 lower densities (0.23, 0.17). Scat analysis in summer and feeding observations in winter indicated a greater use of alternative food resources by wolves at lower moose densities. Each wolf pack killed on average 5.3, 1.8, 1.1 moose·100 days in the area of 0.37, 0.23, and 0.17 moose·km^-2, respectively. Consumption of moose per wolf was 2.8, 1.7, and 1.6 kg/day, respectively. January wolf densities were estimated at 1.38, 0.82, and 0.36 animals·100 km^-2, respectively. Year-long predation rates proved to be density-dependent, increasing with moose density from 6.1 to 19.3% of the postnatal populations. We conclude that moose populations in southwestern Québec are regulated largely by predators (wolves and maybe black bears) at a density where competition for forage produces no detrimental effect. We support the concept that wolf predation can have an important regulatory effect at low moose densities but also a depensatory (inversely density-dependent) effect at higher densities.     

Alternative mechanisms for homeostatic regulation of mammalian cell populations

A model for homeostatic regulation in mammalian tissues is analyzed. The model treats resting and active dividing cells, immature and mature non-dividing cells as separate populations. In the model, regulation is accomplished through control of the proportion of newly-formed cells that will become non-dividers. Four possible regulating substances, produced by dividing cells, non-dividing cells, mature non-dividing cells, and newly-formed cells respectively, are considered. Stability theorems are provided. System behavior in each instance depends on the relative values of the rate at which cells divide and the rate at which non-dividers die.     

The economic consequences of ageing populations.

The effect of low birth rates and lengthening lives on the economy is discussed. Two extreme cases are examined: where pensions are entirely on a pay-as-you-go basis, and where they are entirely funded. It is argued that the economy would grow faster in the latter case. The impact on the levels of consumption of each age cohort during its lifetime is assessed. The possible magnitude of changes in consumption as a result of an increase in the retired part of the population is illustrated. It is shown that, comparing later cohorts to earlier cohorts, the former are better off under a funded system. An argument is then sketched showing that a pay-as-you-go system favours earlier cohorts too much; while most probably, but not certainly, a fully funded system favours the later cohorts excessively. It is claimed that a gradual introduction of partial funding, and some increase in the length of working lives, can deal with the effects of an ageing population without an excessive burden on any cohort or age-group.     

Studies on bacterial conjugational crosses via model populations. I. The model populations

A procedure is presented in which model populations, simulating progenies obtained from Escherichia coli Hfr x F- crosses, are generated. The procedure seems to be appropriate for visualizing hidden features of the genetic analysis, which are not detected by the conjugational crosses.     

Explaining density-dependent regulation in earthworm populations using life-history analysis

At present there is little knowledge about how density regulates population growth rate and to what extent this is determined by life-history patterns. We compared density dependent population consequences in the Nicholsonian sense based on experimental observations and life-history modeling for the earthworms Lumbricus terrestris and Eisenia fetida . Both species differ in their life-histories, L. terrestris being a relatively long-lived species with slow reproduction and occurring at low densities compared to E. fetida which has a more opportunistic strategy with a high reproductive output. E. fetida is able to colonise new habitats rapidly and may occur at relatively high population densities. Density dependency of population growth rate was estimated by incorporating density dependent effects on reproduction and growth using a modified Euler equation. The results point out that E. fetida was not as strongly impacted by density as compared to L. terrestris . Population growth rate in E. fetida was hardly affected at low and moderate density, being reduced only at high level, this compares to L. terrestris where even relatively small density effects resulted in a strong negative effect on population growth rate. Our findings indicate that density-dependent regulation in earthworms can be quantified using life-history analysis. The outcomes are in agreement with empirical field observations for populations (i.e. L. terrestris occurs ar low density, E. fetida at high density). Consideration of the potential importance of Nicholsonian density dependence for field populations of these two species in light of their known biology however produces counterintuitive conclusions. In E. fetida , although density tolerant, rapid population growth may mean this species may be subject to density dependeny regulation. In L. terrestris , although density sensitive, complex behavioural ecology (surface activity, territoriality) may limit of feedback influence on population size.