A numerical solution of theVolterra equation for the growth of an animal population accompanying an autotoxic effect

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Contribution from the Department of Fisheries, Faculty of Agriculture, Kyoto University.     

The fitting of the logistic equation to the rate of increase of population density

Though there are many problems on the usefulness of the logistic curve, it may be necessary to examine before discussing these problems whether or not the actual data fit to the theoretical values. It has been clarified in this paper that the relation between the population density and its rate of increase per individual described by the differential equation (1) is represented by a straight line on a finite difference diagram on which N_i+1−N_i/N_i values are plotted against N_i+1. Utilizing this linear relation we may examine the fittness of the logistic curve to the actual data and when it is fitted we may estimate the parameters of the logistic equation by (5) and (6). The result of the application of this method to the experimental populations of azuki bean weevil indicates that the relation between parent and progeny densities fits well to the logistic type as has been proved byFujita andUtida (1953) who utilized the linear reltion between 1/R+2σ and parent density where R is the apparent rate of reproduction and σ is a constant dependent primarily upon the length of adult life (0≦σ≦1).     

The influence of population density on fission and growth of Holothuria atra in natural mesocosms

Investigation of the population dynamics, asexual reproduction (fission) and growth of holothuroids has been impeded by the difficulty of tagging individuals. We conducted the first tests on the interactions between population density, fission and growth of holothuroids in experimental populations placed in natural mesocosms (microatolls) at One Tree Reef (OTR), Great Barrier Reef. Similarly sized Holothuria atra were translocated to the microatolls in low (LDT) and high (HDT) density treatments. We hypothesised that holothuroids in lower density treatments would have more resources per individual and that this would promote higher frequencies of asexual reproduction and smaller individuals. The seasonal pattern of fission was similar in natural (unmanipulated) and experimental populations, with the maximum number of fission products occurring in winter and spring. The overall density of the LDT (0.19 ind. m^- 2) and HDT (0.59 ind. m^- 2) did not vary over time. This ‘steady state’ suggested that some fission products died and that asexual reproduction compensated for overall mortality and emigration. There was no difference in sediment chlorophyll pigments between treatments indicating that the different densities of H. atra did not affect benthic microalgal biomass. The percentage of fission products was greater in the LDT than the HDT but this difference was not statistically significant, providing some support for the hypothesis that H. atra in the LDT exhibit a higher fission rates. At the end of the experiment H. atra in LDT were significantly longer and heavier than in HDT. H. atra surpassed their initial deployment weight and length after 13 months in the LDT by 115.2% and 45.2% respectively and in the HDT 86.9% and 24.6% respectively, changing from the small to the large phenotype known for this species. This differential growth may be linked to habitat stability and high benthic productivity and demonstrates the phenotypic plasticity of holothuroids and potential to achieve ‘Optimum Individual Size’ with respect to environmental conditions. Our results will assist in finetuning conceptual models on asexual reproduction and future experimental studies on the phenomena of fission and plastic growth in holothuroids.     

On the action of population density in the population fluctuation of the flour moth,Ephestia cautella

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Contributions from the Entomological Laboratory, Kyoto University, No. 228.     

Ecological studies on the population of isaza,Chaenogobius Isaza Tanaka,in Lake Biwa,with special reference to the effects of population density upon its growth

1. In order to get the knowledge on the age composition of “isaza” population in Lake Biwa and the effect of population density on growth, monthly distribution of mean body length and mean body weight has been analyzed on the basis of monthly haul by “isazabiki” trawl during 1949 to 1953 and also 1960 to 1965.
2. There is no apparent sex difference in the growth in the first and second years of life.
3. “Isaza” population is composed of two age groups, age 0 and 1 groups (1+fish), the latter occupying by far the greater part in commercial catch.
4. During the growth season fishes of both ages feed mainly on zooplankton, though in winter frequently take chironomid larvae, gammaridae and others in volume.
5. The growth season falls in the period from April to October in both age groups.
6. A considerable yearly variation occurring in growth is in close connection with the fluctuation of population density of all ages.
7. The influence affected by the density of age 1 group is larger than that by age 0 group.

     

On the estimation of insect population by time unit collecting

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Contributions from the Entomological Laboratory, Kyoto University, No. 230.     

Damped oscillation of population density at equilibrium

It has been theoretically assumed that the population density at the equilibrium oscillates with damping from generation to generation. In the adult population of the southern cowpea weevil, Callosobruchus maculatus, it was exemplified. But, it was not so clear in the adult population of the azuki bean weevil, C. chinensis as seen in that of C. maculatus. This difference seems to be due to the scramble type of competition that occurs in larval stage in C. maculatus, instead of in the egg stage as C. chinensis. Comparing with the oscillation from generation to generation obtained in the present experiment to that of Lucilia population found byNicholson , the oscillation in Lucilia population is composed of the cycle in a generation and the descending phase of each cycle of it is not regulated density-dependently. The present result seems to be more appropriate for the demonstration of the theory of self-adjustment of population.     

Estimating the effect of continual disturbances on discrete-time population models

In this paper, methods for estimating the effect of continual (but bounded) disturbances on ecosystems modelled by difference equations are discussed. The approach adopted is to estimate the region of state space (called a reachable set) which can be reached by the disturbed system from an initial healthy state in a given time period. Liapunov stability methods for estimating these reachable sets are presented and applied to two specific population models.     

Post-pleistocene reductions in human dental structure: a reappraisal in terms of increasing population density

This paper discusses the well-documented acceleration which occurred in the reduction of human dental structure during the post-Pleistocene. It suggests that the process can be explained in terms of different but related factors inherent in a transition from late-Pleistocene hunting and gathering conditions to ones involving a sedentary life in larger groups. It is postulated that directional selective forces acting during Upper Paleolithic to maintain large tooth size had only a poor influence and that the new techniques in food preparation had little or no effect. The phenomenon is seen as a possible side-effect of a more complex overall reduction in body size, of which dental reduction only represents a small but demonstrable part. It is also suggested that stresses may have played an important role in producing a transitory reduced dimensional expression of the genetic background. An interaction between the variables directly or indirectly affecting body mass is shown in the model proposed which relates to post-Pleistocene. An increase in population density is indicated as being the most decisive biological factor in determining the acceleration in the trend towards reduction. A preliminary version of this paper was presented at the Symposium on Upper Paleolithic/Mesolithic of Europe and the Mediterranean Basin, Pisa, September 8–10, 1984.     

The effect of wave action on growth in three species of intertidal gastropods

Summary Populations of the limpets Collisella digitalis and C. scabra, as well as the thaidid whelk Nucella (Thais) emarginata, had greater mean shell lengths at a protected site (Tomales Bay) than at an exposed site (Mussel Point) on the California coast near the Bodega Marine Laboratory. To determine the relative importance of wave action as well as genetic differentiation among populations in explaining this pattern, tagged snails of all three species were reciprocally transferred between the two sites. For C. digitalis, total wet mass (tissue plus shell) increased by 34.4% at the protected site, but decreased by 2% at the exposed site over a two and one-half month period. For C. scabra, growth was 43.1% at the protected, and 2.7% at the exposed site, and for Nucella, 9.5% and 1%, respectively. Although some evidence of population differentiation was found, particularly for the direct-developing whelk, source differences in growth were not as large as the site effect. At least for the whelk, absolute differences in barnacle prey abundances did not occur between sites. However, all three gastropods had higher abundances at the exposed site. While factors such as genetic differentiation and competition may partially explain why gastropods are on the average smaller at exposed sites, we suggest that wave action may also play a role, possibly by limiting time available for feeding, and therefore energy available for growth. Although wave action, acting via size-specific mortality, has been suggested to limit the size that consumers can reach on exposed shores, it may also indirectly affect intertidal gastropod populations by altering foraging behavior, growth and life histories.     

Global asymptotic stability of density dependent integral population projection models

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium.     

On the individual variation of several morphological and physiological characters under different environmental conditions

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Contributions from the Entomological Laboratory, Kyoto University, No. 229.