Dynamics of distribution in animal communities: Theory and analysis

Summary Theoretical and analytical problems of the dynamics of distribution and abundance in animal communities were examined. In many communities, species with low abundance and of limited spatial occurrence (i.e., rare species) typically form a conspicuous peak when a frequency distribution of the number of species is constructed with respect to the proportion of sites occupied within an area of distribution. Models of distribution dynamics, including a new model proposed here, were compared with a range of animal community data using a new procedure to assess single- and bi-modal patterns in frequency distributions of spatial occurrence. Data reveal that single-modality with an excess of rare species occurs more frequently than bimodality. Even when bimodality is detected, the mode representing wide-spread species is in the majority of cases smaller than that for rare species. Thus, a new model in which the rate of local extinctions is assumed to be negatively related to patch occupancy (or population abundance) is in better agreement with observed data than earlier models. Some problems of analysis, in particular model assumptions and testing, are discussed.     

A model of the species rank-abundance relation for a community in an open habitat

Summary A mathematical model is proposed to describe the relationship between the abundance and the rank of species in order from the most abundant to the least in a community in an open habitat. This model is derived as a corollary of a species-area equation (Kobayashi, 1975) which could be expected in the case where the individuals of each species are uniformly distributed over a habitat area. Numerical simulation reveals that a rank-abundance curve for a universe results in different species-area or species-individual curves according to the spatial distribution of individuals, and that the relative abundance of each species in a sample varies with sample size unless the spatial distribution of individuals is uniform. A species-individual curve obtained bySanders’s (1968) rarefaction method agrees with that observed actually only for the spatially uniform distribution. Change in the pattern of rank-abundance curve with species diversity and with sample size is discussed in relation to the present model.     

Simultaneous estimation of mortality and dispersal rates of an artificially released population

Mark-recapture methods cannot estimate both mortality and dispersal rates of a wild population simultaneously. However, when an artificially cultured population is released into an area, the initial population size and the initial population distribution are usually known. If artificially cultured individuals are released with marks or distinguished from wild individuals or if no wild individual exists in the study area, we can estimate both the mortality and dispersal rates of the artificial population. The numbers of dispersed and dead individuals are estimated from the dispersal rate from the diffusion model and the total decreasing rate estimated from a mark-recapture data. We can estimate both the time-dependent and time-independent dispersal rates from the data. We choose the best fit model that has the smallest value of Akaike's Information Criteria. We also consider ‘concentric circles approximation” of spatial distribution, in which the cumulative and frequency distributions are analytically obtained.     

Seasonality parameters for insect populations

Summary The usefulness of a number of parameters is investigated for describing the seasonal variability in insect populations, especially in relation to sample size. It is found that Seasonal Niche Breadth (B) and its maximal value (BM) are useful only for large samples. For smaller samples one tends to find the same values for these parameters whatever the distribution they are supposed to describe. The “standardized” ratio of these two parameters (B/BM) is completely useless. The Season Length (S. L.), defined as 52 minus the longest series of weeks in which the species was absent, or not observed, was found to be quite useful, especially at smaller sample sizes. For species which occur over a large part of the year and have been observed in large numbers, the ratioMin/Max is found to be quite useful. This is the number of individuals during the four weeks at the low point of the season divided by the number observed during the four weeks in the peak of the season. It is suggested that the seasonal distribution be estimated usingS. L. or, when appropriate,Min/Max in order to estimate the Seasonal Standard Deviation (SSD), which assumes a normal seasonal distribution. With thisSSD the 99 per cent range (Seasonal Range) can be calculated to characterize the seasonal distribution. With this Seasonal Range different species or different areas can profitably be compared in their seasonality characteristics even if there is a large difference in sample size.     

Population fluctuation and persistence of one-host–two-parasitoid systems depending on resource distribution: from parasitizing behavior to population dynamics

Population dynamics and variability were examined in one-host–two-parasitoid experimental systems with different resource distributions: resource-clumped and resource-sparse conditions. The system consists of a seed beetle host, Callosobruchus chinensis, and two parasitoid wasps, Anisopteromalus calandrae (Pteromalidae) and Heterospilus prosopidis (Braconidae). In the resource-clumped condition, suitable hosts for parasitism (the late fourth-instar larvae and pupae) were clumped in 1 large resource patch, but they were scattered evenly among 16 small patches in the resource-sparse condition. Population censuses were conducted at 10-day intervals in long-term cultures, renewing 10 g of azuki beans (Vigna angularis). In both resource conditions, the first period was a single-species system of C. chinensis only, and A. calandrae was added in the second period. The one-host–one-parasitoid system with C. chinensis and A. calandrae showed stable population dynamics with small fluctuations. After addition of H. prosopidis in the third period, two of three replicates persisted to day 800 in each resource condition, although one replicate in each went to extinction at an immediate outbreak of the H. prosopidis population after the introduction. Population variabilities of C. chinensis and H. prosopidis were significantly higher and the mean population size of A. calandrae was significantly smaller in the resource-sparse condition than that in the resource-clumped one. A short-term experiment on parasitism efficiencies revealed that H. prosopidis parasitized significantly more at a low host density in the resource-sparse condition than in the resource-clumped one. Mutual interference of H. prosopidis was weak enough at low parasitoid densities but became abruptly stronger with high densities. Providing fresh hosts in a mixture of already parasitized ones, host-searching behaviors of a parasitoid were recorded by video for 3 h and were compared between the two wasp species. H. prosopidis could parasitize fresh hosts more efficiently than A. calandrae through frequent long-distance walks (walking to distant beans at one bout or outside a clump of beans with hosts and back soon on a distant bean of the clump) after reencounters with parasitized hosts. Considering all the experimental results, populations were judged to be more fragile and more likely to go to extinction in the resource-sparse condition than in the resource-clumped one. A higher attacking efficiency of H. prosopidis destabilized population dynamics more in the resource-sparse condition. Received: December 23, 1998 / Accepted: January 20, 1999     

Biogeographical history of northeastern Asiatic soricine shrews (insectivora, mammalia)

A hypothetical biogeographical history of northeastern Asiatic soricine shrews in the late Quaternary was developed by integrating their present distributions, fossil records, a hypothetical phylogeny, and geological investigations. First, a biological area cladogram of the northeastern Asiatic region was constructed by applying the vicariance hypothesis to the phylogeny of thecaecutiens/shinto group, a monophyletic group proposed by Ohdachi et al. (1997). Comparing the biological area cladogram with a geological hypothesis by Ohshima (1990,1991,1992), we hypothesized a geographical history of northeastern Asia. Species were then located on the dendrogram of the geographical history, referring to the present distributions, fossil records, and phylogeny of shrews. According to our hypothesis, higher species diversity of the northern region of northeastern Asia (Hokkaido, Sakhalin, and Eastern Siberia) was achieved by several series of colonizations and habitat expansion. On the other hand, the shrew communities of the southern region (Honshu, Sado, Shikoku, and Kyushu) were created by extinction and isolation followed by speciation.     

A likelihood ratio test for equality of deviations from randomness

The use of the sample variance-to-mean ratio as a measure of deviation from randomness in spatial pattern is reviewed. The likelihood ratio method of constructing a statistical test for the equality of several population variance-to-mean ratios is described, and details are provided for the special case where counts are modelled as arising from a negative binomial distribution. This test is illustrated by application to example data sets in ecology. Likelihood ratio tests represent a general methodology whereby relationships among several indices of aggregation can be systematically investigated, provided one is able to specify a suitable parametric form for the underlying distributions.     

Niche modification and stability of competitive systems. II. Persistence of interspecific competitive systems with parasitoid wasps

Summary Effects of niche shift in ecological time scale on the population dynamics of competing species were studied in the experimental populations of two parasitoid wasp species,Anisopteromalus calandrae andHeterospilus prosopidis (both are solitary parasites), on a host, the azuki bean weevil,Callosobruchus chinensis. Four resource conditions were set up with combination of kind of bean (azuki or black eye), and host distribution (uniform or clumped). In each resource condition, four developmental stages of hosts were provided as a resource spectrum for parasitoid wasps. Population dynamics of the two wasp populations were investigated in each resource condition in Multi-Generation Competitive Systems (MGCS), in which fresh hosts of four developmental stages were periodically introduced and were parasitized competitively by the two wasp species. Competitive coexistence of both wasps occurred in the azuki-clumped condition, where the peaks of the resource utilization curves separated in the two species; pupae inA. calandrae and the early or late fourth instar inH. prosopidis, A. calandrae was eliminated in the azuki-uniform condition andH. prosopidis went extinct in two black eye conditions irrespective of host distributions. The degrees of overlap of the resource utilization patterns of the two wasp species during population dynamics were not significantly different among resource conditions irrespective of the results of coexistence or extinction. Even in the azuki-clumped condition, however, extinction ofA. calandrae was observed when resource partitioning could not be realized with only the late fourth instar larvae available to wasps. Further analytical experiments showed that parasitizing ability ofA. calandrae increased with host density per bean with azuki beans, butA. calandrae could express higher parasitizing ability with black eye beans thanH. prosopidis irrespective of host density per bean. The flexibility in parasitizing ability byA. calandrae for various host stages under different resource conditions was thought to be the major factor in determining the competitive coexistence or the extinction of either species under different resource conditions. The present experiments also suggested that different second-best host stages between competitors could be a major contributing factor to competitive coexistence.     

Numerical Simulation of Population Distribution in China

A model for simulating population distribution (MSPD) of China is developed based on the grid generation method and the Control of MapObjects of geographical information system. Elevation, net primary productivity, land use and land cover, city sizes and their spatial distribution, and spatial distribution of transport infrastructures are taken into full account in the MSPD. The result from the MSPD shows that in 2000, 90.8% of the total population of China distributed on the southeastern side of the Heihe-Tengchong line. The ratio of population on the northwestern side to total population of China has been increasing since 1935. The yearly growth rate was 0.8% from 1935 to 1990 and 6.1% from 1990 to 2000. One important advantage of the MSPD is that when scenarios of land cover, spatial distributions of transport infrastructures and cities are available, scenarios of spatial population distribution can be developed on the basis of total population forecast.     

The temporal and spatial dynamics of city-size distributions in China

Under the communist regime, the Chinese government has developed policies both to limit the growth of large cities and to promote spatial equity in population distribution. The literature provides only very general and inconclusive results regarding the impact of these policies. This paper aims at evaluating the effectiveness of China's urban policies by investigating the temporal and spatial dynamics of the size distribution of China's cities during the period 1922–82. The research framework — which is based on a function relating population size to rank —is used to test for trends of deconcentration (where smaller cities grow faster than larger cities) and spatial decentralization (with a more even spatial distribution) of population over the study period. More formally, the ‘expansion methodology’ is used to investigate the dynamics of the rank-size function in both temporal and spatial dimensions. The findings show that from 1953 to 1970 there was significant population deconcentration, which appeared to be reversed subsequently. However, policies of spatial decentralization were not found to be successful. Among the reasons suggested for the apparent failure are political upheavals and shifts in policies, the inertia within the urban system, the harsh physical environment in the interior, and current trends in economic policies that focus on the coastal areas. In spite of recent criticisms of studies on city-size distributions (which this paper also discusses), the research framework proposed and utilized here is able to portray the dynamics of a national urban system, and the framework can be used to evaluate national urban policies.     

Female size and age-specific fecundity in the small white butterfly,Pieris rapae crucivora Boisduval (Lepidoptera: Pieridae)

Summary Individual differences in several reproductive parameters of femalePieris rapae were investigated in a controlled laboratory condition. Lifetime and age-specific fecundity showed considerable variability between individuals. Larger females began oviposition at an earlier age than smaller ones, and larger females were more fecund than smaller ones. Larger females laid a larger proportion of their eggs in the early stages of their reproductive lifetime, whilst smaller females laid the larger proportion of their eggs later in their reproductive lifetime. The significance of the variance in age-specific fecundity associated with female size is discussed with respect to the seasonal change in size and habitat utilization of this species.     

Decomposition of an aggregate measure of income distribution

Aggregate Gini coefficients, which are measures of the inequality of the distribution of income, can be decomposed in terms of types of income, provided the constituent coefficients are defined over family units ordered according to their total income. This decomposition provides a valuable means of examining cyclical shifts affecting income equality. However, other decompositions associated with specific socio-economic or demographic criteria are shown to yield collective expressions which contain both the distributional coefficients for the particular subgroups into which the population is classified, and significant interaction terms. These interaction terms prevent the identification of a clear relationship between the overall distribution of income and the distribution of income for each of the specified subgroups. Further research in this area should focus on distributions within structurally homogeneous groups, using informal procedures for linking these distributions to form impressions of aggregate developments.     

The dynamics of outbreaks: Further simulation experiments with the western tent caterpillar

Summary A stochastic model of western tent-caterpillar populations on southern Vancouver Island was used to assess conditions leading to outbreaks. Three qualitatively different populations-declining, minimal, and recovering-were exposed to six-year climatic sequences incorporating various combinations of good, bad, and mediocre spring weather. Starting populations were either distributed randomly or concentrated in and around small-, medium-, or large refuges. The results showed that virtually any type of population could temporarily increase in numbers during two highly favorable springs. Only a very few vigorous populations, however, could sustain the momentum required to surge to outbreak proportions. No low-quality population could do so. And even vigorous populations could not achieve outbreak status unless they were initially concentrated in a sufficiently large refuge that was close enough to potentially suitable habitats to permit rapid immigration into such places as soon as their local climates improved. The concept of “climatic release” of insect populations is discussed in the light of these findings. The results demonstrate that climatic release is inextricably linked with a population's qualitative profile and spatial distribution. Order of authorship determined by chance.     

The species-area relation I. A model for discrete sampling

Summary A simple mathematical model describing the species-area relation was developed. This paper dealt with the case that discrete random samples are combined. Modelling was made on the assumption that the occurrence probability of a species in a quadrat has a continuous density distribution. The model, given by the equation (6), holds only for a particular size of quadrat (i.e. the characteristic area). More general form applicable to the quadrats the size of which is near to the characteristic area was represented by the equation (9). Validity of the model was examined for the data of plant and insect communities, and it was concluded that the observation can be predicted by the model unless the size of sampling unit considerably differs from the characteristic area. The uniformity of specific density (i. e. the number of species per quadrat) and the size of characteristic area were discussed as being important in an understanding of community structure. Contributions from JIBP-CT No. 144.     

Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

Estimation of Exposure Time Distributions

In many demographic analyses, such as the assessment of environmental cancer risks, one may be interested not only in the age-by-state distribution of the population but also in the distribution of the population by time spent in a given state. States can represent geographic areas, marital statuses, labor force participation, or states of epidemiologic exposure. Recursive formulas for the calculation of the distribution of the population according to exposure time are derived under time-invariant state transition rates. Although populations can have identical growth rates and identical age-by-state distributions, they can have very different distributions by exposure time. An application to the analysis of carcinogenic exposure states is given, using data from Finland. The effect of population heterogeneity on the estimated exposure time distributions is studied.     

Modeling distances between humans using Taylor’s law and geometric probability

Taylor’s law states that the variance of the distribution of distance between two randomly chosen individuals is a power function of the mean distance. It applies to the distances between two randomly chosen points in various geometric shapes, subject to a few conditions. In Réunion Island and metropolitan France, at some spatial scales, the empirical frequency distributions of inter-individual distances are predicted accurately by the theoretical frequency distributions of inter-point distances in models of geometric probability under a uniform distribution of points. When these models fail to predict the empirical frequency distributions of inter-individual distances, they provide baselines against which to highlight the spatial distribution of population concentrations.     

Aggregation pattern of individuals and the outcomes of competition within and between species: Differential equation models

Summary The influence of spatial distribution pattern on the outcomes of intra- and interspecific competition is studied theoretically. The models developed are the generalized logistic andVolterra equations, whereLloyd’s indices of intra- and interspecies mean crowding were incorporated with their assumed linear relationship to mean density in order to express the intensity of crowding which is really effective to the existing individuals. It is shown that while the increasing patchiness of distribution has a pronounced effect of promoting the intraspecific competition and lowering the equilibrium density for individual populations, it generally relaxes the interspecific competition, making it easy for different species sharing the same niche, which would otherwise be incompatible, to coexist stably. These models thus provide a simplest theoretical basis to explain why many insect populations in nature are kept relatively rare in number and why a number of allied species often coexist freely sharing the same resource, against the “competitive exclusion principle” deduced from the originalVolterra equations.     

Competition and evolutionary stability of plants in a spatially structured habitat

We modelled the population dynamics of two types of plants with limited dispersal living in a lattice structured habitat. Each site of the square lattice model was either occupied by an individual or vacant. Each individual reproduced to its neighbors. We derived a criterion for the invasion of a rare type into a population composed of a resident type based on a pair-approximation method, in which the dynamics of both average densities and the nearest neighbor correlations were considered. Based on this invasibility criterion, we showed that, when there is a tradeoff between birth and death rates, the evolutionarily stable type is the one that has the highest ratio of birth rate to mortality. If these types are different species, they form segregated spatial patterns in the lattice model in which intraspecific competitive interactions occur more frequently than interspecific interactions. However, stable coexistence is not possible in the lattice model contrary to results from completely mixed population models. This clearly shows that the casual conclusion, based on traditional well mixed population models, that different species can coexist if intraspecific competition is stronger than interspecific competition, does not hold for spatially structured population models.     

The changing spatial distribution and concentration of Australias chinese and Vietnamese communities: An analysis of 1986–2006 Australian population census data

This paper describes the changing spatial distribution and concentration of Chinese and Vietnamese communities in Australia over the two past decades. The research analyses data of individuals (i) born in the People’s Republic of China or Vietnam, (ii) of Chinese or Vietnamese ancestry, and (iii) who spoke Chinese or Vietnamese languages at home. Basic demographic and economic factors at the SLA level are considered to provide an initial discussion of meso-level factors which may have contributed to changes in Chinese-and Vietnamese-Australian distributions and concentrations since 1986. As expected, from field observations, the data reveal a contrasting picture of the spatial distribution and concentration of the Chinese- and Vietnamese-Australian communities, and indicate that although a few areas of high Vietnamese spatial concentration have persisted into 2006, and a few areas of high’ Chinese spatial concentration have developed since 1986, overall there is an increasing dispersion of both communities into the broader Australian community.