The species-area relation III. A third model for a delimited community

A mathematical model of the species-area relation is described for a group of limited species. This model is a modification of that proposed earlier (Kobayashi, 1975), being assumed that the limited species are expected to occur in a habitat under consideration. The model equation gives a sigmoid species-log area curve implying that few rare species are found in a group of species. The good agreement between observation and this model is exemplified with the data of plant and arthropod communities. The implication of parameters involved are examined in connection with those of the preceding model, and the underlying ecology of the model is discussed.     

Inconstancy of Taylor'sb: Simulated sampling with different quadrat sizes and spatial distributions

Summary Taylor's power law,s ² =am ^b , provides a precise summary of the relationship between sample variance (s ² ) and sample mean (m) for many organisms. The coefficientb has been interpreted as an index of aggregation, with a characteristic value for a given species in a particular environment, and has been thought to be independent of the sample unit. Simulation studies were conducted that demonstrate that the value ofb may vary with the size of the sample unit in quadrat sampling, and this relationship, in turn, depends on the underlying spatial distribution of the population. For example, simulated populations with hierarchical aggregation on a large scale produced values ofb that increased with the size of the sample unit. In contrast, for a simulated population with randomly distributed clusters of individuals, the value ofb eventually decreased with increasing quadrat size, as sample counts became more uniform. A single value ofTaylor'sb, determined with a particular sample unit, provides neither a fixed index of aggregation nor a complete picture of a species' spatial distribution. Rather, it describes a consistent relationship between sample variance and sample mean over a range of densities, on a spatial scale related to the size of the sample unit. This relationship may reflect, but not uniquely define, density-dependent population and behavioral processes governing the spatial distribution of the organism. Interpretation ofTaylor'sb for a particular organism should be qualified by reference to the sample unit, and comparisons should not be made between cases in which different sample units were used. Whenever possible, a range of sample units should be used to provide information about the pattern of distribution of a population on various spatial scales.     

The species-area relation II. A second model for continuous sampling

Summary A second mathematical model describing the species-area relation was proposed for continuous expanding of sample area. This model is expressed asS=λ ln(1+x/E) whereS is the number of species occurring in an areax, and λ andE are the constants termedspecific diversity andelemental area respectively. As a result of testing the validity of the model for several sets of data, it was shown that the above equation would provide an adequate fit to a group of species belonging to a single synusia which exists in an open habitat. The ecological implications of parameters involved were discussed and the characteristic area presented previously (Kobayashi, 1974) was defined in terms ofE. The relation between results obtained by discrete sampling and continuous sampling was examined and the possibility of converting one to another was suggested. Contribution from the Laboratory of Applied Zoology, Yamagata University, No. 79.     

Ecological studies of collembolan populations in a pine forest soil IV. Comparison of distribution patterns

Summary The distribution pattern of ten species of Collembola was studied during the four years period from July 1971 to May 1975 in a pine forest soil. The distribution patterns were analysed for two scales of distribution, i. e., the distribution over the plot of 10×10 m² and the micro-distribution within a block sample consisting of 36 contigious units each 2×2 cm² in area, by applying the -m regression method. The fundamental pattern which appeared was quite similar for the species examined and individuals were aggregated in response to the heterogeneity of habitat conditions. The causes of aggregations were discussed with regard to some environmental factors. The relative abundances of 10 species within the collembolan community was examined in relation to the habitat utilization and the relative abundance was not related to the degree of aggregation but rather to the area occupied by individuals. This suggests that the more numerically abundant species tend to occupy broader micro-habitat. Biological meaning of aggregation was discussed in connection with the population biology and community organization of collembola.     

Studies on the distribution pattern of the pine needle gall midge,Thecodiplosis japonensisUchida etInouye (Diptera: Cecidomyiidae) in a pine forest

Summary Numerical changes and distribution patterns of the pine needle gall midge,Thecodiplosis japonensis Uchida etInouye, were studied during the period from 1978 to 1979 in a young plantation ofPinus thunbergii in Shiga Prefecture, Japan. The survivorship curve of this species was characterized by a low mortality of larvae in galls and two high mortalities before the formation of galls and during the overwintering period in soil. The within and between-trees distributions of eggs and larvae in galls were examined by using the regression method. The egg distribution per shoot was aggregative both within and between host plants. The within-tree variations in numbers of eggs per shoot were related to the differences in the abundance of available needles for oviposition per shoot among the canopy layers. The between-tree variations reflected the heterogeneous emergence of adult females in the study plot. The degree of aggregation increased from egg to gall stage in both within- and between-tree distributions and the increase was explained by the different mortality of larvae within trees and the inversely density-dependent mortality between trees. The distribution patterns in the soil habitat stages were examined by the patchness index ( ). This species showed aggregative distributions in soil stages. There was a correlation in spatial patterns of adult emergence between the successive generations. The distribution properties of this species were discussed in connection with the population dynamics and the availability of host plants in the study plot.     

A comparison of species diversity estimators

Although having been much criticized, diversity indices are still widely used in animal and plant ecology to evaluate, survey, and conserve ecosystems. It is possible to quantify biodiversity by using estimators for which statistical characteristics and performance are, as yet, poorly defined. In the present study, four of the most frequently used diversity indices were compared: the Shannon index, the Simpson index, the Camargo eveness index, and the Pielou regularity index. Comparisons were performed by simulating the Zipf–Mandelbrot parametric model and estimating three statistics of these indices, i.e., the relative bias, the coefficient of variation, and the relative root-mean-squared error. Analysis of variance was used to determine which of the factors contributed most to the observed variation in the four diversity estimators: abundance distribution model or sample size. The results have revealed that the Camargo eveness index tends to demonstrate a high bias and a large relative root-mean-squared error whereas the Simpson index is least biased and the Shannon index shows a smaller relative root-mean-squared error, regardless of the abundance distribution model used and even when sample size is small. Shannon and Pielou estimators are sensitive to changes in species abundance pattern and present a nonnegligible bias for small sample sizes (<1000 individuals). Received: May 8, 1998 / Accepted: May 6, 1999     

Use of the regression of mean crowding on mean density for estimating sample size and the transformation of data for the analysis of variance

Summary An approximate method for estimating the sample size in simple random sampling and a systematic way of transformation of sample data are derived by using the parameters α and β of the regression of mean crowding on mean density in the spatial distribution per quadrat of animal populations (Iwao, 1968). If the values of α and β have been known for the species concerned, the sample size needed to attain a desired precision can be estimated by simply knowing the approximate level of mean density of the population to be sampled. Also, an appropriate variance stabilizing transformation of sample data can be obtained by the method given here without restrictions on the distribution pattern of the frequency counts. Contribution from the Entomological Laboratory, Kyoto University No. 418. Contributions from JIBP-PT No. 52. Aided in part by a grant from the Ministry of Education for the special project research, ‘Studies on the dynamic status of biosphere’.     

A new method for describing predator-prey relations in discontinous environments

Summary I propose a new method for anlysing predatorprey interactive systems in discontinuous environments. The basic index used here is a generalized version ofLloyd's (1967) “interspecies mean crowding”, which is defined as the number of individuals of one species existing in a given patch per that of the other species in either the same or different patches at either the same or different times. Four indices are derived from different combinations of the numbers of the prey and the predator in habitat patches. Then, the correlation coefficients between the numbers of individuals in patches in both different locations and times are derived by modifying the above new indices. Using this technique, dynamical changes of the joint distributions of the numbers of predators and prey which reflect variation in local conditions, can readily be described. As an example, this method was applied to an analysis of the outcomes of a multi-patch version of theLotka-Volterra model of predator-prey interactions.     

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.     

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.     

Analyses of spatial patterns and population processes of clonal plants

The nonrandom spatial structure of terrestrial plants is formed by ecological interactions and reproduction with a limited dispersal range, and in turn this may strongly affect population dynamics and population genetics. The traditional method of modelling in population ecology is either to neglect spatial pattern (e.g. in transition matrix models) or to do straightforward computer simulation. We review here three analytical mothods to deal with plant populations in a lattice-structured habitat, which propagate both by seeds that scatter over the whole habitat and by vegetative reproduction (producing runners, rhizomes, etc.) to neighboring vacant sites. [1]Dynamics of global and local densities: Dynamical equations of population density considering nearest-neighbor correlation (spatial clumping) are developed as the joint dynamics of global average density and local density (comparable to mean crowding) based onpair approximation. If there is a linear trade-off between seed production and vegetative reproduction, the equilibrium abundance of the population may be maximized by engaging both means of reproduction. This result is accurately predicted by the pair approximation method, but not by mean-field approximation (neglect of spatial structure). [2]Cluster size distributions: Using global and local densities obtained by pair approximation, we predicted cluster size distribution, i.e. the number of clusters of occupied sites of various sizes. [3]Clonal identity probability decreasing with distance: Multi-locus measurement of allozymes or other neutral molecular markers tells us whether or not a given pair of individuals belong to the same clone. From the pattern of clonal identity probability decreasing with the distance between ramets, we can estimate the relative importance of two modes of reproduction: vegetative propagation and sexual seed production.     

Ecological studies on a dragonfly,Nannophya pygmaea ramber (Odonata: Libellulidae) I. seasonal changes of adult population and its distribution in a habitat

Summary Adult population of a dragonflyNannophya pygmaea Ramber inhabited in a damp ground was investigated with mark-and-recapture method in 1975. The following results about the seasonal changes of the population size and distribution in the habitat were obtained. Adults emerged from late May to mid August. The number of the adults was most abundant in early June, but that of matured males in early July. From the recapture data, the estimate of daily survival rate was 0.82, and the length of immature stage in males was estimated as 5 days or so. Total number of post-teneral adults emerged in the habitat was estimated as about 9,000. The mean crowding-mean density regression method was applied for the analysis of the distribution pattern of the adults. Matured males showed a spaced-out distribution, while females and immatured males distributed themselves rather aggregatively. Such a distribution pattern of the matured male would be attributed to their territorial behaviour. The territorial behaviour was considered to force the matured males to extend the distribution area in July when they were most abundant. From the above-mentioned results and some observations, the meaning of the territoriality in this species was discussed.     

Spatial pattern indices based on distances between individuals on a line-segment with finite length

Summary Let us consider a strip-wise habitat of line-segment, like a corridor, to simplify the subject mathematically, and assume that the length of the habitat is γ and there aren individuals. Here, we assume that the spatial pattern of the individuals is random if then distances from the left end of the habitat to each individual follow a uniform distribution on the strip. Under such an assumption, the variance of the distances between any two neighbors is represented by the formulanθ ²(n+1)⁻²(n+2)⁻¹ and the variance betweenn+1 distances betweenn individuals from the left end to the right end to the strip, is represented by the formulanθ ²(n+1)⁻²(n+2)⁻¹. These two kinds of variances can be used for determining (1) the spatial pattern of a population on the strip and (2) the spatial structure within the population, by comparison with the variances calculated from the data. Two examples cited from the literature, a cattle population on a pasture and an aphid population on a sycamore leaf, are presented.     

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.     

Species diversity preserved in different numbers of nature reserves of the same total area

Conclusion and Summary The expected number of species occurring in different numbers of reserves of the same total area is examined on different assumptions of the spatial distribution and the probability of extinction. The advantage of one large reserve or several smaller ones of equal total area depends on the spatial distributions of species and the stage after the establishement of reserves. In general, several smaller reserves maintain more species immediately after the establishments unless the spatial distribution are uniform or random, whereas one large reserve excels several smaller ones after some rare species have gone extinct unless the spatial distributions are strongly contagious. Since the extinction of rare species must be facilitated as the size of each reserve reduces, the area of a reserve should be larger than the critical area that ensures the persistence of the species. Hence it is concluded that one or a few large reserves are a better strategy in order to maintain the species diversity.     

Sex change and spatial distribution pattern in an intertidal holothurian Polycheira rufescens in the reproductive season

The patterns of sex change and spatial distribution in an intertidal holothurian, Polycheira rufescens (Chiridotidae; Echinodermata), were investigated on a stony beach in Amakusa, western Kyushu. Field caging experiments revealed that some individuals of P. rufescens underwent a sequential sex change from male to female via hermaphrodite stages and back to male again within a single reproductive season. The sex ratio of the population gradually changed from male dominance at first to equal proportions of males and females as the reproductive season progressed. Toward the end of the reproductive season, immature or spent individuals increased in proportion. Stone size appeared to be an important factor affecting the occurrence of P. rufescens individuals on a stony beach. Analysis of spatial distribution by means of Morisita's index of dispersion and nearest neighbor distances indicated that (i) males showed a slightly stronger tendency to aggregate than females, while females had a tendency toward uniform distribution; (ii) females tended to attract males, as shown by relatively short female-to-male distances; and (iii) there was a substantial variation in male-to-female distances, such that some males were positioned close to females while others were not. It may be suggested that spatial distribution of P. rufescens individuals during the reproductive period is partly dictated by the differential needs of individuals of different sexual states. Received: January 25, 1999 / Accepted: June 10, 1999     

Anopheles subpictus Grassi: Observations on survivorship and population size using mark-release-recapture and dissection methods

Summary A mark-release-recapture experiment to estimate population survivorship and absolute size was performed with wild-caughtAn. subpictus adults at the village of Khano-Harni, Lahore District, Punjab Province, Pakistan during September 1978, the end of the monsoon rainy season, when temporal population abundance was maximized. Daily survival rate estimated from the recapture sequence of marked adults was low, males=0.192 and females=0.343. Survivorship for females estimated by several vertical age-grading procedures ranged from 0.347 to 0.628. Both stage- and age-specific life tables were calculated from vertical age-grading data determined by the dilatation method. Female and male population size was estimated byBailey’s modification of theLincoln Index and was found to average 4478.4 and 6106.8, respectively. The bionomics, survivorship and population size ofAn. subpictus in the Lahore are indicated that this species was probably not important in the transmission of human malaria.     

Host-dependent association and its implications on the relative abundance of blue alfalfa aphid and pea aphid (Homoptera: Aphididae) on alfalfa in Oklahoma

Summary Field populations of blue alfalfa aphid and pea aphid on alfalfa were sampled during 1985 and 1986 to determine the association of co-occurrence, interspecific interactions and comparative temporal variations in the spatial dispersion patterns of these species in Oklahoma. Relative abundance of these species is discussed in the light of above analyses.Cole's coefficient revealed a high degree of association between these species in terms of their occurrence on the same alfalfa stems in the field. Regression analyses indicated that the species populations tended to increase in concert on the same stems without evidence of competitive displacement. Spatial dispersion patterns of both species were highly aggregated at low population densities early in the season. Over time, both species tended to disperse and became less aggregated as numbers increased. It was concluded that magnitude of interspecific interactions between the blue alfalfa aphid and the pea aphid were not of a nature that they could be termed as competing species. On the contrary, a concept of an “ecospecies” is proposed for practical applications such as sampling plans and economic threshold determinations.     

A stochastic computer model for simulating population growth

Summary A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model’s behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka’s Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values orr _m andK. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetleTribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.