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.     

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.     

Influence of parental density on the distribution pattern of eggs in the common cabbage butterfly,Pieris rapae crucivora

Summary To investigate the relation between the distribution pattern of eggs and the parental density in the common cabbage butterfly,Pieris rapae crucivora, the countings of egg number per plant were made on both cabbage plants cultivated in the farm and planted in the net house in which the female butterflies were released at various densities. The frequency distribution of eggs fits well to the negative binomial excepting the cases where they agree withPoisson series, and the degree of aggregation expressed as the reciprocal of the parameter, 1/k, tends to decrease as the egg or parental density increases. At the same parental density, however, the distribution of eggs can be described by the negative binomial with a common parameter,k _c, regardless of the difference in the density of laid eggs. In the case where a single female butterfly lays eggs, the spatial pattern of egg distribution is always lean, while its frequencies conform toPoisson or the negative binomial series. This lean changes toward patchy with increasing the parental density. From these results, it is concluded that the degree of aggregation in the distribution of eggs decreases with the increase of the parental density.     

Deceleration in the age pattern of mortality at olderages

The rate of mortality increase with age tends to slow down at very old ages. One explanation proposed for this deceleration is the selective survival of healthier individuals to older ages. Data on mortality in Sweden and Japan are generally compatible with three predictions of this hypothesis: (1) decelerations for most major causes of death; (2) decelerations starting at younger ages for more “selective” causes; and (3) a shift of the deceleration to older ages with declining levels of mortality. A parametric model employed to illustrate the third prediction relies on the distinction between senescent and background mortality. This dichotomy, though simplistic, helps to explain the observed timing of the deceleration.     

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.     

The narrowing sex differential in life expectancy in high-income populations: Effects of differences in the age pattern of mortality

Using data from the Human Mortality Database for 29 high-income national populations (1751–2004), we review trends in the sex differential in e(0). The widening of this gap during most of the 1900s was due largely to a slower mortality decline for males than females, which previous studies attributed to behavioural factors (e.g., smoking). More recently, the gap began to narrow in most countries, and researchers tried to explain this reversal with the same factors. However, our decomposition analysis reveals that, for the majority of countries, the recent narrowing is due primarily to sex differences in the age pattern of mortality rather than declining sex ratios in mortality: the same rate of mortality decline produces smaller gains in e(0) for women than for men because women's deaths are less dispersed across age (i.e., survivorship is more rectangular).     

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.     

Interspecific relations in forest floor coleopteron assemblages: Niche overlap and guild structure

Summary In six different environments of the Towada-Hachimantai National Park, the forest floor coleopterons were sampled by means of pitfall traps with five different baits. Their niche breadths and niche overlaps were assessed for the electivity of habitat, bait, and habitat × bait, and compared with those expected from neutral models constructed randomly. The niche breadths in the observed assemblages were smaller than those expected from the neutral model, while the niche overlaps were more widely distributed than those expected from the neutral model. Mean overlaps between species neighbors in niche space, cluster analyses, and ordinations of species revealed a guild for habitat, bait and habitat × bait. Lawlor’s (1979) gamma matrices concerning the habitat electivity show that the rates of mutualism resulted from indirect interspecific competitions are significantly smaller in the guild than in the whole assemblage. This suggests that the interspecific competition among the guild members is mitigated or even converted into mutualism by joining of the species which do not belong to the guild. The rates of mutualism were also significantly larger in the resource state of two dimensions (habitat × bait) than in that of either one. Therefore, if niche overlaps are measured on the basis of resource state of multi-dimensions, the rates of mutualism may increase further.     

Estimation of the individual number entering each development stage in an insect population

Summary A method for estimating the number entering each development stage from data obtained by regular sampling through one generation of an insect population was described. This method is consisted of the following two procedures: The provisional estimates are calculated on the assumption that each stage has a common mortality in a sampling interval. Then these estimates are corrected on another assumption that the mortality is different in each stage but constant during a stage. The result of testing its validity with two laboratory populations of the common cabbage butterfly,Pieris rapae crucivora, showed the availability of the present method.