A distance measure of spatial pattern in a biological population

Summary Suppose thatn individuals locate independently and randomly on a segment of line of finite length (habitat). Let the theoretical and observed ranges of the sites of the individuals on the segment be μ _n-1 andr _n-1, respectively. Then, the degree of dispersion of the individual sites is measured by the ratio, T _n =n _n-1/μ _n-1, as follows: A random spatial pattern forI _r−1 =1 An aggregated spatial pattern for 0≤I _r <1 A uniform spatial pattern for (n+1)/(n−1)≥I _r >1. Another method was derived. Let the probability that an observed range is less thanr _n−1 beI _p , under the hypothesis of a Beta distribution. Then indicates A random spatial pattern forI _p =1/2 An aggregated spatial pattern forI _p <1/2 A uniform spatial pattern forI _p >1/2. The first index can be used for comparing populations having the same number of individuals, whereas the second one can be used for comparing populations with different numbers of individuals.     

Analysis of spatial association between two species based on the interspecies mean crowding

Summary and Conclusion The measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ andC _p, are derived as geometric and weighted arithmetic means of the same component ratios related to inter-and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita's (1959)C _σ index. Indices to measure the degree of spatial correlation between species, Ω andR _μ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion. Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species. The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra-and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested. This study was supported by Science Research Fund (No. 148041) from the Ministry of Education.     

On the momentum of population growth

If age-specific birth rates drop immediately to the level of bare replacement the ultimate stationary number of a population will be given by (9): $$\left( {{\textstyle{{b\mathop e\limits^ \bullet {}_0} \over {r\mu }}}} \right)\left( {\frac{{R_0 - 1}}{{R_0 }}} \right)$$ multiplied by the present number, where b is the birth rate, r the rate of increase, \(\mathop e\limits^ \bullet _0 \) the expectation of life, and R ₀ the Net Reproduction Rate, all before the drop in fertility, and μ the mean age of childbearing afterwards. This expression is derived in the first place for females on the stable assumption; extension to both sexes is provided, and comparison with real populations shows the numerical error to be small where fertility has not yet started to drop. The result (9) tells how the lower limit of the ultimate population depends on parameters of the existing population, and for values typical of underdeveloped countries works out to about 1. 6. If a delay of 15 years occurs before the drop of the birth rate to replacement the population will multiply by over 2. 5 before attaining stationarity. The ultimate population actually reached will be higher insofar as death rates continue to improve. If stability cannot be assumed the ultimate stationary population is provided by the more general expression (7), which is still easier to calculate than a detailed projection.     

The importance of non-linearity: A comment on the views of Taylor

Summary Taylor's (1984) view that his power law is better measurement of the distribution pattern of animals than 1/k, I _ρ and relation because almost all the data on means and variances of given species could be fitted by the power low, was critisized. Changes in values of 1/k, I _ρ and suggest the change of distribution pattern of the species, but the data can still be fitted by the power law because of the great linearizing power of log-log plots, and, using the power law only, we shall overlook the information on the meaningful changes in the distribution pattern.     

The spatial distribution pattern of the brown planthopperNilaparvata lugens St?l (Homoptera: Delphacidae) in west Java, Indonesia

Summary Spatial distribution pattern of the brown planthopper (BPH) was analyzed at 9 experimental fields in the northern part of West Java during two consecutive rice cropping seasons, i.e., wet and dry seasons. The population of each developmental stage and wing form of BPH at each location showed consistent departure from the random (Poisson) distribution, the variances of the densities in most cases exceeding their means. Namely, the distribution pattern of BPH per hill of rice plant was found to have a general tendency to be aggregated or contagious and to fit fairly well to the negative binomial model. The tendency for aggregation was further confirmed by both the β-values of -m regression being larger than unity and theC _A -values being larger than zero for each developmental stage. Although significant variations in the distribution pattern as measured by β- orC _A -value were observed between different developmental stages, between wing forms and among locations, the degree of aggregation for a given developmental stage at each experimental field remained fairly stable throughout the crop period, despite wide temporal changes in population density. Possible factors to explain these characteristics of the spatial distribution pattern of the BPH in West Java were discussed with reference to the process generating it.     

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.     

Overwintering ecology of two social halictine bees,Lasioglossum duplex andL. problematicum

Summary Overwintering of two social halictine bees,Lasioglossum duplex (Dalla Torre) andL. problematicum (Blüthgen), was studied. InL. duplex many females stay near the old nests, each female preparing a hibernaculum separated from the natal nest. InL. problematicum most females overwinter communally within the natal nest. This difference in overwintering habits relates to the social structure in the next spring.L. duplex is nearly always solitary in spring although later becoming eusocial, whereas many nests ofL. problematicum are polygynous, beginning in early spring.L. duplex overwinters much deeper ( ) in the soil than doesL. problematicum ( ), but both species are safe from drops in soil temperature, which is above 0°C even in midwinter, and the bees' supercooling points are lower than −6°C. This cold resistance and the storage of sufficient food in the crop are reflected in the winter survival, which is much higher (79%) than the rate of successful nests in the spring active phase (25%). Bionomics of the eusocial halictine beeLasioglossum duplex VII. Contribution No. 2654 from the Inst. Low Temp. Sci.     

A new method of sequential sampling to classify populations relative to a critical density

Summary A method of sequential sampling for grading population level in relation to a critical density is proposed. The method is based on the relationship and can be used without restrictions on the distribution patterns. The formulae for simple random sampling as well as for two-stage sampling are given. This research was suported by science research fund from the Ministry of Education.     

Mortality process in relation to aggregation in the southern green stink bug

Summary A simple experiment of simulation was done to analyze the natural mortality process of young larval colonies and egg masses of the southern green stink bug. In this experiment, a degree of contagiousness was allowed in regard to the action of a mortality factor, and was defined as the mean number killed per a colony or an egg mass by the mortality factor within a unit time and the number killed per a colony was assumed to follow the Poisson series with the mean . Thus each component of the Poisson series was opposed to each colony or egg mass which was taken at random from 162 egg masses, 135 and 117 colonies of the first and the second instar larvae, respectively. It was revealed that mortality factors in the field did not act with a small degree of contagiosness, e. g. , on all colonies or egg masses, but acted with a large degree of contagiousness, e. g. , on some of the colonies or egg masses. Thus differential survival somewhat in all or none way occurred among the insect colonies irrespective of their initial sizes. These results were well explained by taking actual mortality factors into account.     

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.     

A probabilistic interpretation of the United Nations’ 1995–2005 population projections

I develop probabilistic interpretations for the United Nations’ 10-year population forecasts by comparing 1995 projections for 212 countries to the population sizes reported for 2005. Errors in the estimation of the intrinsic rate of increase, presumably caused by erroneous assumptions about birth, death and/or immigration rates, appear to be more consequential than errors based on inaccurate estimation of the starting, or ‘jump-off’, population size. For only about 20% of the countries did the ‘actual’ 2005 population size fall between the United Nations’ low- and high-variant projections. I propose prediction intervals for country-specific population sizes 10 years in the future of the form [ N_i^￠ (t+10) / k ,  k ·N_i^￠ (t+10) ],[ N_i^{\prime} (t+10) / k , \, k \cdot N_i^{\prime} (t+10) ], where N _i ′(t + 10) is the medium-variant prediction for year t + 10 made in year t, and k is a number that varies with starting population size. Based on the 1995–2005 United Nations’ data, values of k giving 95% coverage range from 1.11 for countries with a population on the order of 10⁹, to 1.45 for countries with a population of 10⁵.     

Some extensions of the keyfitz momentum relationship

A stable population, such that the total birthrateB(t) =B _o e ^ro^t, is abruptly altered by modifying the age-specific birth rate,m(x). The survivor function remains unaltered. The modified population ultimately settles down to a stable behavior, such thatB(t) =B ₁ e ^r ₁ ^t . It is shown thatB ₁/B ₀ = (R ₀ ?R ₁)/[(r ₀ ?r ₁)R ₀ Z ₁], whereR ₀,R ₁ are the net reproduction rates before and after the change, and \(\bar Z_1 \) expected age giving birth for the stable population after the change. The age structure and transients resulting from the change are also described. The effect of an abrupt change in the survivor functionl(x) is also investigated for the simple case where the change is caused by alteringl(x) toe ^?λx l(x). It is shown that the above ratio becomes \(B_1 /B_0 = N_1 /N_0 = [1 - \smallint _0^\infty e^{ - kx} g(x)dx]/\bar Z_1 \lambda \) , whereN refers to the numbers in the population,k =r ₀ + λ, andg(x) =m(x)l(x), the value before the change. A measure for the reproductive worth of the population is also established.     

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.     

Analysis of contagiousness in the action of mortality factors on the western tent caterpillar population by using the \mathop m* - m\mathop m\limits^* - m relationshiprelationship

Summary The contagiousness in the operation of mortality processes on the colonies of the western tent caterpillar,Malacosoma californicum pluviale, was analyzed from two different aspects: successive changes in the frequency distribution of the number of surviving individuals per colony in the course of development, and the distribution pattern of the individuals killed by some biotic mortality factors. Also, for a tachinid parasite,Tachinomyia similis, the analysis was made on the egg-laying pattern on colonies as well as on individual larvae. The methods of these analyses were all based on the relation of mean crowding (m) on mean . A braconid parasite,Rogas sp., tended to kill few individuals together once it attacked a colony, but its effect on host colonies was rather equivalent to the random removal of individuals from all the colonies. Diseases in the late-stage larvae before cocooning was contagious in their action. Nuclear polyhedrosis virus seemed to have no basic contagiousness in its action, but it caused highly contagious distribution of deaths among the colonies when its average incidence was high. A spore-formingBacillus had a tendency to kill several individuals once it appeared in a colony, but the distribution of its incidence (no. of times it appeared per colony) was considered to be nearly at random. The female ofTachinomyia tended to lay more than one egg successively on the same colony. It also attacked individual larvae with a definite tendency for aggregation, which seemed to be resulted from the parasite’s preference to large hosts. When the number of eggs laid on prefered hosts exceeded a certain threshold, however, the fly seemed to change its attention to less attractive, smaller individuals.     

Investigation into the edge effect by use of capture-recapture data in a vole population

Summary A substantial explication of the edge effect has been attempted by use of capture-recapture data for a vole population (Microtus montebelli), gathered intwo plots of 100×100 m or less during 12 days, cheked twice daily, in August 1970; the sample was quite sufficient for the aim. The edge effect as guessed by increased catch per trap is usually suspected to ensue from range-settlers in the outside boundary strip of a plot and immigrants. But by a theoretical analysis I could attain a tentative conclusion that no increased catch per trap will occur unless any invasion takes place. Then it follows that, apart from the effect of invasion, the role of the adjoining outside settlers in the edge effect is essentially required to be studied in the light of knowledge on the truth of size and shift in home range. The variation in range behavior for 183 adult voles, captured 6 times or more, could be grouped into eight types, of which the range-conservative type possessed 52% of the sample and the group of the type was justly utilized for giving averages of range size. Besides, it was seen from the observed frequency of types that a considerable number of immigrants onto the census plot were induced perhaps being allured by trap baits, but the majority of them proved to be assigned to the voles that have their ranges inside the assessment line ofDice; the rest referable to effective immigrants was only a few (7%). I could perceive no reason such as disproves the idea ofDice’s additional boundary strip. Viewed from maps of ingress shift of ranges, the effect of ingress must have been greater in the outer trap rows than in the inner within the plot, so that it might well be called edge effect in general; such effect, however, is seen gradually diminishing toward the center, and hence it is almost unlikely that one should find any clear-cut intra-plot assessment lines demarcating such an inner square as quite free from edge effects. Averages of observed range length and width (ORL and ORW), as reliable measures for the true range size, were determined from the above group of specimens; as a result, the remarkable concept of elliptic range shape was established by regarding ORL as long axis and ORW as short one, and, directly from these averages, the mean range sizes worked out at 0.04 for females and 0.09 for males in acreage which proved to be surprisingly well agreeable with those of isotope-revealed ranges for voles given byGodfrey (1954) andAmbrose (1969). The catchability for marked voles ( ) was estimated by the maximum likelihood method by use ofJolly’s formulae (1965), but that for unmarked ones ( ) was made by the regression census formula; as a result it was shown that the population was clearly of π>p type and that the trap-experience that voles underwent one month or more ago can make them retain as high catchability as π. Contribution from JIBP-PT No. 110, carried out by the grant from the expenditure of Education Department to the specific study on “Dynamics of Biosphere”.     

Comments on Daniel A. Seiver's ‘Recent fertility in Mexico: Measurement and Interpretation.’

In a recent article in this Journal,¹Daniel A. Seiver concludes that ‘fertility’ in Mexico did not decline between 1960 and 1970. His conclusion is based primarily on an increase in the child-woman ratio from 725 per 1,000 in 1960 to 762 in 1970. Seiver simply asserts that this increase cannot be completely explained by declining infant mortality and under-enumeration. ² Ibid, p 343. . ³ Ibid, p 351.      

A reply to Avery and Hakkert

Udry et al., ¹ J. Richard Udry, Charles Teddlie and C. M. Suchindran, ‘The Random Variation in Rates Based on Total Enumeration of Events’, Population Studies, d33, 2, (1979), pp. 353-364. while analysing the variations in observed birth rates, found that the usual binomial model variance underestimates the actual variance of birth rates. Avery and Hakkert's ² Avery, R. C. and Hakkert, R., Comment on ‘The Random Variation in Rates Based on Total Enumeration of Events’ by Udry, Teddlie and Suchindran. analysis offers some help in interpreting these results. Also, it clarifies one possible explanation given by Udry et al., regarding the heterogeneous populations. However, we show below that the narrow approach taken by Avery and Hakkert is difficult to apply to general situations and perhaps leads them to make a number of inappropriate statements.     

Application and Testing the Reliability and Validity of a Modified Version of Herek's Attitudes Toward Lesbians and Gay Men Scale in China

The present study was the first attempt to test the reliability and validity of Herek's Attitudes Toward Lesbians and Gay Men Scale (ATLG; Herek, 1988 Herek, G. M. 1988. Heterosexuals' attitudes toward lesbians and gay men: Correlatesand gender differences. The Journal of Sex Research, 25(4): 451–477. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in the Chinese population. Participants (n = 2,391 for the field trials and n = 200 for test–retest reliability) were asked to complete the translated, slightly modified version of the ATLG. The resulting ATLG has a two-dimensional factor structure as well as good validity and reliability in the Chinese culture. ATLG scores followed distinct patterns according sex and level of education that were consistent with previous studies in other populations. The significance of these findings in Chinese culture is discussed.     

High Levels of Same-Sex Experiences in the Netherlands: Prevalences of Same-Sex Experiences in Historical and International Perspective

Some authors suggest that the public stance toward homosexuality can influence the prevalence of same-sex experiences (e.g., Butler, 2005 Butler, A. C. 2005. Gender differences in the prevalence of same-sex partnering: 1988–2002. Social Forces,, 84(1): 421–449. [Crossref], [Web of Science ®] , [Google Scholar]). Since the Dutch stance toward homosexuality has become more positive during the last decades, it was hypothesized that the current Dutch prevalences of same-sex experiences are higher than in other times and countries. This hypothesis was investigated using the data of a recent Dutch population study, and comparing these results to those from previous and international studies. The current Dutch figures were indeed higher than recent figures from other countries. Among women, the recent figures were also higher than those found in previous Dutch studies. The prevalence of same-sex experiences among Dutch males stayed the same. These results and the methodological aspects of the study are discussed.