Relationship between surplus energy and body weight in fish populations

Summary This paper theoretically analyses the relationship between surplus energy, which is available for either somatic growth or reproduction, and body weight. From the data of metabolism and growth of the biwamasu,Oncorhynchus rhodurus, obtained by Miura et al., a Bernoulli's differential equation is induced to represent the relationship between body weight and the sum of surplus energy and active metabolic rate. Solving this equation gives the amount of surplus energy,f(W_x), as follows:f(W_x) = (αW _x ^1−γ +β^1−γ)^1/(1−γ)−W_x, in which α, β and γ are constants andW _x is body weight at agex. The function is applied to ten fish populations and consequently it is found to be useful for a wider age range and a wider variety of fishes than the conventional function.     

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

Summary The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model,p=1−(1+m/k) ^−k, and the empirical model,p=1−exp(−am ^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.     

Distribution patterns of and sampling plans forTetranychus urticae Koch (Acarina: Tetranychidae) on roses

Summary I sampledTetranychus urticae Koch (Acarina: Tetranychidae) regularly from four rose gardens in Kyoto and Nara Prefectures in 1988–1990. When mite density was low,T. urticae showed an uneven vertical distribution, being more abundant in the lower third and absent from the upper third of the plants. Mite density was less variable within than between plants, suggesting that a sampling plan which includes more leaves from different plants rather than from different levels of a plant is favourable. Spatial distribution ofT. urticae was nonrandom and followed the negative binomial distribution. In addition, both the Taylor’s power law and the Iwao’s patchiness regression described the distribution well. An empty-sample method for estimating mite density from the proportion of empty sampling units was developed. Sampling plans for determining the sample size required to reach a predetermined precision level, based on this method and by directly counting the mites, were designed. The counting method was more accurate than the empty-sample method. However, when the time factor was taken into account, the latter was more favourable, because it was faster than the former at a density range of 1.5–300 mites leaf⁻¹, which was most commonly encountered in the field.     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Summary Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve,Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rater ₀. The equilibrium recruitment rater _s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates ofr _s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger thanr _s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.     

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.     

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.     

Adult population parameters and life tables of an epilachnine beetle (Coleoptera: Coccinellidae) feeding on bitter cucumber in Sumatra

Summary The population dynamics of an epilachnine beetle, which is closely related toEpilachna sparsa Dieke (henceforth called “sp. C”) and feeds on bitter cucumberMomordica charantia, was studied by mark-recapture of adults and the construction of life tables. The study was repeated three times, i.e., March–May, July–September and October–December in 1982, in Padang, Sumatra, Indonesia. After the establishment of the host plants, adults of “sp. C” soon colonized, and each study period ended in the death of the plants due to defoliation by the larvae and adults. The estimated mean length of residence of adults ranged from 6–11 days, but this was probably much shorter than the actual longevity, because the adults were so active that they flew away, or dropped off the plants, when they were approached or slightly disturbed. Life tables indicated that egg mortality ranged from 17.8–53.9%, and a parasitic waspTetrastichus sp. B made up 41.1–64.2% of egg mortality. Two wasps,Tetrastichus sp. C andPediobius foveolatus killed 1.2–19.4% (7.6–100%)^* of 4th instars and only the latter species attacked the pupae, killing 24.6–59.1% (45.1–72.4%). Parasitism and starvation by overcrowding contributed most to the total mortality from egg to adult emergence, which ranged from 89.4–99.5%. “Sp. C” had a higher diversity and level of parasitism than the Japanese species,E. vigintioctopunctata. The high dispersal power of “sp. C”, coupled with the prolongedl _x−m_x schedules shown under laboratory conditions, was advantageous for exploiting the food plant which was available throughout the year, but was rather patchily distributed in space.     

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.     

Relationship between female body size and demographic parameters inBactrocera Malaysian A (Diptera: Tephritidae)

Summary The effect of body size, as measured by the head width, of the femaleBactrocera sp. Malaysian A (kept separately in sexual pairs) on the demographic parameters was investigated in the laboratory under ambient conditions of 28–30°C, 78–85% RH and natural photoperiod. Body size was shown to influence significantly all the demographic parameters. The expectation of life of females at eclosion from pupae was respectively for head widths of 1.6, 1.8, 1.9, 2.0 and 2.1 mm: 76.2, 73.4, 73.8, 102.4 and 115.2 days. The mean number of eggs laid per female in its life time was respectively: 86.4±48.7, 181.8±56.1, 229.7±72.6, 364.3±69.4 and 477.5±109.3 which was significantly different from one another (F=3.73,P<0.05) especially the two smaller sizes from the two larger sizes. The regression line for total eggs laid (Y) against head width (X) wasY=785.2X−1208.7 (R ²=0.35,P<0.001). The net reproductive rate (R ₀) was respectively 15.8, 34.0, 43.5, 66.9 and 88.8 eggs, while the intrinsic rate of increase (r) was respectivley 0.0435, 0.0538, 0.0670, 0.0665 and 0.0711. The results confirm that for mass rearing purposes, larger females which produce more offspring are to be preferred.     

Decrease in respiratory rate in a wolf spider,Pardosa astrigera (L. Koch), under starvation

Summary Effects of starvation on the suryival period and the respiratory rate in adults of a wolf spider,Pardosa astrigera (L. Koch), were investigated. The spiders used were divided into four groups: well-fed, starved and two limited food groups; in the latter two, each spider was supplied with one leafhopper every second or third day. Adult males and females ofP. astrigera could survive for a long time; 28.8±2.7 days and 54.4±18.9 days, respectively, without any food. The longevities shown here were 73.8% for males and 78.6% for females of those of well-fed spiders, indicating thatP. astrigera adults have a strong tolerance to starvation. The respiratory rate of well-fed adults showed no tendency to increase or decrease with their aging; the mean respiratory rates were 4.86×10⁻⁴ mg CO₂/mg f.w. (fresh body weight)/hr for males and 3.80×10⁻⁴ mg CO₂/mg f.w./hr for females. The respiratory rates of starved spiders increased during the first two days of starvation but decreased markedly from the third to the twelfth day, and thereafter retained an almost constant level for each sex. The mean respiratory rates after the twelfth day of starvation were 2.49×10⁻⁴ mg CO₂/mg f.w./hr for males and 2.76×10⁻⁴ mg CO₂/mg f.w./hr for females; these values were respectively 48.4% and 63.0% of those prior to starvation. The fresh body weight of starved spiders decreased linearly with time but the rate was small. The respiratory rates of the limited food groups tended to decline with time and thereby their weight losses were minimized. The decrease in the respiratory rate under starvation was considered not to be due to spider exhaustion or senescence but due to an intrinsic change in behaviour and/or metabolism, because when the spiders were supplied with ample food for five days after starvation, the respiratory rate and the body weight rapidly recovered to near the levels prior to starvation. It is suggested that starved spiders use a higher ratio of fat as catabolic substrate than normally fed or satiated ones. Feeding strategies of poikilo-therm predators are discussed. This work was partially supported by the Nippon Life Insurance Foundation Research Fund and Grant-in-Aid (No. 56480039) from the Ministry of Education, Science and Culture, Japan.     

Binomial sampling plans for estimatingBemisia tabaci populations in cantaloupes

Early season infestations of the sweet potato whitefly,Bemisia tabaci (Gennadius), on cantaloupes,Cucumis melo L., were determined by counts of the number of adults per leaf in fields near Yuma, Arizona. We used these data to develop binomial sampling plans based on the relationship between mean densities of whiteflies per leaf,m, and proportion of leaves infested with more thanI whiteflies,P _I, according to the empirical model lnm=a′+b′ ln[−ln(1−P _I)]. The models were developed for the presence-absence approach (I=0) and for a cutoff value of three whiteflies per leaf (I=3). Four independent data sets were used to evaluate the models. Both methods yielded reliable predictions at low infestation levels, but some of the higherm values were overestimated. As the tentative economic threshold forB. tabaci is three adults per leaf, which corresponds to lowP _I values, results of the binomial sampling were satisfactory for pest management purposes.     

Counter-Examples about Lower- and Upper-Bounded Population Growth

ABSTRACT

For a unimodal growth function f having its maximum at a critical state x _c , the interval bounding the population size asymptotically is usually presented as being equal to [f ^○2(x _c ), f(x _c )]. This interval however does not represent the maximum range within which the population size can vary, even asymptotically. The actual invariant interval containing the population size is equal to: [min(x*, f ^○2(x _c )), f(x _c )], where x* denotes the non-zero fixed point, assumed to be unique, of the iteration of f.     

Functional response and searching efficiency inPseudogonatopus flavifemur Esaki and Hash. (Hymenoptera: Dryinidae), a parasite of rice planthoppers

Summary The functional response ofPseudogonatopus flavifemur E & H (Hym., Dryinidae) was investigated by offering hosts (brown planthopper) at densities ranging from 8 to 160 per cage. The response curve was found to be sigmoid, i. e.Holling's (1959) Type III curve. In experiments involving 310 hosts per cage distributed unevenly in 5 densities (10, 20, 40, 80 and 160 per hill), and a different female parasite density each time (viz. 1, 2, 4, 8 or 16 per cage), the behavioral response was described well by the “random predator equation” ofRoyama (1971) andRoger (1972), which is a convex exponential curve. The area of discovery (a) decreased with an increase in female parasite density (P), and the relationship was described by the equation: loga=−1.0099−0.3638 logP. There was an apparent increase in handling time per host as the number of female parasites increased. Superparasitism, a rare phenomenon under natural conditions, was often observed in the laboratory. The potential ofP. flavifemur as a biocontrol agent of the brown planthopper is discussed.     

Body Image and Quality of Life in a Group of African American Women

African American (AA) women’s preference for a larger body size and underestimation of their body weight may affect the relationship between their body weight and weight-related quality of life (QOL). We wanted to examine the relationship between weight-related QOL and body mass index (BMI) in a sample of overweight AA women. Thirty-three overweight AA women completed a clinic visit to measure height, weight, and complete surveys including the Impact of Weight on Quality of Life-Lite (IWQOL-Lite) and the Stunkard Figure Rating Scale. BMI was calculated using measured height and weight. Correlations and linear regression models were estimated using SAS v 9.1. In this sample, the mean total quality of life score was 78.00 ± 17.68 on a 100 point scale. There was a modest correlation between BMI and total weight-related QOL (r = −0.034, p = 0.053). Body image dissatisfaction was the strongest predictor of total quality of life score (p = 0.04). African American women’s unique cultural perception of body image may play a key role in weight-related QOL.     

An index of spatial distribution

Summary The index , which takes the value of −1 for a perfectly regular distribution, +1 for a highly aggregated distribution and 0 for the distribution implied by the theoretical varianceσ ², is proposed and a significance table provided.     

Studies on the spatial distribution pattern of larvae of the mosquito,Anopheles sinensis, in rice fields

Summary The spatial distribution patterns of the population ofAnopheles sinensis larvae were studied in the rice field area in the suburb of Urawa city in Japan, during the summer seasons in 1973 and 1974. The distribution pattern of the larval population within the field, analysed by the m−m regression method, indicated that the basic component of larval distribution was not a group of individuals but a single individual and such components were distributed contagiously over the field. This basic pattern did not change significantly according to developmental stage, census date or field. Therefore, we could describe the distribution pattern of the population in a rice field by the single linear regression, x=0.021+1.339x(r²−0.912). Also, the relation for the whole population in the field area including the five fields could be shown by the linear regression, x=0.049+1.749x(r²−0.959). The value of α remained to be nearly equal to zero, but the value of β became larger than the value for the single-field relation. Such a change in distribution pattern seemed to reflect the greater heterogeneity in conditions among the fields than within individual field. Using the information on the distribution patterns mentioned above, some considerations were given on the sampling plans for mosquito larvae, including samplesize determination and application of sequential methods to estimate population size as well as to classify population level.     

Childhood nutrition and later fertility: Pathways through education and pre-pregnant nutritional status

Better childhood nutrition is associated with earlier physical maturation during adolescence and increased schooling attainment. However, as earlier onset of puberty and increased schooling can have opposing effects on fertility, the net effect of improvements in childhood nutrition on a woman’s fertility are uncertain. Using path analysis, we estimate the strength of the pathways between childhood growth and subsequent fertility outcomes in Guatemalan women studied prospectively since birth. Height for age z score at 24 months was positively related to body mass index (BMI kg/m²) and height (cm) in adolescence and to schooling attainment. BMI was negatively associated (−0.23 ± 0.09 years per kg/m²; p < . 05) and schooling was positively associated (0.38 ± 0.06 years per grade; p < .001) with age at first birth. Total associations with the number of children born were positive from BMI (0.07 ± 0.02 per kg/m²; p < .05) and negative from schooling (−0.18 ± 0.02 per grade; p < .01). Height was not related to age at first birth or the number of children born. Taken together, childhood nutrition, as reflected by height at 2 years, was positively associated with delayed age at first birth and fewer children born. If schooling is available for girls, increased growth during childhood will most likely result in a net decrease infertility.     

Survival Convergence and the Preceding Mortality Crossover for Two Population Subgroups

In this paper, we present and develop the argument that if the survival functions for two population subgroups converge in later life, a mortality crossover must precede the occurrence of this convergence. Specifically, two survival curves, S ₁(x) and S ₂(x), associated with two distinct population subgroups, G₁ and G₂, tend to converge before all members die out, as often observed and anticipated. This convergence leads to an increased mortality acceleration for the “advantaged” group, and eventually fosters the occurrence of a mortality crossover. We present a mathematical proof for this relationship and offer several explanations for the mechanisms involved in the process of survival convergence and the preceding mortality crossover. This new presentation demonstrates that mortality crossover is a highly observable demographic event given the trend of survival convergence in later life.     

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.