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.     

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.     

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.     

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.     

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.     

Measurement of non-randomness in spatial distributions

Summary The measurement of departure from randomness in spatial distributions has widespread application in ecological work. Several “indices of non-randomness” are compared with regard to their dependence on sample number, sample size and density. Criteria for the best choice of index for specific situations are discussed. A new coefficientC _x is proposed for use with positively contagious distributions and tests of significance are given. WhenC _x and another index (S ²/m−1) are used for positive and negative contagion respectively, values ranging from −1 through 0 (random) to +1 are obtained, regardless of sample number, sample size or density.     

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 comparative study of the searching efficiencies of a parasite and a hyperparasite

Summary The searching efficiencies of a primary parasite (Diaeretiella rapae (McIntosh)) and a hyperparasite (Alloxysta brassicae (Ash.)) were investigated and compared. In both species, at all parasite densities, there was a curvilinear relationship (P<0.001) between the number of hosts parasitised and the host density. A linear regression (loga=logQ−m logP) was fitted for log area of discovery against log parasite density (P<0.001). The area of discovery for its immediate (i.e. primary) host (viz.Diaeretiella for the hyperparasite and aphid forDiaeretiella) is lower in the hyperparasite than in the primary parasite. InDiaeretialla both the searching efficiency and the mutual interference constant increased (but not significantly,P>0.05) in the presence of its males.     

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.     

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.     

On the mathematical basis of the variance-mean power relationship

The mathematical basis of a widely-known variance-mean power relationship of ecological populations was examined. It is shown that the log variance (S ²)—log mean, (m) plot is virtually delimited by two lines logS ²=logn+2 logm and logS ²=logm, thus increasing the chance that a linear regression line can be successfully fitted, without a profoundly behavioural background. This makes difficult the task of interpreting a successful fit of the power law regression and its parameterb in a biologically meaningful manner. In comparison with the power law regression, Iwao'sm ^*-m regression is structurally less constrained, i.e. has a wider spatial region in which data points can scatter. This suggests that a comparison between the two methods in terms of how good a fit is achieved for a particular data set is largely meaningless, since the power law regression may inherently produce a better fit due to its constrained spatial entity. Furthermore, it could be argued that a successful fit in Iwao's method, when found, is less taxed with mathematical arterfacts and perhaps more clearly linked to some biological mechanisms underlying spatial dispersion of populations.     

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.     

Safe drinking water and satisfaction with environmental quality of life in some oil and gas industry impacted cities of Nigeria

The availability and safety of drinking water and the environmental quality of life was investigated in five cities located in an oil-producing area of Nigeria using questionnaire-based scales, discussion and laboratory tests. Polythene-packaged sachet water and commercial and non-commercial private boreholes largely met the drinking water requirement of the cities. Consumption of sachet water was high (14.0–20.0 points vs. 25.0 points) but regression analysis indicated strong negative relationships with income group (β = −0.75, P < 0.005) and educational level (β = −0.77, P < 0.005) of respondents (658). Private borehole water was prevalent (18.7–19.9 vs. 20.0) while public water supplies were almost non-existent (4.8–5.6 vs. 20.0) in the cities. Vulnerability to contamination in all water sources was indicated following unacceptable counts of total and faecal coliform bacteria in 10–62.5 and 3–25% of samples, respectfully. Respondents were not satisfied with environmental quality of life indicated by the quality of housing, school, health services, refuse disposal, recreation, streetlight, transport and police (3.43–4.01 vs. 10). It is concluded that modernization and industrialization due to the oil and gas industries, tended to increase individualization to the negligence of common services as evidenced by the preponderance of private boreholes and sachet water.     

Dynamics of age- and size-structured populations in fluctuating environments: Applications of stochastic matrix models to natural populations

Recent developments of the theory of stochastic matrix modeling have made it possible to estimate general properties of age- and size-structured populations in fluctuating environments. However, applications of the theory to natural populations are still few. The empirical studies which have used stochastic matrix models are reviewed here to examine whether predictions made by the theory can be generally found in wild populations. The organisms studied include terrestrial grasses and herbs, a seaweed, a fish, a reptile, a deer and some marine invertebrates. In all the studies, the stochastic population growth rate (ln λ _s ) was no greater than the deterministic population growth rate determined using average vital rates, suggesting that the model based only on average vital rates may overestimate growth rates of populations in fluctuating environments. Factors affecting ln λ _s include the magnitude of variation in vital rates, probability distribution of random environments, fluctuation in different types of vital rates, covariances between vital rates, and autocorrelation between successive environments. However, comprehensive rules were hardly found through the comparisons of the empirical studies. Based on shortcomings of previous studies, I address some important subjects which should be examined in future studies.     

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.     

Process generating the ditribution pattern of eggs of the common cabbage butterfly,Pieris rapae crucivora

Summary The process generating the negative binomial in the distribution pattern of eggs of the common cabbage butterfly,Pieris rapae crucivora, was investigated by releasing the female adults in a net house where cabbages were planted. The distribution of butterflies visited and laid an egg or more per plant followed thePoisson series under the uniform light condition, while that of eggs laid per visit conformed to the logarithmic distribution. From these results, it may be concluded that the negative binomial arises from compounding of thePoisson and the logarithmic distribution. The observed frequency of eggs found per plant fitted to the negative binomial with parameter thus computed theoretically. The change in the degree of aggregation with the increase of the parental density was considered in connection with the above results. Aided by a grant from Scientific Research Expenditure of the Ministry of Education.     

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.     

Preference and performance linkage in aPhyllocolpa sawfly on the willow,Salix miyabeana, on Hokkaido

A leaf-folding sawfly in the genusPhyllocolpa (Hymenoptera: Tenthredinidae) attackingSalix miyabeana (Salicaceae) was studied near Sapporo, Hokkaido, along the Ishikari River in 1993. Host plant individuals were young trees 4–7 years old which were growing rapidly, producing some long shoots with large leaves. On a gradient of shoot length classes from 0–5 cm long to over 80 cm long, shoots were much more abundant in the shorter shoot length classes. However, attacks by ovipositing females increased as shoot length increase from 0 attacks on the shortest shoots to 5.17 attacks per shoot on the longest shoots. The frequency of attack per leaf increased from 0 to 0.13 over the same range of shoot lengths. This pattern of attack resulted in a high frequency of larval establishment in feeding sites, between 0.96 and 1.00, in all attacked shoot length categories. However, probability of survival to a late instar larva increased with shoot length and corresponded to the attack pattern, indicating a preference-performance linkage between female ovipositional decisions and larval survival. The patterns found for thisPhyllocolpa species are similar for galling sawflies in North America and Europe, especially in the genusEuura, members of which make stem, bud and leaf midrib galls. Extending the pattern to aPhyllocolpa species broadens identification of pattern and ultimately the generality of the emerging theory on populations of galling sawflies.     

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.     

The Association Between Perceived Spirituality, Religiosity, and Life Satisfaction: The Mediating Role of Self-Rated Health

This study examined the mediating role of self-perceived health between perceived spirituality, religiosity, and life satisfaction among a stratified, random sample of college students, while controlling for gender. Although both models displayed excellent fit criteria, the perceived spirituality and life satisfaction model was fully mediated by self-perceived health χ² (n=459, 4) = 1.64, p=0.80, CFI =0.99, TLI=0.99), and the perceived religiosity and life satisfaction model was partially mediated by self-perceived health χ² (n=459, 10) = 22.29, p=0.01 CFI = 0.99, TLI = 0.99). Both models were equal for men and women. Students who describe themselves as spiritual (or religious) are likely to report greater self-perceived health and greater self-perceived health likely influences life satisfaction for both men and women. Results preliminarily support the contention that life satisfaction is related to differing reported health status, whether physical or mental, and that life satisfaction may be influenced by religiosity and spirituality engagement. Implications for colleges and universities are discussed.