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

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.     

Multi-stage sampling for population estimation

Summary Multi-stage sampling is a convenient technique suited to the desnity estimation of biological populations living in habitats with complicated structures. This paper describes a general method of its application to population estimation in which the preliminary information on the spatial distribution pattern of the population under study can be incorporated as the parameters of the mean crowding-mean relationship. The formulae that are necessary to perform sequential or double sampling plans for its efficient application are derived. The procedure of application of the method is explained with a numerical example. This study was supported by science research fund from the Ministry of Education.     

On fixed precision level sequential sampling

Summary It is proposed that the sequential sampling design ofKuno (1969) for estimating populations with a fixed level of precision be modified by using σ²=am ^b for the variance-mean relationship for most field distributions of organisms. This function yields a straight line “stop line” rather than a curve. An example is calculated and used with field data.     

A new method of sequential sampling to obtain the population estimates with a fixed level of precision

A simple method of sequential sampling is developed which would make it automatically possible to secure, without excess sampling, a predetermined level of precision for a series of population estimates being required. It appears to have wide application to sampling field populations under various situations since it is simply based upon the relationship of variance to mean for which a comprehensive formula deduced for biological populations from the linearity in the regression of mean crowding on mean density could be adopted. Some problems that may arise in practical application of the method are also discussed.     

A sequential estimation technique for capture-recapture censuses

A simple technique of sequential estimation was proposed for capture-recapture census by thePetersen method. In theory this technique makes it possible to secure automatically a required precision level for the population estimate to be obtained, irrespective of the population size. Some problems about its practical application were discussed.     

A sequential estimation technique for capture-recapture censuses

Summary A simple technique of sequential estimation was proposed for capture-recapture census by thePetersen method. In theory this technique makes it possible to secure automatically a required precision level for the population estimate to be obtained, irrespective of the population size. Some problems about its practical application were discussed. This study was supported by science research fund from the Ministry of Education.     

Stepwise mutation likelihood computation by sequential importance sampling in subdivided population models

An importance sampling algorithm for computing the likelihood of a sample of genes at loci under a stepwise mutation model in a subdivided population is developed. This allows maximum likelihood estimation of migration rates between subpopulations. The time to the most recent common ancestor of the sample can also be computed. The technique is illustrated by an analysis of a data set of Australian red fox populations.     

Some notes on fig-eating by arboreal mammals in Malaysia

During a study of avian fig-eating at Kuala Lompat, Malaysia, observations were also made of fig-eating by mammals. Four species of primate, seven species of squirrel, and two species of civet consumed figs. Twenty-six species ofFicus were of importance to arboreal mammals. Observations suggest that there were differences in the importance of figs in the diets of sympatric langurs (Presbytis) and congeneric squirrels. Dusky langursPresbytis obscura ate carbohydrate-rich ripe figs despite their ruminant-like digestive system and the danger of bloat.     

Some notes on the ecology of a GermanBranchipus schaefferi population (Crustacea: Anostraca)

Habitat preference, seasonal occurrence, starvation resistance, hatching eggs ofBranchipus schaefferi, and effects of predation onB. schaefferi were studied.Branchipus was only present in turbid, unvegetated ponds and absent in ponds which contain higher aquatic vegetation and theSpirogyra sp. The first individuals ofB. schaefferi appeared in April when water temperature was 10 °C and the last adults in November at a water temperature of 3.5 °C. Up to 6 reproducing generations were observed during this period. Abundance ofB. schaefferi was higher in temporary ponds than in permanent ponds. Sex ratio was close to unity for most of the year. Body size ofB. schaefferi males and females was significantly positively correlated with pond volume. Without foodB. schaefferi could survive for 1.5 to 2 days at 20 °C and 4 to 5 days at 10 °C. Hatching success of eggs decreased when eggs were dried for 7 months. Freezing of eggs had no effect on hatching success. From] the predators tested,Chaoborus sp. larvae clearly selected smallB. schaefferi; one consumed approximately 6Branchipus d–1 at a density of 6 to 12 prey 1–1. The other predators, dragonfly larvae, and larvae and adults ofTriturus alpestris selected alternative prey types, for exampleTubifex sp. and ostracods.     

Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance

In numerous species, individual dispersal is restricted in space so that "continuous" populations evolve under isolation by distance. A method based on individual genotypes assuming a lattice population model was recently developed to estimate the product Dsigma2, where D is the population density and sigma2 is the average squared parent-offspring distance. We evaluated the influence on this method of both mutation rate and mutation model, with a particular reference to microsatellite markers, as well as that of the spatial scale of sampling. Moreover, we developed and tested a nonparametric bootstrap procedure allowing the construction of confidence intervals for the estimation of Dsigma2. These two objectives prompted us to develop a computer simulation algorithm based on the coalescent theory giving individual genotypes for a continuous population under isolation by distance. Our results show that the characteristics of mutational processes at microsatellite loci, namely the allele size homoplasy generated by stepwise mutations, constraints on allele size, and change of slippage rate with repeat number, have little influence on the estimation of Dsigma2. In contrast, a high genetic diversity (approximately 0.7-0.8), as is commonly observed for microsatellite markers, substantially increases the precision of the estimation. However, very high levels of genetic diversity (>0.85) were found to bias the estimation. We also show that statistics taking into account allele size differences give unreliable estimations (i.e., high variance of Dsigma2 estimation) even under a strict stepwise mutation model. Finally, although we show that this method is reasonably robust with respect to the sampling scale, sampling individuals at a local geographical scale gives more precise estimations of Dsigma2.