Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence |
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Authors: | Eizi Kuno |
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Institution: | (1) Entomological Laboratory, College of Agriculture, Kyoto University, 606 Kyoto, Japan |
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Abstract: | 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. |
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