Quantitative Method for Determining a Representative Algal Sample Count'

A method for determining a representative count of a sample dependent on number of species is presented for application to various algal communities. Constant species curves are calculated as ejiciencj = (number of individuals number of species)/nurnber of individuals and diagrammed on a plot of eficiencj versus number of individuals counted. Eficiencj is deJined as the probability that a new species encountered is minimal. That is, as the ratio of number of species to number of individuals approaches 1, more individuals will need to be counted in order to achieve a representatiue count. Data and calculations of e@ciencj f rom tulo algal communities are presented f o r illustration. Key index words: constant species curves; eficiencj; frobabilitj; specimen counting Methods of obtaining a representative sample of algal assemblages from various habitats have been an ongoing matter of discussion. Furthermore, preparation of slide mounts and subsequent counting of specimens are also a matter of concern. How many individuals should be counted from a slide mount to represent a sample of an algal assemblage in a given habitat? What is the difference in number of individuals that should be counted to assure adequate representation of different habitats or communities? These broader questions are of interest to algal ecologists. Representative counts of samples involve a significant investment of time and effort. Generally, maximum number of species in a community is given by the mode of a log normal distribution, when number of species is plotted versus number of individuals in intervals on a logarithmic scale (Patrick et al. 1954, Patrick 1963, Patrick and Strawbridge 1963). However, what is the relation between maximum number of species in numbers of communities and the number of individuals counted in numbers of communities? Consideration of sample size may be important for comparison of different algal collections from different kinds of communities; that is, collections may be compared if collection area size is the same or each collection consists of a random sample of 1 Received 23 October 1995. Accepted 25 April 1996 * Author for reprint requests. individuals (Hurlbert 197 1). However, number of species for a single sample size may also indicate an erroneous proportion of number of species to number of individuals (Hurlbert 197 1); for example, counting 500 specimens for a benthic community would not necessarily be indicative of proportion of number of species to number of individuals. According to Hurlbert (1971), the most useful approach would be to calculate, plot, and compare species richness curves or plots of a random selection of a fixed number of individuals in a collection versus expected number of species in a sample. In palynology, pollen grains are classified as categories or types, and counts are viewed as multiple Bernoulli trials. If a specific type(s) of grain(s) is (are) chosen to be counted to a fixed total, various distributions of the counts emerge. Counting to a fixed number for each of three types produces a joint multinomial distribution with each type following a binomial distribution (Mosimann 1965). If two types are counted while only the third type is counted to a fixed number, the two types jointly follow a negative multinomial distribution with each of the two types following a negative binomial distribution. Once the sampling plan is chosen, either the multinomial or negative multinomial distribution applies. Multinomial distribution applies to within the pollen sum, whereas negative multinomial distribution applies to outside the pollen sum (Mosimann 1965). The assumption of multiple Bernoulli trials means that specimens are independent and that each specimen counted has an equal probability of occurrence. For algal counts, is the distribution of species on a slide truly random, and therefore does each species have an equal probability of occurrence? There are many colonial forms so that the next specimen within a colony is the only real possibility for that trial. In addition, if algal slide preparations reveal clumped rather than random distributions, then the proportion of number of species to number of individuals counted will not be accurate with the assumption of multiple Bernoulli trials. How does one choose a valid number for a fixed count prior to commencing the count? What are reasonable criteria for number of specimens to be counted? Slide preparations from same-size samples of different algal communities have a wide range in number of species and specimens per slide. Counting a marker specimen to a fixed number may not en-