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Population Dispersion AccessScience from McGraw-Hill Education Page 1 of 7 www.accessscience.com Population dispersion Contributed by: Francis C. Evans Publication year: 2014 The spatial distribution at any particular moment of the individuals of a species of plant or animal. Under natural conditions organisms are distributed either by active movements, or migrations, or by passive transport by wind, water, or other organisms. The act or process of dissemination is usually termed dispersal, while the resulting pattern of distribution is best referred to as dispersion. Dispersion is a basic characteristic of populations, controlling various features of their structure and organization. It determines population density, that is, the number of individuals per unit of area, or volume, and its reciprocal relationship, mean area, or the average area per individual. It also determines the frequency, or chance of encountering one or more individuals of the population in a particular sample unit of area, or volume. The ecologist therefore studies not only the fluctuations in numbers of individuals in a population but also the changes in their distribution in space. See also: POPULATION DISPERSAL. Principal types of dispersion The dispersion pattern of individuals in a population may conform to any one of several broad types, such as random, uniform, or contagious (clumped). Any pattern is relative to the space being examined; a population may appear clumped when a large area is considered, but may prove to be distributed at random with respect to a much smaller area. Random or haphazard. This implies that the individuals have been distributed by chance. In such a distribution, the probability of finding an individual at any point in the area is the same for all points (Fig. 1a). Hence a truly random pattern will develop only if each individual has had an equal and independent opportunity to establish itself at any given point. In a randomly dispersed population, the relationship between frequency and density can be expressed by Eq. (1), Image of Equation 1 (1) where F is percentage frequency, D is density, and e is the base of natural or napierian logarithms. Thus when a series of randomly selected samples is taken from a population whose individuals are dispersed at random, the numbers of samples containing 0, 1, 2, 3,. , n individuals conform to the well-known Poisson distribution AccessScience from McGraw-Hill Education Page 2 of 7 www.accessscience.com ImageFig. 1 Basic of 1 patterns of the dispersion of individuals in a population. (a) Random. (b) Uniform. (c) Clumped, but groups random. (After E. P. Odum, Fundamentals of Ecology, Saunders, 1953) described by notation (2). (2) Image of Equation 2 Randomly dispersed populations have the further characteristic that their density, on a plane surface, is related to the distance between individuals within the population, as shown in Eq. (3), (3) Image of Equation 3 where r̄, is the mean distance between an individual and its nearest neighbor. These mathematical properties of random distributions provide the principal basis for a quantitative study of population dispersion. Examples of approximately random dispersions can be found in the patterns of settlement by free-floating marine larvae and of colonization of bare ground by airborne disseminules of plants. Nevertheless, true randomness appears to be relatively rare in nature, and the majority of populations depart from it either in the direction of uniform spacing of individuals or more often in the direction of aggregation. Uniform. This type of distribution implies a regularity of distance between and among the individuals of a population (Fig. 1b). Perfect uniformity exists when the distance from one individual to its nearest neighbor is the same for all individuals. This is achieved, on a plane surface, only when the individuals are arranged in a hexagonal pattern. Patterns approaching uniformity are most obvious in the dispersion of orchard trees and in other artificial plantings, but the tendency to a regular distribution is also found in nature, as for example in the relatively even spacing of trees in forest canopies, the arrangement of shrubs in deserts, and the distribution of territorial animals. Contagious or clumped. The most frequent type of distribution encountered is contagious or clumped (Fig. 1c), indicating the existence of aggregations or groups in the population. Clusters and clones of plants, and families, AccessScience from McGraw-Hill Education Page 3 of 7 www.accessscience.com flocks, and herds of animals are common phenomena. The degree of aggregation may range from loosely connected groups of two or three individuals to a large compact swarm composed of all the members of the local population. Furthermore, the formation of groups introduces a higher order of complexity in the dispersion pattern, since the several aggregations may themselves be distributed at random, evenly, or in clumps. An adequate description of dispersion, therefore, must include not only the determination of the type of distribution, but also an assessment of the extent of aggregation if the latter is present. Analysis of dispersion If the type or degree of dispersion is not sufficiently evident upon inspection, it can frequently be ascertained by use of sampling techniques. These are often based on counts of individuals in sample plots or quadrats. Departure from randomness can usually be demonstrated by taking a series of quadrats and testing the numbers of individuals found therein for their conformity to the calculated Poisson distribution which has been described above. The observed values can be compared with the calculated ones by a chi-square test for goodness of fit, and lack of agreement is an indication of nonrandom distribution. If the numbers of quadrats containing zero or few individuals, and of those with many individuals, are greater than expected, the population is clumped; if these values are less than expected, a tendency toward uniformity is indicated. Another measure of departure from randomness is provided by the variance:mean ratio, which is 1.00 in the case of the Poisson (random) distribution. If the ratio of variance to mean is less than 1.00, a regular dispersion is indicated; if the ratio is greater than 1.00, the dispersion is clumped. In the case of obviously aggregated populations, quadrat data have been tested for their conformity to a number of other dispersion models, such as Neyman’s contagious, Thomas’ double Poisson, and the negative binomial distributions. However, the results of all procedures based on counts of individuals in quadrats depend upon the size of the quadrat employed. Many nonrandom distributions will seem to be random if sampled with very small or very large quadrats, but will appear clumped if quadrats of medium size are used. Therefore the employment of more than one size of quadrat is recommended. A measure of aggregation that does not depend on quadrat size of the mean density of individuals per quadrat and that can be applied to patterns consisting of a mosaic of patches with different densities has been developed by Morisita. His index of dispersion is a ratio of the observed probability of drawing two individuals randomly from the same quadrat to the expected probability of the same event for individuals randomly dispersed over the set of quadrats being studied. Index values greater than 1.0 indicate clumping, and values between 0 and 1.0 point to regularity of dispersion. The fact that plot size may influence the results of quadrat analysis has led to the development of a number of techniques based on plotless sampling. These commonly involve measurement of the distance between a randomly selected individual and its nearest neighbor, or between a randomly selected point and the closest individual. At least four different procedures have been used (Fig. 2). The closest-individual method (Fig. 2a) AccessScience from McGraw-Hill Education Page 4 of 7 www.accessscience.com ImageFig. 2 Distances of 2 measured in four methods of plotless sampling. (a) Closest individual. (b) Nearest neighbor. (c) Random pairs, with 180◦ exclusion angle. (d) Point-centered quarter. The cross represents the sampling point in each case. (After P. Greig-Smith, Quantitative Plant Ecology, Butterworths, 1987) measures the distance from each sampling point to the nearest individual. The nearest-neighbor method (Fig. 2b) measures the distance from each individual to its nearest neighbor. The random-pairs method (Fig. 2c) establishes a base line from each sampling point to the nearest individual, and erects a 90◦ exclusion angle to either side of this line. The distance from the nearest individual lying outside the exclusion angle to the individual used in the base line is then measured. The point-centered quarter method (Fig. 2d) measures the distance from each sampling point to the nearest individual in each quadrant. In each of these four methods of plotless sampling, a series of measurements is taken which can be used as a basis for evaluating the pattern of dispersion. In the case of the closest-individual and the nearest-neighbor methods, a population whose members are distributed at random will yield a mean distance value that can be calculated by use of the density-distance equation (3). In an aggregated distribution, the mean observed distance will be less than the one calculated on the assumption of randomness; in a uniform distribution it will be greater. Thus the ̄ ̄ ̄ ̄ ratio rA∕rE ,whererA is the actual mean distance obtained from the measured population and rE is the mean distance expected under random conditions, affords a measure of the degree of deviation from randomness. Students of human geography have used the nearest-neighbor measure as a basis for a highly sophisticated methodology to analyze the dispersion of towns, department stores, and other features of land-use patterns. Additional information about the spatial relations in a population can be secured by extending these procedures to measurement of the distance to the second and successive nearest neighbors, or by increasing the number of sectors about any chosen sampling point.
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