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Population dispersion

Contributed by: Francis C. Evans Publication year: 2014

The spatial distribution at any particular 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, area, or the average area per individual. It also determines the , 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 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 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 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 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 :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 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. However, since all of these methods assume that the individuals are AccessScience from McGraw-Hill Education Page 5 of 7 www.accessscience.com

small enough to be treated mathematically as points, they become less accurate when the individuals cover considerable space.

Factors affecting dispersion

The principal factors that determine patterns of population dispersion include (1) the action of environmental agencies of transport, (2) the distribution of soil types and other physical features of the habitat, (3) the influence of temporal changes in weather and climate, (4) the behavior pattern of the population in regard to reproductive processes and dispersal of the young, (5) the intensity of intra- and interspecific competition, and (6) the various social and antisocial forces that may develop among the members of the population. Although in certain cases the dispersion pattern may be due to the overriding effects of one factor, in general populations are subject to the collective and simultaneous action of numerous distributional forces and the dispersion pattern reflects their combined influence. When many small factors act together on the population, a more or less random distribution is to be expected, whereas the domination of a few major factors tends to produce departure from randomness.

Environmental agencies of transport. The transporting action of air masses, currents of water, and many kinds of animals produces both random and nonrandom types of dispersion. Airborne seeds, spores, and minute animals are often scattered in apparently haphazard fashion, but aggregation may result if the wind holds steadily from one direction. Wave action is frequently the cause of large concentrations of seeds and organisms along the drift line of lake shores. The habits of fruit-eating birds give rise to the clusters of seedling junipers and cherries found beneath such perching sites as trees and fencerows, as well as to the occurrence of isolated individuals far from the original source. Among plants, it seems to be a general principle that aggregation is inversely related to the capacity of the species for seed dispersal.

Physical features of the habitat. Responses of the individuals of the population to variations in the habitat also tend to give rise to local concentrations. Environments are rarely uniform throughout, some portions generally being more suitable for life than others, with the result that population density tends to be correlated directly with the favorability of the habitat. Oriented reactions, either positive or negative, to light intensities, moisture gradients, or to sources of food or shelter, often bring numbers of individuals into a restricted area. In these cases, aggregation results from a species-characteristic response to the environment and need not involve any social reactions to other members of the population. See also: ENVIRONMENT.

Influence of temporal changes. In most species of animal, daily and seasonal changes in weather evoke movements which modify existing patterns of dispersion. Many of these are associated with the disbanding of groups as well as with their formation. Certain birds, bats, and even butterflies, for example, form roosting assemblages at one time of day and disperse at another. Some species tend to be uniformly dispersed during the summer, but flock together in winter. Hence temporal variation in the habitat may often be as effective in determining distribution patterns as spatial variation. AccessScience from McGraw-Hill Education Page 6 of 7 www.accessscience.com

Behavior patterns in reproduction. Factors related to reproductive habits likewise influence the dispersion patterns of both plant and animal populations. Many plants reproduce vegetatively, new individuals arising from parent rootstocks and producing distinct clusters; others spread by of rhizomes and runners and may thereby achieve a somewhat more random distribution. Among animals, congregations for mating purposes are common, as in frogs and toads and the breeding swarms of many insects. In contrast, the breeding territories of various fishes and birds exhibit a comparatively regular dispersion. See also: REPRODUCTIVE BEHAVIOR.

Intensity of competition. Competition for light, water, food, and other resources of the environment tends to produce uniform patterns of distribution. The rather regular spacing of trees in many forests is commonly attributed largely to competition for sunlight, and that of desert plants for soil moisture. Thus a uniform dispersion helps to reduce the intensity of competition, while aggregation increases it. See also: POPULATION ECOLOGY.

Social factors. Among many animals the most powerful forces determining the dispersion pattern are social ones. The social habit leads to the formation of groups or societies. Plant ecologists use the term society for various types of minor communities composed of several to many species, but when the word is applied to animals it is best confined to aggregations of individuals of the same species which cooperate in their life activities. Animal societies or social groups range in size from a pair to large bands, herds, or colonies. They can be classified functionally as mating societies (which in turn are monogamous or polygamous, depending on the habits of the species), family societies (one or both parents with their young), feeding societies (such as various flocks of birds or schools of fishes), and as migratory societies, defense societies, and other types. Sociality confers many advantages, including greater efficiency in securing food, conservation of body heat during cold weather, more thorough conditioning of the environment to increase its habitability, increased facilitation of mating, improved detection of, and defense against predators, decreased mortality of the young and a greater life expectancy, and the possibility of division of labor and specialization of activities. Disadvantages include increased competition, more rapid depletion of resources, greater attraction of enemies, and more rapid spread of parasites and disease. Despite these disadvantages, the development and persistence of social groups in a wide variety of animal species is ample evidence of its overall survival value. Some of the advantages of the society are also shared by aggregations that have no social basis. See also: ECOLOGICAL COMMUNITIES; SOCIAL MAMMALS.

Optimal population density

The degree of aggregation which promotes optimum population growth and survival, however, varies according to the species and the circumstances. Groups or organisms often flourish best if neither too few nor too many individuals are present; they have an optimal population density at some intermediate level. The condition of too few individuals, known as undercrowding, may prevent sufficient breeding contacts for a normal rate of reproduction. On the other hand, overcrowding, or too high a density, may result in severe competition and excessive that will reduce fecundity and lower the growth rate of individuals. The concept of an intermediate optimal population density is sometimes known as Allee’s principle. See also: POPULATION GENETICS. Francis C. Evans AccessScience from McGraw-Hill Education Page 7 of 7 www.accessscience.com

Bibliography

A. A. Berryman (ed.), Dynamics of Forest Insect Populations, 1988

A. A. Berryman (ed.), Dynamics of Insect Populations: Patterns, Causes, Implications, 1988

P. Greig-Smith, Quantitative Plant Ecology, 3d ed., 1983

S. K. Jain and L. W. Botsford (eds.), Applied Population Biology, 1992

S. A. Levin (ed.), Applied Mathematical Ecology, 1989

A. G. Pakes and R. A. Maller, Mathematical Ecology of Plant Species Competition, 1990

E. C. Pielou, Population and Community Ecology: Principles and Methods, 1974

Additional Readings

T. D. Schowalter, Insect Ecology: An Ecosystem Approach, 3d ed., Academic Press, London, UK, 2011