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# Species Competition

Ecological Statistics

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vac038

Copyright © 2002 John Wiley & Sons, Ltd

Book Title

## Encyclopedia of Environmetrics

Additional Information

#### How to Cite

Young, L. J. 2006. Species Competition. Encyclopedia of Environmetrics. 4.

#### Publication History

- Published Online: 15 SEP 2006

This is not the most recent version of the article. View current version (15 JAN 2013)

Interspecific competition arises when the interaction of two species has an adverse effect on both species [14]. Competition may occur due to (a) exploitation (individuals from different species share the same limited resource(s)) or (b) interference (individuals from different species fight or exhibit other directly damaging behavior) [18]. Examples include two bird species seeking the same supply of insects, and tree seedlings of differing species sharing sunlight, water, and nutrients in the forest understory.

Interest in competition dates at least to the time of Charles Darwin [2]. Early studies tended to focus on discovering examples of one species replacing another. Competition studies have expanded to include investigations of the effect of environmental conditions on the competitive ability of one species relative to another, the role of competition in determining the distribution and abundance of organisms, and the conditions needed for species to coexist.

### Models of Competition

- Top of page
- Models of Competition
- Designed Experiments
- Indices for Measuring Competition
- Logistic Regression
- References

Statistical approaches to competition have been through modeling, designed experiments both in the laboratory and the field, and observational studies. The *Lotka–Volterra equations* [4, 10, 21, 22] have been the primary model for competition in the ecological literature since the 1920s. The Lotka–Volterra equations for competition between two species may be written as

- (1)

- (2)

where *N*_{1} and *N*_{2} are the population densities of species 1 and 2, *r*_{1} and *r*_{2} are the intrinsic (maximum per capita) rates of increase of species 1 and 2, *K*_{1} and *K*_{2} are the carrying capacities of species 1 and 2, and α and β are the competition coefficients. To reflect some of the randomness inherent in nature, stochastic simulations of these deterministic equations to assess the fate of competing species have been suggested [1]. These models have been extended and others developed (see, for example, [5] and [17]).

### Designed Experiments

- Top of page
- Models of Competition
- Designed Experiments
- Indices for Measuring Competition
- Logistic Regression
- References

Replacement series experiments are a standard method of evaluating the competitive relationships of two or more species [6]. These are conducted in either the field or the laboratory. For two species *X* and *Y*, a replacement series experiment varies the proportions of *X* and *Y* present in a mixture while holding the total density of species *X* and *Y* constant throughout the experiment. Typically, the experimental ratios are 0 : 1, 1 : 3, 1 : 1, 3 : 1, and 1 : 0. For plants, the responses of interest are the total yield and the contribution of each species to that yield. Such experiments usually have few replications because of the expense of conducting the studies. Harper [6] suggests four models that can describe possible outcomes from these experiments.

In replacement series experiments, the focus is on interspecific competition for a given set of environmental conditions. However, changes in the environment may have an impact on the relative ability of one species to compete against another. Experimental studies have been used to evaluate the effect of various environmental factors on the competitive responses of species. Grover [5] summarizes much of this literature.

### Indices for Measuring Competition

- Top of page
- Models of Competition
- Designed Experiments
- Indices for Measuring Competition
- Logistic Regression
- References

Numerous indices have been used to draw inference about the competition between two species. Most are based either on the presence/absence (*see* Binary Data) of species across habitats or on the extent to which their niches overlap. First, consider the indices based on the presence and absence of two species at each of *n* sites, resulting in count data of the form shown in Table 1. The simple matching coefficient *S*_{1} = (*a* + *d*)/*n*, the Ochiar index *S*_{2} = *a*/[(*a* + *b*)(*a* + *c*)]^{0.5}, the Dice index *S*_{3} = 2*a*/(2*a* + *b* + *c*), and the Jaccard index *S*_{4} = *a*/(*a* + *b* + *c*) are commonly used measures of association. If abundance, and not just presence or absence, is recorded for each site, then a correlation coefficient can be used to measure the similarity between two species.

Species 2 | |||
---|---|---|---|

Species 1 | Present | Absent | Total |

Present | a | b | a + b |

Absent | c | d | c + d |

Total | a + c | b + d | n |

Because the environment may not be suitable to either species, the value of indices that indicate strong positive association as a result of a large number of joint absences *d*, or a large number of zeros when computing correlation, has been questioned (see [8]). Another concern has been that many similarity indices effectively incorporate a measure of the frequency of occurrence of species that distorts the results [9].

Measures of niche overlap have also been used as measures of competition (*see* Species Overlap). The indices differ depending on whether the resources are considered to be in a number of distinct categories or measured on a continuous scale. When resources are in distinct categories, indices are generally based on the relative proportions *p*_{ij} of the total resources used by species *j* that are in category *i*(*i* = 1, 2, …, *R*; *j* = 1, 2, …, *s*). Examples include Morisita's [13] index:

- (3)

and Pianka's [16] index:

- (4)

where the summations are over the *R* resource categories. Numerous other indices have been proposed, including those based on information theory [7] and the likelihood functions [15]. Schatzmann et al. [19] review 13 such indices.

Sometimes resources are measured on the continuous scale. For example, two species may compete for prey, and the extent of overlap is the extent to which they utilize prey of similar size where prey size is measured on a continuous scale. Assuming the size of prey consumed by each species is normally distributed with mean μ_{i} and standard deviation σ_{i} the niche overlap is measured by the overlap in the two normal distributions for species *i* and *j* [11]:

- (5)

The usage distribution of a continuous resource used by a species is not always normally distributed and may be highly skewed. Manly and Patterson [12] suggested use of a Weibull distribution when the usage distribution is skewed. Often the measure of niche overlap is taken as a measure of competition. The difficulty here lies in the fact that competition may engender a reduction in niche overlap, leading to an underestimate of the effect of competition.

### Logistic Regression

- Top of page
- Models of Competition
- Designed Experiments
- Indices for Measuring Competition
- Logistic Regression
- References

Because competing species require similar resources, positive measures of association and little niche overlap are often observed for species that are known to compete based on experimental studies. In these cases, any tendency of the presence of one species to reduce the probability of the presence of the other species is more than offset by their common preferences for the same habitat. As Diamond [3] noted, enemies are ‘doomed to associate’, making the assessment of competition in terms of species association problematic. Schoener and Adler [20] suggested using logistic regression to relate the probability of presence of a species to both habitat variables and the presence of other species. They found that the positive association between species indicated by traditional indices became mostly negative after accounting for the ecological covariates.

### References

- Top of page
- Models of Competition
- Designed Experiments
- Indices for Measuring Competition
- Logistic Regression
- References

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