ASSOCIATION AND DISPERSION

I. Objectives:

1. Use quadrat sampling to obtain data on species distribution and association patterns
2. Learn the basic statistics necessary to analyze dispersion for a species and association among two or more species.

II. Introduction:

Because distribution patterns can provide information concerning the biology of a species and the factors limiting that organism, ecologists are often interested in determining whether individuals of a species are clumped, randomly distributed, or uniformly dispersed in space.

For example, a clumped distribution may indicate that a species is responding to fine gradations in the environment or that it has a form of reproduction that keeps juveniles near adults. Conversely, a uniform distribution may indicate territoriality or some other aggressive interaction among individuals. The primary approach to determining dispersion patterns is to compare observed patterns with what would be expected if the dispersion were random (using a statistical test). If there is no difference, then you assume the distribution is random. If there is a difference, then you examine the data to determine whether individuals are found together (clumped) or are spaced apart (uniform).

There are several analytical methods to measure dispersion. The most common technique is to compare the data to the expectations of the Poisson distribution, but this approach is difficult and cumbersome. We will use the Chi Square test (X²) to compare the sum of squares (a measure of variability) to the mean to determine dispersion patterns for the organisms we study. According to this test, if a species is uniformly distributed, variability should be low (similar numbers in all quadrats). If species are clumped, variability should be high (some quadrats with many individuals, others with few or none). Random distributions would have intermediate variability.

Another potentially interesting aspect of distribution patterns is whether two species usually occur together (are positively associated), seldom occur together (negatively associated), or are randomly associated with respect to each other. If the species are positively associated, it may indicate some sort of obligate interaction, such as mutualisms or predation, or it may indicate similar habitat requirements. If they are negatively associated, it may reflect the results of competition or different habitat preferences.

To determine how species are associated, we first compare observed patterns to what would be expected if they are random. If they are not random, we can then calculate an index of association (V) to see whether the species are positively or negatively associated and how strong that association is. To do this, first construct the following table:

                                                        Species 1

                                            present    absent  row sums

                    present                 a             b                m
Species 2   
                    absent                  c             d                 n    

                    column sums        r             s                 N (grand total)

a = no. quadrats where both species are present
b = no. of quadrats with only species 2
c = no. of quadrats with only species 1
d = no. of quadrats with neither species
m = sum of a+b
n = sum of c+d
r = sum of a+c
s = sum of b+d
N = sum of a+b+c+d

To determine if the association pattern is random, use the following modification of the X² test:

X² = N(ad-bc-N/2)² with 1 d.f.
               mnrs

If the test is not significant, the association is random.

If it is significant, calculate the Index of Association (V) to determine the strength of the association and whether it is negative or positive.

V = ad-bc
    Sqrt(mnrs)

V ranges from +1 to –1. A +1 means the species are completely positively associated (always found together). A –1 means they are completely negative associated (never found together). Values in between indicate weaker positive or negative associations, depending on the sign and how close the value of V is to 1 or –1.

III. Methodology:

A. Data collection

We will count the numbers of dandelions and cudweed within 0.25 m² quadrats on the lawn near Friday Hall on the UNCW campus. Each group (four students/group) will record the numbers of both plants within 60 quadrats taken randomly in an area designated by the instructor. The instructor will demonstrate the proper techniques for selecting a "random" quadrat. Record the data in the data sheet provided.

B. Analysis of Dispersion Patterns

Calculate the sum of squares (SS) and mean for the number of plants/quadrat for both cudweed and dandelions (calculate the means for each species separately). For each species, next calculate:

X² = SS/mean d.f.= total no. quadrats – 1

Look up this value in the figure in your lab manual.

C. Analysis of Association

Using the formulas outlined in the introduction, determine the association between cudweed and dandelions.

IV. Laboratory Assignment:

1. Showing all calculations and your raw data, determine the dispersion patterns for both cudweed and dandelion.
2. Showing all calculations and your raw data, determine the association between dandelions and cudweed.
3. What are some likely explanations for the dispersion and association patterns observed for these species? (Hint: both are weeds that colonize disturbed areas).

Association and Dispersion Data Sheet

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