C4.1.15 Use of the chi-squared test for association between two species Notes

Using the Chi-Squared Test for Association Between Two Species

1. The test essentially compares observed data with expected data under a given hypothesis.
2. In ecology, it helps determine whether two species are:
   1. Independently distributed → No ecological relationship.
   2. Associated (positively or negatively) → Potential competition or mutualism.

Key Terms

1. Null Hypothesis ($H_0$): The species are distributed independently, with no association between them.
2. Alternative Hypothesis ($H_1$): There is an association between the species, they may be found together more often or less often than expected by chance.

Steps to Perform a Chi-Squared Test

1. Collect Data Using Quadrat Sampling

1. Select random quadrats across a study site.
2. Record the presence or absence of both species in each quadrat.

2. Construct a Contingency Table

1. Organize the collected data in a 2 × 2 table:

3. Calculate Expected Values ($E$) for Each Category

Use the formula:

\[
E = \frac{\text{Row Total} \times \text{Column Total}}{\text{Overall Total}}
\]

4. Apply the Chi-Squared Formula

\[
\chi^2 = \sum \frac{(O - E)^2}{E}
\]

Where:

• O = Observed value
• E = Expected value

5. Compare with Critical Value

1. Use a chi-squared table to find the critical value at p = 0.05 with 1 degree of freedom.
2. If $χ^2$ exceeds the critical value, reject $H_0$ (species are associated).

Interpreting Results

1. Reject $H_0$ (Association Exists)
   1. Positive Association: The species occur together more often than expected (e.g., mutualism).
   2. Negative Association: The species occur together less often than expected (e.g., competition).
2. Fail to Reject $H_0$ (No Association)
   1. The species are distributed independently, meaning no significant relationship.

Applications in Ecology

1. The chi-squared test is widely used to assess species interactions, such as:
   1. Competition: If species occur together less frequently than expected, it may suggest competitive exclusion.
   2. Mutualism: If species occur together more frequently than expected, it may indicate a beneficial relationship.

Reflection and Review

1. The chi-squared test is a powerful tool for analyzing species interactions.
2. It helps ecologists understand patterns of distribution and potential competition or cooperation.