use Spearman’s rank correlation and Pearson’s linear correlation to analyse the relationships between two variables, including how biotic and abiotic factors affect the distribution and abundance of species (the formulae for these correlations will b

Biodiversity – Analysing Relationships with Correlation

Understanding how biotic (living) and abiotic (non‑living) factors influence the distribution and abundance of species is a core aim of the A‑Level Biology syllabus. Statistical tools such as Spearman’s rank correlation and Pearson’s linear correlation allow us to quantify these relationships.

Key Concepts

• Distribution – the geographical area where a species occurs.
• Abundance – the number of individuals of a species in a given area.
• Biotic factors – interactions with other organisms (e.g., competition, predation, symbiosis).
• Abiotic factors – physical and chemical elements of the environment (e.g., temperature, pH, moisture).

When to Use Each Correlation

• Spearman’s rank correlation (\$\rho\$) – appropriate for ordinal data or when the relationship is monotonic but not necessarily linear.
• Pearson’s linear correlation (\$r\$) – suitable for interval/ratio data where a linear relationship is expected.

Mathematical Formulas

Spearman’s rank correlation coefficient:

\$\$

\rho = 1 - \frac{6\sum d_i^{2}}{n\,(n^{2}-1)}

\$\$

where \$d_i\$ is the difference between the ranks of each pair and \$n\$ is the number of observations.

Pearson’s linear correlation coefficient:

\$\$

r = \frac{\displaystyle\sum{i=1}^{n}(xi-\bar{x})(y_i-\bar{y})}

{\sqrt{\displaystyle\sum{i=1}^{n}(xi-\bar{x})^{2}\;\displaystyle\sum{i=1}^{n}(yi-\bar{y})^{2}}}

\$\$

\$\bar{x}\$ and \$\bar{y}\$ are the means of the \$x\$ and \$y\$ variables respectively.

Step‑by‑Step Procedure

1. Collect paired data for the two variables of interest (e.g., species abundance and soil nitrogen concentration).
2. Choose the appropriate correlation method:

   • If data are ordinal or the relationship is monotonic → use Spearman’s \$\rho\$.
   • If data are continuous and a linear trend is expected → use Pearson’s \$r\$.

3. Calculate the necessary statistics:

   • For Spearman: assign ranks, compute \$d_i\$, then apply the formula.
   • For Pearson: compute means, deviations, products of deviations, and sums of squares.

4. Interpret the coefficient:

   • Value range: \$-1 \leq \text{coefficient} \leq +1\$.
   • Positive value → variables increase together; negative value → one increases while the other decreases.
   • Magnitude indicates strength (e.g., \$|r|>0.7\$ strong, \$0.3<|r|<0.7\$ moderate, \$|r|<0.3\$ weak).

5. Assess significance (usually via a \$t\$‑test for Pearson or a table of critical \$\rho\$ values for Spearman) to determine if the observed correlation could arise by chance.

Example: Influence of Temperature on Insect Abundance

The table below shows hypothetical data collected from five sites.

Because both variables are continuous and a linear trend is expected, Pearson’s \$r\$ is appropriate.

Calculation outline (values shown for illustration):

• \$\bar{x}=21\$ °C, \$\bar{y}=310\$ individuals.
• Compute \$(xi-\bar{x})(yi-\bar{y})\$, \$(xi-\bar{x})^{2}\$ and \$(yi-\bar{y})^{2}\$ for each site.
• Sum the products: \$\sum (xi-\bar{x})(yi-\bar{y}) = 2\,250\$.
• Sum of squares: \$\sum (xi-\bar{x})^{2}=180\$, \$\sum (yi-\bar{y})^{2}=140\,000\$.
• Insert into the formula:

  \$r = \frac{2\,250}{\sqrt{180 \times 140\,000}} \approx 0.99\$

The very high positive \$r\$ indicates a strong linear relationship: as temperature rises, insect abundance increases.

Biotic vs. Abiotic Influences – How Correlation Helps

• Abiotic example: Correlating soil pH with plant species richness using Pearson’s \$r\$ to test whether more neutral soils support greater diversity.
• Biotic example: Using Spearman’s \$\rho\$ to examine the rank order of predator density against prey abundance across habitats, where the relationship may be monotonic but not strictly linear.
• Combining both: Multiple correlation analyses can reveal whether abiotic factors (e.g., temperature) or biotic interactions (e.g., competition) have a stronger influence on a target species.

Interpreting Results in an Ecological Context

1. Identify the direction of the relationship (positive/negative).
2. Consider causality – correlation does not prove cause; experimental or longitudinal data are needed.
3. Relate statistical strength to ecological significance (e.g., a moderate \$r\$ may still be biologically important if the factor is a key limiting resource).
4. Discuss possible confounding variables that could affect the observed correlation.

Summary

Spearman’s rank correlation and Pearson’s linear correlation are essential quantitative tools for A‑Level Biology. They enable students to:

• Quantify how biotic and abiotic factors are associated with species distribution and abundance.
• Choose the appropriate statistical test based on data type and relationship form.
• Interpret the ecological meaning of statistical outcomes and recognise the limits of correlation analysis.

Mastery of these techniques prepares students for higher‑level investigations into biodiversity patterns and informs evidence‑based conservation strategies.