Marine Biodiversity and Statistical Analysis

Quantifying Marine Biodiversity

  • Biodiversity can be quantified using two primary factors: richness and evenness.

Species Richness

  • Definition: The number of different species in a community.

  • A sample with more species is considered richer.

  • Limitation: Richness does not consider the population size of each species. For example, one whelk has the same influence on richness as 1,000 barnacles, thus giving an equal rating to species regardless of their abundance.

  • A community with numerous species is regarded as richer than one with fewer species.

Species Evenness

  • Definition: A measure of the relative abundance of different species in an area.

  • Communities where one species is predominant are considered less diverse than communities where several species have similar abundance.

Simpson's Index of Diversity (d)

  • A biodiversity measure that incorporates both species richness and evenness.

  • Formula: D=1−(Σ(nN)2)D = 1 - \left( \Sigma \left( \frac{n}{N} \right)^2 \right) Where:

    • D = Simpson's Index of Diversity

    • n = number of individuals of each species

    • N = total number of individuals across all species

    • Σ = sum over all species.

Interpretation of Biodiversity Indices

  • Low Simpson's Index:

    • Indicates few successful species.

    • Suggests extreme or unstable environments.

    • Fewer ecological niches and complex food webs; biodiversity is susceptible to environmental changes.

  • High Simpson's Index:

    • Indicates many successful species and a stable ecosystem.

    • More ecological niches available, complex food webs; robust against environmental changes.

Application in Marine Ecosystems

  1. Biodiversity Index in Coral Reefs:

    • A decrease may indicate harm (e.g., oil spills, overfishing).

    • An increase may demonstrate successful conservation efforts.

Spearman's Rank Correlation

  • Used to analyze the relationship between two species in relation to abiotic factors (e.g., time above tide).

  • Null Hypothesis (H0): No correlation between the two species.

Visual Representation

  • Scatter Graphs:

    • Graph A: Positive correlation (as x increases, y increases).

    • Graph B: Negative correlation (as x increases, y decreases).

    • Graph C: No association (no link between x and y).

Testing Correlations

  • If the graph suggests a correlation:

    • Use correlation coefficient calculations to determine strength.

  • Spearman's Rank Correlation (r_s):

    • Used for non-normally distributed variables.

    • Values range between -1 and +1:

    • Close to +1 indicates a strong positive correlation.

    • Close to -1 indicates a strong negative correlation.

Formula for Spearman's Rank Correlation Coefficient

  • Formula: rs=1−(6ΣD2n3−n)r_s = 1 - \left( \frac{6 \Sigma D^2}{n^3 - n} \right) Where:

    • r_s = Spearman's Rank Correlation Coefficient

    • ΣD² = sum of the squared differences between ranks

    • n = number of pairs of data items.

Data Types for Analysis

  • Can involve:

    • Quantitative Data: Distance from high tide, light intensity, number of animals, or % cover of plant species in quadrats.

    • Qualitative Data: ACFOR abundance scale for species in quadrats.