Statistical Analysis and Data Visualization

Mean and Density

• Mean of observed grades: 85.08

• Density representation of observed grades against the normal curve depicted:

  • Density values (in arbitrary units):

  • 0.05

  • 0.04

  • 0.03

  • 0.02

  • 0.01

  • 0.00

  • Grade scales span from 40 to 100.

Morphology and Measuring Phenotype

Historical Context

• Previous topics covered:

  • Maths

  • The Normal Distribution

  • Probability Values

  • T-Test

  • F-Test

  • Shapiro-Wilkes Test

  • Pearson Correlation Test

  • Covariates (Nuisance Parameters)

  • Biology-related topics: Plasticity and Canalisation, Dimorphism, Extended Concepts of Phenotype.

Upcoming Topics

1. Box and Whisker Plots

2. Selection and the Normal Distribution

   • Types of Selection:

   1. Stabilizing Selection

   2. Directional Selection

   3. Diversifying Selection

   4. Relaxed Selection

3. Allometry

Box and Whisker Plots

• Components of Box and Whisker Plots:

  • Lower Quartile (Q1): Marks the 25th percentile of the data.

  • Median: The middle value of the dataset.

  • Upper Quartile (Q3): Marks the 75th percentile of the data.

  • Interquartile Range (IQR): The range between Q1 and Q3, measuring middle 50% of the data.

  • Whiskers:

  • Extend from Q1 to minimum value and from Q3 to maximum value.

Example Data Representation

• Example for Abundance and Size:

  • Abundance values: 70, 80, …, 150.

  • Size specified on an axis (e.g., length in mm).

Natural Selection Types

Stabilizing Selection

• Definition: A type of natural selection favoring intermediate phenotypes while selecting against extremes; reduces genetic diversity and maintains the population’s status quo.

• Testing Method: Can be tested using the F-Test or Levene Test.

Directional Selection

• Definition: Selection of one extreme phenotype over another within a population.

• Example: Long-necked giraffes adapted better for feeding than short-necked ones.

• Application in assessments through the t-test for variations in traits.

Historical Example: Peppered Moth

• Population Dynamics:

  • Pre-Industrial vs Post-Industrial Revolution study by Bernard Kettlewell.

  • Evolution example: Light-colored moths camouflaged well in non-polluted environments, while dark moths adapted in polluted areas.

• Graphical representation indicates population shifts over time.

Relaxed Selection

• Definition: A condition where the strength of natural selection decreases, allowing for mutation accumulation due to decreased pressures like elimination of predators.

• Application: Use of the F-Test or Levene Test for empirical testing.

Diversifying Selection

• Definition: Favors extreme traits in a population, increasing genetic variability and leading to distinct groups, an important mechanism for sympatric speciation.

Case Study: Cactus Spine Number

• Observations show:

  • Both predators influence spine number outcomes over generations:

  • Stabilizing selection observed with both predator types.

  • Herbivores prompted more spines due to adaptive pressure.

Adaptive Radiation and Speciation

• Adaptive Radiation seen in species like Hawthorn Maggot Fly with distinct genetic signatures across various fruit types indicating continuum in speciation.

• Life Cycle Dynamics explained:

  • Apple Maggot (Rhagoletis pomonella) life cycle with reliance on specific host fruits throughout the growing season.

Allometry

• Definition: The study of how different parts of an organism grow at different rates relative to each other, opposite of isometry.

• Relevance in ecological dynamics studied by comparing shell morphology across snail populations:

  • Assessing isometric vs allometric relationships concerning predator presence.

Data Collection and Analysis

• Measurements includes:

  • Shell length, width, aperture area to determine relationships and control for covariates.

• Impacts of predators on shell morphology studied across different environments like Liberty Trail Pond vs Gobble-Gobble Pond.

Measurement Parameters

1. Morphological measurements used:

   • Shell Length (SL)

   • Shell Width (SW)

   • Aperture Length (AL)

   • Aperture Width (AW)

2. Experimental Setup:

   • Image and measure two snails from each population including data specifications for ratios and corresponding comparisons.

   • Instructions specify proper working directories for data handling.

Conclusion

Each section presents critical components of statistical methodologies related to ecological and evolutionary principles with practical examples from natural selection, testing mechanisms, and data visualizations in biological contexts.