Ecological Interactions and Population Dynamics

Key Definitions and Concepts

Plant Defense Mechanisms

• H: Proportion of plant tissue damaged without defenses.
• D: Protection level provided by defenses other than ants (e.g., chemical defenses).
• 1 - D: Tissue damage extent despite alternative defenses.
• A: Amount of herbivory prevented by ant presence.
• 1 - A: Herbivory occurrence despite ant protection.
• IIA: Investment by the plant in benefits provided to ants.
• IID: Investment in defenses other than those against ants.
• p: Proportion of plant population attracting sufficient ants for defense.
• n: Number of extrafloral nectaries per plant.
• m: Energy content of nectary structures.
• d: Duration during which the nectaries are active.
• a: Cost of producing amino acids in nectar.
• c: Cost of producing carbohydrates in nectar.
• h: Cost of providing water for nectar.

Mutualism, Fitness and Evolution

• Relative Fitness (w): Survival and reproduction ability of a genotype compared to others.
• Selection Coefficient (s): Measures the extent a genotype is selected against.
• Mutualist Fitness (wm):
  • Formula: wm = 1 - sm (where sm is the selection coefficient for mutualists).
• Nonmutualist Fitness (wn):
  • Formula: wn = 1 - sn (where sn is the selection coefficient for nonmutualists).
• Mutualism Persistence: Mutualisms evolve and persist when mutualist fitness exceeds nonmutualist fitness.

Ecological Dynamics and Population Growth

Photosynthetically Active Radiation (PAR)

• PAR: Light wavelengths from 400-700 nm crucial for photosynthesis, accounting for about 45% of solar energy at sea level.
• Measurement of PAR: Measured as photon flux density (µmol photons/m²/s).
• Nutrient-rich and low-light environments:
  • More investment in leaves for photosynthesis.
• Light-rich and nutrient-poor environments:
  • Greater investment in roots to access nutrients.

Population Dynamics

• Rate of Prey Consumption (g): A function dependent on prey abundance: g = g(N) (where N is the prey population size).
• X: Maximum carrying capacity without mutualists.
• dN₁: Growth rate of population 1 in an ecological model.
• X (Carrying Capacity): Maximum population size a species can sustain independently.
• aN₂: Positive effect of species 2 on species 1.

Biodiversity Measures

Shannon-Wiener Index (H')

• Shannon-Wiener Index (H'): A measure accounting for species diversity, combining both richness and evenness.
  • Formula: H' = -∑(piln(pi)) (where pi is the proportion of individuals of species i).
• Species Richness (s): Total count of different species in a community.
• Proportional Abundance of Species i (pi):
  • Formula: pi = ni / N (where ni is the number of individuals of species i and N is total individuals).
• Natural Logarithm of pi (ln(pi)): Natural logarithm computation of the species' proportional abundance.
• Evenness (E): Measures distribution uniformity among species.
  • Formula: E = H' / ln(s), ranges from 0 (dominance by one species) to 1 (equal abundance).

Important Reminders

• Understanding these concepts is crucial for topics related to ecology, evolution, and plant biology. Each definition, measurement, and relationship can significantly influence ecological interactions and biodiversity assessments.