Ecological Modeling - Common Functional Forms

Linear Equations

y = b₀ + b₁ x Intercept b₀ = 0.2 Slope b₁ = 1
y = b₀ - b₁ x Intercept b₀ = 1.2 Slope b₁ = 1

Quadratic Equations

y = b₀ + b₁ x - b₂ x²

Intercept b₀ = 0.2
b₁ = 3.5
b₂ = 3.6
Quadratic positive-negative equation

y = b₀ - b₁ x + b₂ x²

Intercept b₀ = 1.2
b₁ = 3.5
b₂ = 3.6
Linear negative-positive equation

Cubic Equations

y = b₀ + b₁ x - b₂ x² + b₃ x³ Intercept b₀ = 0.2 b₁ = 3.5 b₂ = 3.6 b₃ = 3.6
y = b₀ - b₁ x + b₂ x² - b₃ x³ Intercept b₀ = 1.2 b₁ = 3.5 b₂ = 6.6 b₃ = 3.6
y = b₀ - b₁ x + b₂ x² + b₃ x³ Intercept b₀ = 0.2 b₁ = 3.5 b₂ = 6.6 b₃ = 3.6
y = b₀ + b₁ x - b₂ x² - b₃ x³ Intercept b₀ = 1.2 b₁ = 3.5 b₂ = 6.6 b₃ = 3.6

y = b₀ + b₁ x - b₂ x² Intercept b₀ = 0.2 b₁ = 3.5 b₂ = 3.6
y = b₀ - b₁ x + b₂ x² Intercept b₀ = 1.2 b₁ = 3.5 b₂ = 3.6