1. What is the Intrinsic Rate of Increase?

The intrinsic rate of increase (r) is a fundamental concept in population ecology that represents the per capita growth rate of a population under ideal conditions. It's calculated as the natural logarithm of the finite growth factor (λ).

2. How Does the Calculator Work?

The calculator uses the intrinsic rate of increase equation:

Where:

• \( r \) — Intrinsic rate of increase (per unit time)
• \( \lambda \) — Finite growth factor (unitless)

Explanation: The equation converts the multiplicative growth factor (λ) into an additive growth rate (r) that can be used in continuous population models.

3. Importance of r Calculation

Details: The intrinsic rate of increase is crucial for population modeling, conservation biology, and understanding population dynamics. It helps predict how populations will change over time under ideal conditions.

4. Using the Calculator

Tips: Enter the finite growth factor (λ) which must be a positive number. The value represents the multiplicative growth per time period (e.g., λ = 1.5 means 50% growth per time period).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between r and λ?
A: λ is the finite growth factor (multiplicative growth per discrete time period), while r is the intrinsic rate of increase (continuous growth rate).

Q2: What does a negative r value mean?
A: A negative r indicates population decline (λ < 1), while positive r indicates population growth (λ > 1).

Q3: What are typical values for λ in nature?
A: Most populations have λ values between 0.5 and 2.0, though extreme values can occur in rapidly growing or declining populations.

Q4: How is this related to exponential growth?
A: The exponential growth equation N(t) = N₀eʳᵗ uses r, while the geometric growth equation N(t) = N₀λᵗ uses λ.

Q5: When would you use r instead of λ?
A: r is used in continuous-time models (differential equations), while λ is used in discrete-time models (difference equations).