Modeling & Population Growth

Define a model.

An idealized, simplified representation of reality.

Why simplify models?

To make them easier to understand and interact with (some details are omitted).

Can models be abstract or quantitative?

Yes—abstraction focuses on key components; quantitative models use math.

List reasons to model in ecology.

Clarify thinking; understand relationships; derive new insights/hypotheses; design better experiments; make predictions; understand other models.

Define an ecological model.

A simplified representation of stocks and flows relevant to a population, community, ecosystem, or the ecosphere.

List the three model types discussed.

Phenomenological/statistical; mechanistic/mathematical; empirical/machine learning.

What do phenomenological models ask?

What are the relationships between key variables? (e.g., regression).

What do mechanistic models ask?

What will happen if key variables change? (e.g., growth, competition, SIR).

What do empirical/ML models ask?

What is happening here? (focus on prediction, minimal assumptions).

List three problems with ecological models.

Too many parameters to measure; equations insoluble/too big; results (quotients of sums of products) may be uninterpretable.

What is the simplest ecological population model?

One population N with births (B) and deaths (D): Nt+1 = Nt + B − D.

When is a population at equilibrium in the simple model?

When B = D (flat trend).

When does population growth occur in the simple model?

When B > D (trend goes up).

When does population decline occur in the simple model?

When B < D (trend goes down).

Define exponential growth.

Rate of change proportional to current size; unchecked increase when resources are unlimited and environment doesn’t restrict growth; J‑shaped curve.

Write the continuous exponential growth equation.

dN/dt = rN.

Interpret terms in dN/dt = rN.

dN/dt: rate of change; r: intrinsic growth rate; N: population size.

Write the discrete density‑independent growth equation.

Nt = λ^t N0.

What is λ (lambda) in population growth?

Finite rate of increase in discrete time.

What does λ = 1 (or r = 0) indicate?

Population equilibrium.

What does λ < 1 (or r < 0) indicate?

Population decline.

What does λ > 1 (or r > 0) indicate?

Population increase.

In a full balance, which terms modify N across steps?

Births (B), deaths (D), immigration (I), emigration (E): Nt+1 = Nt + B − D + I − E.

How are b and d used in continuous models?

Per‑capita birth and death rates: dN/dt = (b − d)N = rN.

Define density‑dependent growth.

Growth where rates depend on N (e.g., resource limits, space, competition).

Define age‑structured growth.

Population growth tracked by age classes with age‑specific survival and reproduction.

What date was the Unit 1 midterm scheduled?

10/6/2025.

Which lectures lead up to the midterm?

9/5 to 10/3 (methods, systems, climate, biodiversity, evolution/life history, modeling, growth).