An overview of population dynamics, including the study of how populations change in size, density, age structure, and distribution over time.
Introduction to Population Dynamics
Key concepts, models, and applications
| Term | Meaning |
|---|---|
| Population | A group of individuals of the same species that live in a defined area and interbreed. |
| Growth Rate (r) | Net change per individual per unit time (births – deaths). |
| Carrying Capacity (K) | Maximum sustainable population size that the environment can support. |
| Density‑dependent factors | Processes whose intensity changes with population density (e.g., competition, disease). |
| Density‑independent factors | Processes that affect populations regardless of density (e.g., weather, natural disasters). |
| Age structure | Distribution of individuals among age classes; influences reproductive output and mortality. |
| Life table | Tabular summary of survival and fecundity by age or stage. |
| Leslie matrix | A matrix model that projects age‑structured populations forward in time. |
[ \frac{dN}{dt}=rN \quad\Longrightarrow\quad N(t)=N_0e^{rt} ]
[ \frac{dN}{dt}=rN\left(1-\frac{N}{K}\right) ]
Geometric (Ricker) Model
[
N_{t+1}=N_t e^{r\left(1-\frac{N_t}{K}\right)}
]
Beverton‑Holt Model (common in fisheries)
[
N_{t+1}= \frac{R_0 N_t}{1+(R_0-1)N_t/K}
]
Why Discrete?
[ \mathbf{n}_{t+1}= \mathbf{L},\mathbf{n}_t ]
| Category | Examples | Typical Effect |
|---|---|---|
| Biotic | Competition, predation, parasitism, mutualism | Usually density‑dependent; can regulate (N). |
| Abiotic | Temperature, precipitation, habitat loss, pollutants | Often |