Population Ecology Calculator

Act as an IB Biology tutor. Help me understand population dynamics: **Population growth models:** **Exponential growth:** - Occurs when resources are unlimited - J-shaped curve - Formula: $N_t = N_0 e^{rt}$ - $N_t$ = population size at time t - $N_0$ = initial population - $r$ = growth rate - $t$ = time **Logistic growth:** - Occurs with limited resources - S-shaped curve - Approaches carrying capacity (K) - Formula: $\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right)$ **Key terms:** - **Carrying capacity (K)**: Maximum population size environment can support - **Limiting factors**: Resources, space, predation, disease - **Density-dependent factors**: Effect increases with population density - **Density-independent factors**: Effect regardless of density (e.g., natural disasters) **Population sampling:** - **Quadrat method**: For plants and sessile animals - **Capture-mark-recapture**: For mobile animals - Formula: $N = \frac{MC}{R}$ where M=marked, C=total in second sample, R=recaptured marked **IB Tip:** Draw growth curves and label key features **My ecology question:** [ASK ABOUT POPULATIONS]