Population ecology Study Guide

📖 Core Concepts Population ecology – study of how species’ numbers change over time and interact with the environment (births, deaths, immigration, emigration). Intrinsic rate of increase ($r$) – the maximum per‑capita growth possible under ideal conditions; a density‑independent driver. Carrying capacity ($K$) – the highest sustainable population size given resource limits; a density‑dependent factor. Exponential growth – unlimited resources → population grows as $N(t)=N{0}e^{rt}$. Logistic growth – growth slows as $N$ approaches $K$: $\displaystyle \frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$. r‑ vs. K‑selection – life‑history strategies at opposite ends of the $r$–$K$ continuum (many small offspring, low parental care vs. few large offspring, high care). Survivorship curves – Type I (K‑selected), Type II (constant mortality), Type III (r‑selected). Metapopulation – network of spatially separated subpopulations (source ↔ sink patches) with local extinctions and recolonizations. Top‑down vs. Bottom‑up control – predators limiting prey abundance vs. primary producers limiting higher trophic levels. --- 📌 Must Remember Malthusian model = exponential growth; assumes constant environment. Logistic equation predicts an S‑shaped curve; growth rate = $r\left(1-\frac{N}{K}\right)$. Maximum Sustainable Yield (MSY) = largest harvest that can be taken indefinitely without reducing $K$. r‑selected traits: high $r$, many offspring, low survival early → Type III curve. K‑selected traits: low $r$, few offspring, high parental care → Type I curve. Rescue effect – immigration into a small patch can prevent its extinction. Lotka–Volterra predator‑prey produces coupled oscillations (not detailed in outline but important to remember). --- 🔄 Key Processes Exponential Growth Calculation Compute $N(t)$ with $N(t)=N{0}e^{rt}$. Logistic Growth Step‑by‑Step Determine $r$, $K$, and current $N$. Plug into $\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)$. Update $N$ over a time step (e.g., Euler: $N{t+\Delta t}=N{t}+\frac{dN}{dt}\Delta t$). Metapopulation Patch Dynamics For each patch: assess occupancy → calculate emigration (source) or immigration (sink). Apply rescue effect if immigration > local extinction risk. r/K Selection Evaluation Identify life‑history traits → place species on the $r$–$K$ spectrum. Survivorship Curve Assignment Observe mortality pattern → assign Type I, II, or III. --- 🔍 Key Comparisons Exponential vs. Logistic Growth Exponential: unlimited resources, constant per‑capita growth → $N$ rises forever. Logistic: limited resources, growth slows as $N\to K$ → S‑shaped curve. r‑selected vs. K‑selected Species r‑selected: high $r$, many small offspring, low parental care, Type III curve. K‑selected: low $r$, few large offspring, high parental care, Type I curve. Top‑down vs. Bottom‑up Control Top‑down: predators suppress lower trophic levels. Bottom‑up: primary producer abundance drives the whole food web. Source Patch vs. Sink Patch Source: net exporter of individuals, can sustain itself. Sink: net importer, would go extinct without immigration. --- ⚠️ Common Misunderstandings “$r$ is always positive.” – $r$ can be negative when mortality > births (population decline). “Logistic growth stops at exactly $K$.” – $N$ asymptotically approaches $K$; fluctuations can overshoot or undershoot. “All K‑selected species have Type I curves.” – Most do, but exceptions exist (e.g., some long‑lived reptiles). “Top‑down control means predators are always the most important factor.” – Bottom‑up effects can dominate in many ecosystems; the balance is context‑dependent. “Metapopulation = single large population.” – It’s a set of distinct patches with independent extinction/recolonization dynamics. --- 🧠 Mental Models / Intuition “Growth ceiling” – Imagine a balloon inflating: exponential = unlimited air; logistic = balloon hits its elastic limit ($K$). “Life‑history spectrum” – Visualize a seesaw: r‑selected on the “many‑kids” side, K‑selected on the “few‑big‑kids” side. “Patch board game” – Think of a game board where pieces (individuals) move between squares (patches); source squares generate extra pieces, sink squares need pieces from elsewhere to stay occupied. --- 🚩 Exceptions & Edge Cases Variable $K$ – Environmental changes (e.g., habitat loss) can shift $K$ over time; logistic equation still applies locally but $K$ must be updated each step. Allee effect – At very low $N$, per‑capita growth can become negative (not in outline but a common edge case). Mixed top‑down/bottom‑up – Marine fisheries often shift from predator‑driven (top‑down) to productivity‑driven (bottom‑up) regimes after intense harvest. --- 📍 When to Use Which Exponential formula – Use when resources are clearly unlimited (short‑term lab cultures, early colonization). Logistic model – Apply for most natural populations where resource limitation is evident. r/K selection framework – Helpful for predicting reproductive strategy, conservation needs, and survivorship type. Metapopulation model – Choose when habitat is fragmented and local extinctions/recolonizations drive dynamics (e.g., island species, patchy forests). Top‑down vs. Bottom‑up analysis – Use top‑down focus when predator densities change dramatically; use bottom‑up when primary productivity or habitat quality shifts. --- 👀 Patterns to Recognize S‑shaped population curves → logistic growth with a clear $K$. Oscillating predator–prey numbers → classic Lotka–Volterra dynamics. High early‑life mortality followed by survivorship plateau → Type III curve → r‑selected. Stable, low early mortality then rapid senescence → Type I curve → K‑selected. Patch occupancy that fluctuates but never reaches 100 % → metapopulation with source‑sink dynamics. --- 🗂️ Exam Traps Mistaking $r$ for “growth rate” in logistic equation – $r$ is the intrinsic rate; the actual per‑capita rate is $r\left(1-\frac{N}{K}\right)$. Choosing exponential model when $K$ is mentioned – Any reference to carrying capacity forces the logistic model. Confusing density‑dependent vs. density‑independent – $r$ is density‑independent; $K$ is density‑dependent. Assuming all predators imply top‑down control – If primary productivity is limiting, bottom‑up control may dominate despite predator presence. Identifying a species as K‑selected solely from long lifespan – Must also consider low $r$, few offspring, high parental care. Selecting “MSY = K/2” without context – The classic MSY occurs at $N = K/2$ only for the simple logistic model; real populations often deviate.