Advanced Study Notes – Ecology
Paramedical Entrance – Biology
(MIT‑style, first principles, rigorous reasoning, edge cases, challenging problem)
These notes are intended for students who already have a solid background in biology, chemistry, and mathematics.
The material is organized into logical blocks, each building on the previous one. Where appropriate, derivations are shown explicitly, and “corner‑case” scenarios are highlighted.
1. Foundations
| Concept | First Principle | Key Take‑away |
|---|---|---|
| Energy & Matter | Conservation of Energy (1st Law of Thermodynamics) & Mass Balance | All ecosystems obey energy conservation; matter cycles. |
| Information | Information theory (Shannon) | Biodiversity can be quantified as Shannon entropy of species abundances. |
| Emergence | Non‑linear dynamics, self‑organisation | Ecosystem properties cannot be reduced to individual organisms alone. |
2. Ecosystem Structure
2.1 Abiotic Components
- Abiotic factors: temperature, light, soil pH, nutrients, hydrology.
- Physical constraints: energy input (sunlight, geothermal), water availability.
2.2 Biotic Components
- Producers: autotrophs (photosynthetic, chemosynthetic).
- Consumers: primary, secondary, tertiary, etc.
- Decomposers: fungi, bacteria.
- Microbiome: symbionts, mutualists.
2.3 Interaction Types
| Interaction | Symbol | Example |
|---|---|---|
| Competition | (C) | Two plant species for light |
| Predation | (P) | Lion & zebra |
| Mutualism | (M) | Bees & flowers |
| Parasitism | (S) | Tapeworm in pig |
3. Energy Flow
3.1 Basic Pathway
- Primary production: (P_{\text{net}} = P_{\text{gross}} - R)
- Trophic transfer: Efficiency (\eta \approx 10%).
- Losses: respiration, excretion, detritus.
3.2 Food Chains vs Food Webs
- Food chain: linear sequence.
- Food web: network of multiple chains; represented by adjacency matrix (A).
3.3 Ecological Pyramids
- Energy pyramid: area decreases with trophic level.
- Biomass pyramid: may invert (e.g., fish vs plankton).
- Number pyramid: species count per level.
3.4 First‑Principle Derivation
Let (B_i) be biomass of level (i).
Energy balance:
[
\frac{dB_i}{dt} = \eta_i B_{i-1} - \sum_{k} \epsilon_{ik} B_i - d_i B_i
]
where (\eta_i) = assimilation efficiency, (\epsilon_{ik}) = predation rates by predators (k), (d_i) = respiration.
Solve for steady state (dB_i/dt=0) to derive trophic transfer ratios.
4. Nutrient Cycling
| Cycle | Key Steps | First Principles |
|---|---|---|
| Carbon | Photosynthesis → Respiration → Decomposition → Atmospheric exchange | CO₂ mass balance; kinetic rate equations for photosynthesis (Farquhar model). |
| Nitrogen | Nitrification, denitrification, fixation | Stoichiometry: (\mathrm{N_2} + 8e^- + 16H^+ \to 2NH_3 + 5H_2O). |
| Phosphorus | Weathering, plant uptake, mineralization | Solubility limits; leaching modeled by advection‑diffusion. |
| Water | Irrigation, runoff, evaporation | Conservation of mass; Richards equation for unsaturated flow. |
Edge Cases
- Eutrophication: Excess nitrogen → hypoxia → anoxia.
- Phosphorus limitation in oligotrophic lakes: models predict long‑term stability.