Expert-level ecology covering population ecology, community ecology, ecosystem ecology, food webs, energy flow, nutrient cycling, biodiversity, and conservation biology.
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Population growth: exponential (dN/dt = rN) and logistic (dN/dt = rN(K-N)/K). Carrying capacity K: maximum population size environment can support. Life tables: age-specific survival (lx) and fecundity (mx), net reproductive rate R0. Population regulation: density-dependent (competition, predation) vs density-independent. Metapopulation: network of subpopulations connected by dispersal, patch dynamics.
Species interactions: competition, predation, herbivory, mutualism, commensalism, parasitism. Competitive exclusion: two species with identical niches cannot coexist indefinitely. Niche theory: fundamental vs realized niche, niche partitioning enabling coexistence. Keystone species: disproportionate effect on community structure relative to abundance. Succession: primary and secondary, pioneer to climax communities.
Energy flow: trophic levels, 10% rule, primary productivity (GPP, NPP). Nutrient cycling: carbon, nitrogen, phosphorus cycles — reservoirs and fluxes. Trophic cascades: top-down effects of apex predators on lower trophic levels. Decomposition: detritivores, decomposers, mineralization of organic matter.
Alpha diversity: species richness and evenness within a habitat (Shannon, Simpson). Beta diversity: species turnover between habitats (Bray-Curtis, Jaccard). Gamma diversity: total diversity across a region. Species-area relationship: S = cA^z — islands and habitat fragments.
Extinction risk: IUCN Red List criteria, minimum viable population. Habitat fragmentation: edge effects, corridors, landscape connectivity. Invasive species: competitive displacement, novel weapons hypothesis. Climate change impacts: range shifts, phenological mismatches, coral bleaching.
| Pitfall | Fix |
|---|---|
| Ignoring scale dependence | Patterns differ at local vs regional vs global scales |
| Assuming equilibrium | Many ecological systems are non-equilibrium |
| Overlooking indirect interactions | Trait-mediated indirect effects can dominate |
| Confusing correlation with competition | Test with removal experiments |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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