Ecology

Exponential growth: dN/dt = rN. Logistic growth: dN/dt = rN(K − N)/K. The logistic growth rate is fastest at N = K/2. Density-dependent factors (competition, disease) intensify as a population grows. Density-independent factors (weather, disturbance) do not.

Life tables and survivorship curves (types I, II, III) summarize age-specific mortality. r- and K-selection are useful shorthand, but real life histories are more varied.

Competition (−/−), predation and parasitism (+/−), mutualism (+/+), and commensalism (+/0). Competitive exclusion predicts that two species cannot share exactly the same niche indefinitely. Resource partitioning and character displacement are common outcomes.

Keystone species have effects far larger than their abundance would suggest. Removal experiments are the classic test, such as removing a predatory sea star from an intertidal community.

Species diversity combines richness (how many species) and evenness (how equal their abundances are). Primary succession starts without soil, and secondary succession starts after a disturbance leaves soil behind. The intermediate disturbance hypothesis predicts the highest diversity at moderate disturbance levels.

Island biogeography: larger islands and islands closer to the mainland tend to hold more species.

Energy flows through an ecosystem, and matter cycles. Typically only about 10% of the energy at one trophic level becomes biomass at the next (the actual efficiency varies). Net primary production = gross primary production − autotroph respiration.

Know the major steps of the carbon, nitrogen (fixation, nitrification, denitrification, ammonification), and phosphorus cycles, and which organisms carry out each step.