Population Dynamics and Ecological Models: Growth, Regulation, and Interactions

Intrinsic growth rate (r)

Highest possible per‑capita growth rate for a population.

Exponential growth model

Population increases continuously at an exponential rate (Nt = N0eʳᵗ).

Geometric growth model

Population changes in discrete time steps (Nt = N0λᵗ).

λ (lambda)

Ratio of population size from one year to the next.

Relationship of r and λ

r describes continuous growth; λ describes discrete growth.

Density‑independent factors

Limit population size regardless of density (e.g., weather, natural disasters).

Density‑dependent factors

Affect population size in relation to density.

Negative density dependence

Growth rate decreases as population density increases.

Positive density dependence

Growth rate increases as population density increases (Allee effect).

Self‑thinning

Pattern where plant density decreases as biomass increases.

Carrying capacity (K)

Maximum population size the environment can support.

Logistic growth model

Growth slows as population approaches carrying capacity.

Age structure

Proportion of individuals in different age classes.

Type I survivorship

High survival until old age (e.g., humans).

Type II survivorship

Constant mortality rate across lifespan.

Type III survivorship

High early mortality, few survivors reach adulthood.

Population fluctuation

Natural rise and fall of population size over time.

Age structure

Distribution of individuals among age classes in a population.

Stable age structure

When age distribution does not change over time.

Overshoot

When a population exceeds its carrying capacity.

Die‑off

Rapid population decline due to exceeding carrying capacity.

Cyclic population fluctuations

Regular oscillations in population size over time.

Delayed density dependence

Population regulation based on density from a previous time period.

Time delay (τ)

Lag between environmental change and population response.

Deterministic model

Predicts outcomes without random variation.

Stochastic model

Includes random variation in birth and death rates.

Demographic stochasticity

Random variation in individual birth and death events.

Environmental stochasticity

Random environmental changes affecting population growth.

Extinction risk

Probability that a population will go extinct.

Small population extinction risk

Smaller populations are more vulnerable to extinction.

Habitat fragmentation

Breaking habitat into smaller, isolated patches.

Metapopulation

Set of subpopulations linked by dispersal.

Basic metapopulation model

Suitable habitat patches in a matrix of unsuitable habitat.

Source‑sink model

Recognizes that habitat patches vary in quality.

Source habitat

High‑quality patch producing excess individuals.

Sink habitat

Low‑quality patch requiring immigration to persist.

Landscape metapopulation model

Includes patch quality and dispersal pathways (corridors).

Patch isolation

Distance between habitat patches affecting colonization.

Patch size

Larger patches are more likely to be occupied.

Corridors

Habitat connections that increase dispersal between patches.

Mesopredator

A relatively small carnivore that consumes herbivores.

Top predator

A predator that consumes both herbivores and mesopredators.

Herbivory

Consumption of plant tissues by animals.

Biological control

Use of natural enemies to control pest populations.

Invasive species success

Often due to lack of natural enemies in the invaded area.

Predator-prey cycle

Regular oscillations in predator and prey population sizes.

Huffaker experiment

Classic mite study showing predators and prey coexist with refuges and dispersal barriers.

Refuge

A location or condition that protects prey from predators.

Lotka-Volterra model

Mathematical model describing predator-prey oscillations with predator numbers lagging behind prey.

Capture efficiency (c)

Rate at which predators capture prey.

Assimilation efficiency (a)

Efficiency with which predators convert consumed prey into predator offspring.

Predator mortality (m)

Background death rate of predators.

Functional response

Relationship between prey density and predator feeding rate.

Type I functional response

Linear increase in prey consumption until satiation.

Type II functional response

Consumption slows at high prey density due to handling time.

Type III functional response

S‑shaped curve; low consumption at low prey density due to learning or prey refuges.

Behavioral defenses

Prey behaviors that reduce predation risk (e.g., alarm calling, reduced activity).

Cryptic coloration

Camouflage that allows prey to blend into their environment.

Structural defenses

Physical features like spines or shells that deter predators.

Chemical defenses

Toxins or noxious chemicals used to deter predators.

Aposematism

Warning coloration signaling chemical defenses.

Batesian mimicry

Harmless species mimics a harmful one to avoid predation.

Müllerian mimicry

Multiple harmful species share similar warning coloration.

Cost of defenses

Energetic or reproductive trade‑offs associated with maintaining defenses.

Infection resistance

Ability of a host to prevent an infection from occurring.

Infection tolerance

Ability of a host to minimize harm once infection occurs.

Parasite load

Number of parasites a host carries.

Ectoparasite

Parasite living on the outside of a host (e.g., ticks, fleas).

Endoparasite

Parasite living inside a host (e.g., tapeworms, viruses).

Exposure to natural enemies (ecto vs. endo)

Ectoparasites high; endoparasites low.

Exposure to environment (ecto vs. endo)

Ectoparasites high; endoparasites low.

Movement difficulty (ecto vs. endo)

Endoparasites have high difficulty; ectoparasites low.

Exposure to immune system (ecto vs. endo)

Endoparasites high; ectoparasites low.

Ease of feeding (ecto vs. endo)

Endoparasites high; ectoparasites low.

Horizontal transmission

Parasite moves between unrelated individuals.

Vertical transmission

Parasite passes from parent to offspring.

Vector

Organism that disperses a parasite between hosts.

Reservoir species

Species that carry parasites without severe disease.

Deadly pathogen persistence

Favored by reservoir species and multiple host species.

Host-parasite population cycles

Parasite abundance often lags behind host abundance.

Forest tent caterpillar cycles

Classic example of parasite‑driven population fluctuations.

Measles cycles

Human disease showing cyclical outbreaks due to changing immunity.

S‑I‑R model

Simplest infectious disease model including immunity.

S (susceptible)

Portion of population not yet infected.

I (infected)

Portion currently infected and infectious.

R (resistant)

Portion recovered and immune.

Transmission rate (β)

Rate at which susceptible individuals become infected.

Recovery rate (γ)

Rate at which infected individuals recover.

R₀ (basic reproductive number)

Ratio of new infections to recoveries.

R₀ > 1

Infection spreads (epidemic).

R₀ < 1

Infection dies out.

Parasite‑induced behavior change

Parasites manipulate host behavior to enhance transmission.

Trophic transmission

Parasite benefits when host is eaten by next host in life cycle.

Coevolution

Reciprocal evolutionary changes between parasites and hosts.

Myxoma virus & Australian rabbits

Classic example of host-parasite coevolution.

Intraspecific competition

Competition among individuals of the same species.

Interspecific competition

Competition among individuals of different species.

Limiting resource

A resource that restricts population growth when scarce.

Competition for limiting resource

Species compete most strongly for the resource in shortest supply.

Resource interaction

Availability of one resource can influence the need for another.