Lecture 11: Populations: Spatial and Temporal Dynamics

Vocabulary flashcards covering temporal population dynamics, delayed density dependence, metapopulation models, and Lotka-Volterra predator-prey interactions from Lecture 11.

Inflection point

The point of fastest growth on a logistic population growth curve, after which population growth begins to slow.

Periodic population cycling

Repeated, regular fluctuations in population size over time.

Intrinsic population stability

The tendency of a population to maintain a steady size near carrying capacity ($K$), favored by traits such as large body size, homeostasis, long life spans, and significant overlap of generations.

Overshooting

A phenomenon in which a population expands beyond its carrying capacity ($K$), producing more individuals than can be sustained at adulthood.

Die-off

A severe population crash well below carrying capacity ($K$) driven by the intense density-dependent effects of overpopulation and resource depletion.

Delayed density dependence

A situation where density dependence operates based on the population density at some point in the past rather than the current population density.

Tau ($\tau$)

The parameter representing the magnitude of the time delay in delayed density-dependent population models.

Damped oscillations

A pattern of population cycling around carrying capacity ($K$) in which the amplitude of oscillations diminishes over time, occurring when $0.37 < r\tau < 1.57$.

Stable limit cycle

Persistent, regular population oscillations of constant amplitude around carrying capacity ($K$), occurring in delayed density-dependent models when $r\tau > 1.57$.

Deterministic model

A mathematical model designed to predict population outcomes without accounting for random variation in population growth rates.

Stochastic model

A mathematical model that incorporates random variation in population growth rates over time.

Demographic stochasticity

Random variation in population birth and death rates caused by individual-level differences in reproductive success or survival.

Environmental stochasticity

Random variation in birth and death rates resulting from unpredictable fluctuations in environmental conditions, such as weather shifts or natural disasters.

Metapopulation model

A spatially explicit model describing a set of subpopulations occupying discrete patches of suitable habitat within an unsuitable habitat matrix, between which individuals can move.

Source-sink model

A spatially explicit population model that incorporates differences in patch quality, where individuals disperse from high-quality (source) patches to lower-quality, less productive (sink) patches.

Landscape model

A spatially explicit population model that accounts for the structure and habitat composition of the matrix, including dispersal barriers that dictate the actual movement paths of individuals between patches.

Rescue effect

The process by which dispersal from large, productive habitat patches prevents small, declining subpopulations from going locally extinct.

Metapopulation equilibrium ($p_e$)

The equilibrium proportion of occupied habitat patches in a metapopulation, described by the formula $p_e = 1 - \frac{e}{c}$, where $e$ is the extinction rate of patches and $c$ is the colonization rate.

Lotka-Volterra model

A pair of mathematical equations independently developed in the 1920s by Alfred Lotka and Vito Volterra to model simultaneous, reciprocal oscillations in predator and prey populations.

Equilibrium isocline

A line on a predator-prey state diagram representing the population sizes where the rate of change for one species is zero ($\frac{dN}{dt} = 0$ or $\frac{dP}{dt} = 0$), determined by the density of the other species.

Joint equilibrium point

The point in a Lotka-Volterra model where the prey isocline and predator isocline cross, representing the exact population densities at which neither population changes over time.