Lecture 11: Population Growth & Regulation

Geometric Growth Model

A model of population growth in which the population increases at regular time intervals.

Geometric Growth Model Equation

N_t=N₀λ^t

N = Number of individuals / population size

N_t= Population size at time, “t”

N₀ = Initial population

λ^t = Ratio of a population size in one year to the size in the previous year

Growth Rate

The # of individuals produced in a given amount of time minus the individuals that die.

Intrinsic Growth Rate (r)

The highest possible per capita growth rate for a population that occurs under ideal conditions (abundant resources, enough mates, etc.)

Exponential Growth Model

N_t=N₀e^rt

N_t = Future population size

N₀ = Current size

e = a mathematical constant (2.71828)

^r = Growth rate

^t = Time

This model applies to species that reproduce throughout the year rather than on a seasonal basis (ex: not animals that reproduce only in the summer).

J-Shaped Curve

The shape of exponential growth when graphed.

Exponential Growth Model

dN/dt = rN

dN = change in population

dt = change in time

r = rate of increase

N = # of individuals

Population Doubling Time

The time required for a population to double in size.

Density-Independent Factors

Factors that limit population size regardless of the population’s density.

Examples:

• - Natural disasters such as tornadoes, hurricanes, floods, and firse.

• - Extreme temperatures

• - Droughts

• - Seasonal variation in temperature and rainfall

Density-Dependent Factors

Factors that affect population size in relation to the population’s density. Split into two categories: positive and negative.

Negative Density Dependence

Occurs when the rate of population growth decreases as population density increases.

Examples:

• - Limited supply of resources (food, nesting sites, and/or physical space)

• - Crowded populations

• - Fruit fly experiment: higher number of adults (greater density) → higher competition for food → # of progeny decreased

• 
  

Positive Density Dependence (also known as inverse density dependence or the Allee effect)

When the rate of population growth increases as population density increases.

Examples:

• - Low densities make it harder for individuals to find mates (or plants to obtain pollen

• - Very low densities can lead to inbreeding so higher densities are preferred

• - Uneven sex ratio in low densities

• 
  

Carrying Capacity (K)

The maximum population size that can be supported by the environment

Logistic Growth Model

A growth model that describes slowing growth of populations at high densities.

S-Shaped Curve (Sigmoidal Curve)

The shape of the curve when a population is graphed over time using the logistic growth model.

Inflection Point

The point on a s-shaped growth curve at which the population achieves its highest growth rate.

Survivorship Curves

Graphed curves illustrating the differences in survival among different age classes.

*Graphed as survival over time (age).

Life Tables

Tables that contain class-specific survival and fecundity data.

*Used to determine how age, size, or life history classes affect the growth of a population.

Stable Age Distribution

When the age structure of a population does not change over time.

Age Structure

The proportion of individuals in a population that occurs in different age classes.

Generation Time (T)

The average time between the birth of an individual and the birth of its offspring.

Net Reproductive Rate (R₀)

The total number of female offspring that we expect an average female to produce over the course of her life.

Cohort Life Table

A life table that follows a group of individuals born at the same time from birth to the death of the last individual.

Static Life Table

A life table that quantifies the survival and fecundity of all individuals in a population during a single time interval.

What is one limitation of the exponential model?

It assumes continuous births and deaths throughout the year, but does not describe animals such as quail that have a distinct breeding season.