Logistic Growth and Life History Strategies

Logistic Growth Equation

Models the effects of density and invokes carrying capacity.

Pearl and Reed (1920)

Introduced the logistic growth equation.

dN/dt

Represents the change in population size over time.

rmax

Intrinsic growth rate; maximum possible growth rate during early growth.

K

Carrying capacity of the environment; the maximum number of individuals of the same species that the environment can support.

N

Population size.

Cockroach Population Example

A dormitory can sustain a population of 3000 roaches (K=3000).

Maximum Reproductive Rate (rmax)

For a typical dorm roach population, rmax is 1.55.

Calculation of r

When N = 2000, r is calculated as r(2000) = (1.55)(2000)((3000-2000)/3000).

Final Calculation of r

r = (1.55)(1000/3000) = (1.55)(0.33) = 0.52.

Life History Traits

Major components of individual fitness.

Ecological Conditions

Conditions that favor particular life history strategies.

Life Table

Contains assumptions and can answer questions about population dynamics.

Age-specific Survival Rates

Estimated from population cohort data.

Age-specific Reproductive Output

Estimated from life table data; requires specific information to estimate.

Population Growth Indication

Life tables indicate whether a population is growing.

Life History Traits

Phenotypes that affect the life history strategy of an individual.

Life History Strategy

Age-specific schedule of survival and reproduction determined by the distribution of energy across survival, growth, and reproduction at different ages.

Offspring number

A measure of how many offspring an organism produces.

Size and age at sexual maturity

The physical size and age at which an organism can reproduce.

Dwarf superpunch males

Males that sexually mature at birth.

Magicicada

A species that produces 300 million eggs and has 1 offspring every 5 years for 17 years.

Life span

The duration of time an organism lives.

Bristlecone pine

A species known for its long life span.

Mayfly

An organism with a life span of 1 day.

Kiwi (bird)

Lays eggs that weigh half of the mother's weight.

Darwinian Demon

An organism that reproduces at birth, produces an infinite number of offspring, and lives forever.

Trade-offs among traits

Limited energy and competing demands that produce compromises among life history traits.

Optimal Life History Strategy

A strategy that varies with ecological characteristics such as abiotic conditions, community composition, and resource availability.

Life-history continuum

A spectrum ranging from low fecundity and high survivorship to high fecundity and low survivorship.

High adult mortality rates

Selection favors high levels of energy allocation to reproduction, early age at sexual maturity, many small offspring.

High juvenile mortality rates

Selection favors delayed allocation to reproduction, later age at sexual maturity, fewer large offspring.

Trinidadian guppies (Poecilia reticulata)

A species used to study the effects of predation on life history traits.

High adult predation

Occurs below waterfalls where large predators eat large guppies, resulting in high adult mortality.

High juvenile predation

Occurs above waterfalls where small predators eat small guppies, resulting in low adult mortality.

Life Tables

Tools that summarize age-specific survival and reproduction for a given population.

Mortality risk

The likelihood of death faced by individuals at different ages.

Reproductive allotment

The allocation of energy towards reproduction in relation to survival and growth.

Population growth rate

The rate at which the number of individuals in a population increases.

Estimated future population size

A prediction of how many individuals will be in a population at a future date.

Cohort Life Table

A life table that follows a cohort of individuals over time.

Static Life Table

A life table that provides estimates of age structure and vital rates as a snapshot in time.

Fecundity

The potential reproductive capacity of an individual or population.

Survivorship

The proportion of individuals surviving at each age interval.

Mortality rate (qx)

The rate at which individuals in a specific age group die.

Proportion surviving (lx)

The proportion of the original cohort surviving to age 'x'.

Number alive (nx)

The number of individuals alive at the beginning of age 'x'.

Number dying (dx)

The number of individuals dying in the interval from year 'x' to 'x + 1'.

Life Table Construction

The process of creating a life table using raw data on survival and reproduction.

Assumptions of Life Table models

Assumptions made when constructing life tables, such as an all-female population.

Cohort tagging

The process of tagging a cohort of individuals to track their survival over time.

Census population yearly

The annual counting of tagged individuals to determine survivors.

Age interval

The specific age range used to gather data in life table construction.

Cohort of individuals

A group of individuals of the same age that are studied over time.

Age-specific survival

The survival rate of individuals at specific ages.

Investment in reproduction

The allocation of resources by individuals towards reproduction at different ages.

Smith 1988

A reference to a study or publication related to life tables.

Observed years

The actual years during which data is collected for life table analysis.

Probability of survival (lx)

The likelihood that an individual will survive from birth to age 'x'.

Cohort surviving at start of age interval (nx)

The number of individuals from the original cohort that are alive at the beginning of a specific age interval.