Data Analysis and Mathematical Models

EK 4.A.5 Communities are composed of populations of organisms that interact

in complex ways

PopulationsSize is usually

designated as N (total number of individuals)

Density – total number of individuals per area or volume

Dispersion – how individuals in a population are distributed

Growth Patterns & InteractionsAge structure – is a description of the abundance of

individuals of each ageRapid growth – many young, few elderly; developing

countriesSlow growth – larger at the bottom that slowly narrow;

the USZero growth – tiers of equal width; Italy

Growth Patterns & Interactions

About 1,000 years ago the human population began population growth thanks to increasing the carrying capacity of our environmentIncrease in food

supplyReduction in diseaseReduction in human

wasteExpansion of habitat

Growth Patterns and InteractionsSurvivorship Curves

describe how mortality of individuals in a species varies during their lifetimes

3 types of curvesType 1Type 2Type 3

Growth Patterns & InteractionsType 1 Survivorship

describe species in which most individuals live to middle age; after that mortality is high

Examples: Humans, Elephants

Growth Patterns & InteractionsType 2 Survivorship

describes organisms in which the length of survivorship is random, that is, the likelihood of death is the same at any age – constant death rate

Examples: Rodents and invertebrates

Growth Patterns & InteractionsType 3 Survivorship

describe species in which most individuals die young, with only a relative few surviving to reproductive age and beyond

Examples: oysters, plants, free-swimming larvae, frogs

Growth Patterns & InteractionsBiotic Potential is the

maximum growth rate of a population under ideal conditions

Take into consideration the following:Age at reproductive

maturityClutch sizeFrequency of

reproductionReproductive lifetimeSurvivorship of offspring

to reproductive maturity

Growth Patterns & InteractionsLimits to Growth

Density-Dependent factors are those factors whose limiting effect becomes more intense as the population density increases

Examples – parasite & disease transmission; competition for resources; predation

Growth Patterns & InteractionsLimiting Growth

FactorsDensity-Independent

factors occur independently of the density of the population

Examples – natural disasters such as fires, earthquakes, volcanic eruptions; extreme climates such as storms and frosts

Growth Patterns & InteractionsExponential Growth in a

population occurs whenever the reproductive rate is greater than zero.

Producing a J shaped curve

G=rNG stands for growth, r

stands for the per capita rate of increase, and N stands for the population size

Growth Patterns & InteractionsLogistic Growth occurs when limiting factors restrict the

size of the population to the carrying capacity of the habitatProducing a S shaped curveG=rN*(K-N)/KK stands for the carrying capacity; as N approaches K the

growth rate is slowed, eventually reaching zero growth

Growth Patterns & InteractionsExponential and logistic growth patterns are

associated with two kinds of life-history strategies:R-selected speciesK-selected species

Growth Patterns & InteractionsR-selected species –

Rapid growth (J shaped curve)

Opportunistic species – grasses and insects

Quickly invade a habitat and reproduce immediately (after reproducing they die)

Produce many offspring that are small, mature quickly and require little if any parental care

Growth Patterns & InteractionsK selected species

Population size remains relatively constant at carrying capacity, K – s shaped curve

Produce few offspring that are larger in size and require extensive parental care

Reproduction occurs repeatedly during their lifetime

Growth Patterns & Interactions