Population Growth & Regulation

Exponential Growth

Represents growth in ideal & unrestricted conditions

Relates population growth over time to births & death

simplest model of population growth

Exponential Growth equation

𝒅𝑵/𝒅𝒕 = 𝒓𝑵

r = intrinsic rate of increase

N = current population size

Intrinsic growth rate

determines how fast the population grows

when exponential growth occurs

Species grow exponentially when recovering from a catastrophe

Introduced species often grow exponentially

Emerging diseases often grow exponentially

Malthusian Catastrophe

theory that states w/out regulation human population size will become too large, leading to famine/war/disease and a population crash back to subsistence levels

problems w/ Malthusian Catastrophe

global carrying capacity & resource scarcity

applying mathematical theory human society w/out considering social, political, & ethical context leads to misleading and harmful conclusions

Demographic transition

a shift from high birth & death rates to low birth & death rates,

Carrying capacity (K)

maximum population size that can be supported

keeps things from getting out of contro

Carrying capacity determining factors

Determined by limited resources:

energy, shelter, refuge from threats, nutrient availability, water, suitable nesting sites, disease, waste accumulation

As population size increases, each individual has access to

fewer resources

Logistic Growth

Population growth levels off as a population reaches carrying capacity

Growth rate decreases as population gets closer to

carrying capacity

As population approaches carrying capacity birth rate must

decrease OR death rate must increase (or both)

How logistic growth works

Individuals must obtain sufficient resources to reproduce, or per capita birth rate will decrease

Starvation or disease may increase, causing per capita death rate to increase

Logistic Growth equation

𝒅𝑵/𝒅𝒕 = 𝒓𝑵 (𝑲 − 𝑵)/𝑲

(K-N)/K = fraction of capacity still available for population growth

rN = Exponential Model

Population Regulation

Everything will grow exponentially unless something limits it

Density dependent and independent factors

Density dependent factors

alter birth or death rate as population increases

As a population grows:

-Availability of resources per individual decreases

-Risk of predation, disease, parasites increase

only these can consistently cause populations to increase or decrease

Density dependent factor types

Competition

Intrinsic Factors

Territoriality

Waste Accumulation

Disease

Predation

Competition

More individuals = more competition for resource

Fewer resources = lower growth & survival

Fewer resources = lower fecundity

Reduction in growth impacts reproductive output & investment

Intrinsic Factors

More individuals = physiological change

Even when resources are abundant, high density conditions increase stress

- Hormonal changes suppress growth & reproduction

-Stress suppresses immune function & increases disease vulnerability

Territoriality

individuals divide & defend resources

Territoriality secures sole access to resources

Not enough territories = decrease in population

Territory size decreases with population density: fewer resources per individual.

Reproductive output declines as a result

Toxic Wastes

More individuals = accumulating waste

Disease

More individuals = increased likelihood of disease transmission

Predation

More individuals = easier food for predators

Density independent factors

alter population size regardless of density

all individuals of a population equally likely to be affected

Outcome is the same regardless of population size or density

Lead to unpredictable & abrupt population changes

most often abiotic