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Wize AP Biology Textbook > Ecology

Population Growth

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Population Growth


Population growth deals with the net change in individuals for a given population
  • Birth and immigration into
  • increase population
  • Death and emigration away
  • decrease population=emigratio

We can define a change in population (ΔN\Delta N) as a function:
ΔN=(B−D)+(I−E)\boxed{\Delta N=(B-D)+(I-E)}
where BB=birth, DD=death, II=immigration, EE=emigration



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What if we want to know the rate at which the change in population is occurring?
  • We must determine the per capita (intrinsic) growth rate (rr), which depends on time:
r=(ΔN/Δt)/N1\boxed{r=(\Delta N/\Delta t)/N_1}
where ΔN\Delta N=change in population, Δt\Delta t= change in time, N1N_1=initial population size

  • intrinsic growth rate: maximum rate of growth
  • no environmental factors limit population increase

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If we want to determine what the population size will be sometime in the future, then we use the following formula:
Nt=N1(1+r)t\boxed{N_t=N_1(1+r)^t}

where NtN_t= future population, rr=intrinsic growth rate, tt=time
  • Exponential growth: when the rr is constant through time
  • The number of individuals added to the population at any time is proportional to the size of the population at that tim

Photo by CNX OpenStax | CC BY



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Density Dependence

  • Density Independent Factors: forces that do not depend on population size
  • Often environmental disasters Examples: Fire, Lightning
  • Density Dependent Factors: forces that are related to population size
  • Predation and disease Examples: High density populations are at high risk of disease outbreaks
  • As a population grows, crowding results in a decrease in available space
  • Carrying Capacity (K): the maximum number of individuals any habitat can support.
  • Population is typically below K due to predation and parasitism.
  • These do not effect K since K is based on the habitat
  • Small populations:
  • resources are not limiting
  • Growth rate = r
  • Large populations:
  • Populations near or at K
  • Overcrowding reduces available resources
  • Growth rate < r
  • Determine how close the population is to K:
(K−N)/K\boxed{(K-N)/K}
where K= carrying capacity, N=population number


Photo by CNX OpenStax | CC BY
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  • Intrinsic growth rate (rr) is also scaled by how close the population is to K:
r=rmax⁡(K−N/K)\boxed{r=r_{\max}(K-N/K)}


Photo by CNX OpenStax | CC BY

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Calculate the change in population size given that there are:
50 births
35 deaths
10 immigrants
5 emigrants
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Calculate the intrinsic growth rate for a population that increased from 100 individuals to 150 individuals in one year.
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Given an intrinsic growth rate of 0.5, how much will a population of 100 individuals increase in 5 years?
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What will the intrinsic growth rate be for a population of 500 individuals given density dependent factors?
The carrying capacity for the population is 400 individuals and the maximum intrinsic growth rate is 1.2.