High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize University Biology Textbook > Ecology

Population Growth

SurvivorshipPrevious Section
Popular Courses
Find My Course
0:00 / 0:00

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



PAGE BREAK

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

PAGE BREAK

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



0:00 / 0:00

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
PAGE BREAK
  • 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

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Calculate the change in population size given that there are:
50 births
35 deaths
10 immigrants
5 emigrants
checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Calculate the intrinsic growth rate for a population that increased from 100 individuals to 150 individuals in one year.
checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Given an intrinsic growth rate of 0.5, how much will a population of 100 individuals increase in 5 years?
checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
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.
Extra Practice
In a density dependent population growth mode, a sudden increase in population size will cause the population growth rate to:
Which of the following is NOT a density-dependent control that influences the black crow population size?
Complete the following life table for a population of fruit flies:
Is this population growing? Explain.
Complete the following life table for a population of fruit flies:
Is this population growing? Explain.
Which of the following changes the genetic structure of a population due to immigration/emigration?
Consider an environment in which some year have good growing conditions and other years have very poor growing conditions. Would this environment favor r selected or K selected organisms? Explain.
The main differences between density-dependent and density-independent factors is
You are studying a population of ferrets with the following life table.
a) Fill in the missing data in the table.
b) The ferret population keeps increasing due to excess resources and lack of predators. To control this population there is a decision to prevent all ferrets from class 2-3 to mate or to sterilize all ferrets in class 3-4. Which of the above strategies will be more effective in slowing the population growth?
Factors that affect carrying capacity include all of the following except
Consider a closed population where density independent birth and death rates occur, which of the following could happen:
Which one of the following is a cost associated with living in a group?
You are studying a population of lizards and find that over the time period studied, 5 eggs hatch, 10 lizards leave the area, 3 lizards die of hypothermia and 4 lizards move into the area.
What is the population change over this period?
What is the equation you would use to calculate the above?
True or False.
The carrying capacity of an ecosystem is the same for all species that exist within.
In a density dependent population growth mode, a sudden increase in population size will cause the population growth rate to:
The population of squirrels in a forest has increased and there are no longer enough Maple trees to nest in.
This is an example of:
What are some differences between density dependent and density independent factors? How doe each limit population size?
Give some examples.
Consider the following scenario: Country A has 40% of its population under the age of 15 and 5% over the age of 65 while Country B has 25% of its population under the age of 15 and 25% over the age of 65. Which population will increase faster in the future. Explain.
Stage (x) Complete the following life table for a population of fruit flies:
Is this population growing? Explain.
Which of the following is NOT a density-dependent control that influences the black crow population size?
All of the following are density dependent factors that limit animal populations except
Consider a closed population where density independent birth and death rates occur, which of the following could happen:
In a density dependent population growth mode, a sudden increase in population size will cause the population growth rate to:
You are studying a population of lizards and find that over the time period studied, 5 eggs hatch, 10 lizards leave the area, 3 lizards die of hypothermia and 4 lizards move into the area. What is the population change over this period?
What is a necessary requirement for exponential growth to occur?
Ecology
Complete the following life table for a population of fruit flies:
Is this population growing? Explain.
All of the following are density dependent factors that limit animal populations except:
You collect data on birth and mortality in three populations of butterflies.
Are the following statements T or F?
b d
The carrying capacity of an ecosystem is the same for all species that exist within it
What are some differences between density dependent and density independent factors? How does each limit population size? Give some examples.
What factors place limits on the logistic model of growth?
Which of the following changes the genetic structure of a population due to immigration/emigration?
Compared to a population on a main continent, how will a population on an isolated island evolve?
What factors place limits on the logistic model of growth?
What is a necessary requirement for exponential growth to occur?
Why are logistic growth curves S shaped?
Refer to the following graph. What is happening at position C?
Carrying capacity refers to:
Factors that affect carrying capacity include all of the following except:
You collect data on birth and mortality in three populations of butterflies.
b d
Population A 0.90 0.80
The population of squirrels in a forest has increased and there are no longer enough Maple trees to nest in. This is an example of: