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Biology 30
Unit 4 – Population Genetics
General Outcome D1: Students will describe a community as a composite of
populations in which individuals contribute to a gene pool that can change over time.
Bananas and Biodiversity
Read the following news story, and then answer the questions.
On Sunday May 21, 2006, Robin McKie, the science editor of the Observer, a weekly on-line
publication of the Manchester Guardian, filed a report speculating on a possible crisis in the
world food supply.
Convenient for handling and eating, with a tab for wrapper-removal, a pleasing taste, an
obvious sell-by-date mechanism (its skin turns black), and perfectly biodegradable, the
banana is considered by many to be the perfect food. Sales of the fruit have recently reached
all-time highs and more than 95 percent of UK households buy bananas every week. Only
lottery tickets and gasoline sales outstrip them.
There is trouble on the horizon, however. According to reports by biologists, the
banana could be on the way to extinction. Or, to be more specific, the Cavendish—the
variety sold in stores throughout Britain and around the world—may be in danger.
According to Ann Vezina, of the International Network for the Improvement of Banana
and Plantain, virtually all bananas traded internationally are this variety, and biologists have
discovered that several predators—such as the black Sigatoka fungus—are attacking the
Cavendish.
Fungi such as the black Sigatoka are extremely dangerous. However, the situation is
compounded by the biological heritage of the Cavendish. It is sexless, seedless, and sterile
and can only be bred by growing plants from identical cuttings. All Cavendish bananas are
clones, which means they are genetically identical.
The fungi are not hampered by the same lack of genetic diversity. They are constantly
developing new combinations to attack the Cavendish’s natural defences. Once a fungus
develops a variation that is successful in its attack on one stand of bananas, that fungus
population will spread like wildfire through the rest in the plantation.
“One thing we can be sure of is that the Sigatoka won’t lose this battle,” said Dr Emile
Frison, of the Consultative Group on International Agricultural Research.
This story of the supermarket banana once again highlights the workings of natural
selection. In fact, this looming crisis is a repeat of the fate of the Cavendish’s predecessor. In
the 1950s, the banana of choice was the Gros Michel, until it was wiped out by Panama
disease. And that fact has triggered alarm among biologists—small plantation managers have
discovered that the Panama fungus—which the Cavendish was formerly immune to—has
begun to attack and kill Cavendish plants.
Scientists are looking for new varieties of wild banana plants that could be grown
instead of the Cavendish or whose genes could be introduced to strengthen the Cavendish’s
defences in its battle against the Panama, Sigatoka, and other diseases. But these attempts
may be doomed to failure, as the UN Food and Agriculture Organization (FAO) warned this
month. Wild banana plants species are being wiped out at an alarming rate as natural forests
are destroyed across the sub-continent.
“Due to eco-system destruction, it is probable that many valuable gene sources have
now been lost,” said FAO Agricultural Officer NeBambi Lutaladio. Many of the genes that
could have saved the Cavendish are likely already gone. For example, India’s lost bananas
include a variety that might be able to confer genetic resistance to Sigatoka. Today that
species exists as a single plant, found in the Indian Botanic Gardens in Calcutta.
1.
How are small, isolated populations such as the sage grouse, wood bison, or peregrine falcon like
the Cavendish banana?
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2.
Why have the suppliers of foods such as bananas so carefully bred the biodiversity out of their
plants? Name some examples of foods that have been managed the same way as bananas. Name at
least one food you have seen in greater varieties.
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3.
When you return from a trip out of the country, you are usually asked if you visited any farms and
reminded of regulations that forbid bringing foreign soil or plants into the country. Do you think
this is an effective way to protect Canada’s crops and wildlife from biological threats? Why or
why not?
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A. Genetic Variation
• Main source of variation in a population lies in the differences in the genes carried by
chromosomes (Modern theory of evolution )
• All the genes found in a population are called its gene pool.
• A larger population will have a more diverse gene pool (more different alleles).
• A stable population will have a fairly constant, unchanging gene pool.
•Within this gene pool, the frequencies of different alleles remains the same.
• This can be shown mathematically using the Hardy-Weinberg principle.
B. Hardy-Weinberg Principle
• Developed independently by an Englishman (Hardy) and a German (Weinberg).
• States “in the absence of any outside forces, the frequency of each allele in a population will
not change as generations pass” – genetic equilibrium.
• This is useful for predicting allele frequencies in a population that are not evolving over time.
So Why Use it?
no change = no evolution
• If this is true then the following 5 conditions must hold:
1. no mutations
2. no migration
3. large population size
4. random mating
5. no selection (artificial or natural)
Symbols
• p = frequency of the dominant gene
• q = frequency of the recessive gene
• p2 = frequency of the homozygous dominant trait
• q2 = frequency of the recessive trait
• 2pq = frequency of the heterozygous dominant trait
Formula’s
p+q=1
p2 + 2pq +q2 = 1
Summary
Allele frequencies in a population will remain the same from one generation to the next, as long
as five conditions are met:
1. The population is large enough that chance events will not alter allele frequencies.
2. Mates are chosen on a random basis.
3. There are no net mutations.
4. There is no migration.
5. There is no natural selection against any of the phenotypes.
For a trait with two alleles, the sum of the allele frequencies must be 1.00, or 100%.
The Hardy-Weinberg equation can be used to determine the frequencies of different genotypes in
a population:
Example 1
Four percent of the members of a population of pea plants are short. What is the genotypic
frequency of the recessive allele and the dominant allele? What are the genotype frequencies in
this population?
First what is q2? Then calculate q.
• q2 = 4% = 0.04
• q = 0.2
• therefore p = 0.8, (p + q = 1)
• homozygous dominant = p2 =(0.8)2 = 0.64
• heterozygous dominant = 2pq = 2(.8)(.2) = 0.32
• homozygous recessive = q2 = (0.2)2 = 0.04
total 1.00
Example 2
An island population of monkeys with striped fur has a recessive characteristic of
fur with no stripes. Out of a population of 14 000 monkeys, 1 260 of them do not
have stripes. Calculate the frequencies of each allele and each genotype.
First what is q2 ? Then find q.
• q2 = 1260/14000 = 0.09
• q = 0.3 (p + q = 1 or 1 - 0.3 = 0.7)
• p = 0.7
• homozygous dominant p2 = 0.49
• heterozygous dominant 2pq = 0.42
• homozygous recessive q2 = 0.09
total 1.00
Hardy-Weinberg Worksheet
1. Suppose that within a population of 325 ghosts, 58 exhibit the recessive trait, which
makes them visible to humans. What is the frequency of the homozygous recessive
genotype of the ghosts>
2.
In the land of Krynn, a fire breath weapon is dominant to an acid breath weapon in
dragons. If 90 out of 400 dragons display the acid breath what is the frequency of the
dominant allele?
3.
In cats, yellow eyes are controlled by a dominant allele and green eyes are recessive. If
90 out of 250 cats have green eyes, how many cats have at least one recessive allele?
4. Suppose that within the community of Sexsmith, 25 out of 101 children exhibit a
homozygous recessive trait for lactose intolerance. Determine the frequency of the
homozygous dominant individuals within this community.
5.
In a hypothetical population of parrots, the dominant feather color is green. The
recessive trait for multicolored feathers occurs in a frequency of 0.3. What is the
genotypic frequency of the homozygous dominant trait?
6.
In a pumpkin patch there are 400 pumpkins, 32% of the pumpkins have a recessive trait
of purple spots. Assuming pumpkins reproduce sexually, how many pumpkins could
have offspring with purple spots?
7. Out of 589 dolphins, 30 were found to give birth to human babies. The ability to give
birth to human babies is a recessive trait. What is the genotypic frequency of the
homozygous trait?
8. In a population of 4000 fairies, there is a dominant allele that produces green wing color.
The recessive allele produces blue wing color. If 35% of the population expresses the
homozygous dominant trait, calculate the number of fairies with the heterozygous trait.
9. A population of birds is in Hardy-Weinberg (genetic) equilibrium. 20 percent of the birds
have short tail feathers, which is a recessive trait. Determine the genotype and allele
frequencies of the population.
10. In a population of ferns, a biologist has determined that 60 percent of leaf-shape genes in
the population carry the dominant allele for curly leaves (C). The remaining 40 percent of
the genes carry the recessive allele for straight leaves (c). Determine the genotype and
allele frequencies of the next generation of ferns. Use a Punnett square to show your
work.
11. Allele Z is dominant, and is present in a population at a frequency of 37 per 100
individuals. Assuming the population is in Hardy-Weinberg equilibrium, what proportion
of individuals in the population would be expected to be (a) homozygous dominant, (b)
heterozygous, and (c) homozygous recessive? Show your work.
12. In a large, random-mating population, 85 in every 1000 humans carry the recessive allele
for red hair.
a) What percentage of the population carries this allele but does not exhibit red hair?
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b) Would you expect to see a change in allele frequencies if members of this population
preferentially mated with individuals with red hair? Explain your answer.
13. If a small, random-mating population has 18 percent of individuals exhibiting a recessive
trait, could you calculate the genotype and allele frequencies of the next generation?
Explain your answer.
14. 45 percent of individuals in a population of raccoons have a recessive trait. If the
population is in Hardy-Weinberg equilibrium, calculate the frequency of the dominant
allele in the population.
Thought Lab – The Spirit Bear
Purpose: Assessing the role of the Hardy-Weinberg principle in explaining natural phenomena.
The Kermode bear (Ursus americanus
kermodei) is a white variety of black bear
that is found only in small island
populations and in populations on the
coastal mainland of British Columbia.
Known to local Aboriginal peoples as the
spirit bear, the Kermode is rare and
people are unclear about how best to
ensure its survival. Scientists know that
its white coat colour is due to a recessive
allele. They rely on bear counts and DNA
testing of hair samples to estimate the
frequency and distribution of this allele.
Estimated Frequency of White Kermode Bears on Two British Columbia Islands
Location
Frequency of white bears
Gribbell Island
Princess Royal Island
0.3
0.1
Procedure
Use the information and table above to answer the following Analysis questions.
Analysis
1. Predict the frequency of the white coat allele in the Kermode bear population of
a) Gribbell Island
b) Princess Royal Island
2. Predict the frequency of the heterozygous genotype for coat colour in the Kermode bear
population of
a) Gribbell Island
b) Princess Royal Island
3. Suggest why the frequency of the white coat allele is different on Gribbell Island and
Princess Royal Island.
4. Suggest why some conservationists are concerned about inland black bears having access to
the coastal bears’ territories.
5. Scientists are unsure if Kermode bears select mates based on coat colour. Suggest how this
form of non-random mating might affect coastal black bear populations.
C. Evolution
• Evolution may be defined as: changes of allele frequencies within a population over time.
• Hardy-Weinberg has the 5 conditions which must be met.
•It provides a theoretical standard to compare real populations with.
• The process of evolution is constantly taking place in our populations.
• There are several agents of evolution:
1. genetic drift
2. founder effect
3. bottleneck effect
4. gene flow
5. mutation
6. non-random mating
1. Genetic Drift
• A change in genetic makeup of a population
resulting from chance.
• Usually in small populations.
• Decrease or alters the frequency of alleles in a
population.
2. Founder Effect
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Genetic drift that results when a small number of individuals separate from their original
population and find a new population.
Allele frequencies of the new population may deviate as the new population expands.
Worksheet – Founder Communities
Read the following news story and then answer the questions.
The total population of Iceland is less than 300,000 people, and genealogy (family history) is a national
interest. Most Icelanders can trace their families back around 1200 years.
In December of 1998, after much heated debate, the parliament of Iceland passed a bill that mandated the
creation of a centralized database of all the Icelandic peoples’ genealogical, genetic, and personal medical
information. The original bill did not include genetic information; this provision was added when the bill
was amended during parliamentary review. The Icelandic parliament then granted an exclusive contract to
deCODE genetics, a biomedical company, giving deCODE access to Iceland’s national health records.
About a year before the bill was passed, deCODE signed an agreement with Hoffman-LaRoche, a Swiss
pharmaceutical corporation, on the understanding that deCODE would get the contract from the
government of Iceland. deCODE requested the contract because it was searching for genes associated
with over 30 diseases (for example, heart disease, emphysema, and Alzheimer’s); 12 of these searches
would be financed by Hoffman-LaRoche.
To research these diseases, deCODE initially worked with the voluntarily donated DNA of small groups
of Icelanders. Later, the company launched a media campaign to attract DNA donors on a larger scale.
deCODE has been able to combine genetic information with the genealogical and health records of each
Icelander in order to create a comprehensive database. On January 1, 2000, deCODE announced that it
had almost completed “The Book of Icelanders,” an extensive family history database of all Icelandic
citizens, past and present, and was planning to publish it on the Internet. According to deCODE, an
individual’s information is encrypted. Most experts who reviewed the project’s privacy measures consider
the information in the database to be personally identifiable.
Icelanders can refuse to continue to participate in the database but cannot petition to have any information
already in the database removed. Furthermore, the law does not require that Icelanders be told what kind
of research will be done with their personal data.
1.
With respect to the “founder effect,” explain why the Icelandic population would be ideal
for this type of study.
2.
Why would scientists want to study a population rather than an individual?
3.
Do you think there might be opposition to the project? If you lived in Iceland, would you
want your family data to be part of the project? Why or Why not?
3. Bottleneck Effect
• A dramatic population reduction in size.
• Often temporary.
• Significant genetic drift.
• Allele frequency in survivors differ from the original population.
• Caused by severe environmental event.
4. Gene Flow
• Movement of large numbers of a population either in (immigration) or out (emigration).
• Many alleles may be lost or gained which affects the frequencies.
• Few populations are so isolated that they escape this gene flow.
5. Mutations
• Changes one allele into a different allele.
• They are neither ‘good’ nor ‘bad’ - it all depends upon the environment.
• Chromosome mutations cause many problems (chromosomal number change i.e. Down
Syndrome).
• Gene mutations may be passed on via gametes and are the main reason for the process of
natural selection (Darwin).
6. Non-Random Mating
• Sexual selection: favours the selection of any trait that influences the mating success of the
individual.
• Sexual dimorphism: traits favoured in sexual selection (differences in the appearance of male
and females in a population and behavioral differences) i.e. female mate choice and from maleversus-male competition.
Thought Lab
Maintaining Genetic Diversity in the Whooping Crane Population
Purpose: Assessing the value of captive breeding programs in preserving the genetic diversity of
an endangered species.
The whooping crane (Grus americana) is
the tallest bird in North America. Standing
1.5 m high, this graceful white bird has a
wingspan of 2.5 m. The whooping crane—
affectionately referred to as the
whooper—lives and breeds in shallow
wetlands surrounded by bulrushes
(Scirpus sp.) and other sedges. Its diet
includes plant roots, crustaceans,
mollusks, and insects. At age 3 to 4, it
reaches sexual maturity. The adult
whooper is known for its magnificent
mating behaviour, which involves displays of plumage, courtship dances, and synchronized
honking to signal its choice of a life mate. The female lays two eggs a year, but the couple will
raise only one, usually the first to hatch, and may push the other from the nest.
The largest current population of whooping cranes migrates between Wood Buffalo
National Park in northern Alberta and Aransas National Wildlife Refuge in southern Texas.
Scientists estimate that there were 1400 migrating whooping cranes in the late 1800s. The total
population fell to about 15 in the 1940s. Loss of habitat, excessive hunting, avian disease, and
lead poisoning were some of the factors that contributed to their decline. The discovery and
preservation of the whoopers’ nesting and over-wintering grounds has helped to reverse this
trend. The introduction of hunting regulations and the establishment of captive breeding
programs, one of which is at the Calgary Zoo, has also helped. The world population of
whoopers has now increased to over 300.
Procedure
Use the preceding information to answer the following Analysis questions. You may also use
library, Internet, or other resources to help you answer the questions.
Analysis
1. All the whooping cranes that are alive today are descendants of the 15 or so that remained in
the 1940s. Make a hypothesis about the degree of genetic diversity within current whooping
crane populations, and justify your thinking.
2. Does the fact that pairs bond for life help or hinder captive breeding programs? Explain your
answer.
3. DNA technologies, such as DNA sequencing, are being used to determine the relatedness of
all the whooping cranes in the main migrating population. How could conservationists use
this information to assess the vulnerability of the population to environmental change?
4. To re-establish another wild population of whooping cranes, conservationists placed
whooping crane eggs in the nests of sandhill cranes (Grus canadensis). The whooping cranes
reared by the sandhill cranes feed normally and migrate, but are not breeding. Suggest a
reason why the breeding program has not been successful.
D. Speciation
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A way of altering the gene pool.
A species is a group of similar organisms that can interbreed and produce fertile
offspring.
Speciation id caused by either geographical or reproductive isolation.
A population gets separated from the others and over time, mutations produce fertile
offspring.
Selective pressures will vary – geographical barriers include water, mountains and
canyons.
Species end up evolving in different directions based on varying habitat conditions and
therefore, different adaptations evolve.
Reproductive barriers may mean incompatibility of the chromosomes, different mating
rituals, or different mating seasons.
General Outcome D2: Students will explain the interaction of individuals in a
population with one another and with members of other populations.
E. Population Relationships
• Populations affect each other in many complex ways.
• There are symbiotic relationships, there are predator-prey relationships, and all species are in
competition with each other over the available resources. These resources are usually: food,
water and living space. Competition may be interspecific: where different populations are
competing or intraspecific: where the competition is within the one population.
• Gause’s principle (competitive exclusion principle) states that if two populations
are competing for a limited resource then one will be eliminated.
• Normally, populations can coexist within the same ecosystem. An organisms niche is its role
or its place within an ecosystem. Most organisms competing for a resource have a different
enough niche that they may coexist.
Symbiotic Relationships
• Close relationships between two different species.
1. Parasitism
• One organism benefits and the other is harmed.
• Every parasite requires a host organism, usually it is a
very specific host.
• There are three different types of parasites:
• exoparasites - fleas, ticks, leeches
• endoparasites - tapeworms, liver flukes,
protozoans
• social parasites – cuckoos
2. Commensalism
• One species benefits but the other is neither
harmed nor helped.
Examples:
 fox and caribou
 shark and remora
 orchids and trees
3. Mutualism
• Both species will benefit from the relationship.
• This relationship may be obligatory mutualism - each depends upon the other exclusively or
facultative mutualism - neither is wholly dependent upon the other.
Examples:
 plants and pollinators
 bacteria and human intestines
 ants and aphids
Complete the following concept map by:
a) Defining the term symbiosis.
b) Defining the terms mutualism, parasitism, and commensalism.
c) Identify two examples of each.
Symbiosis
Definition:
Mutualism
Parasitism
Commensalism
Definition
Definition
Definition
Example
Example
Example
Example
Example
Example
Predation
• One organism feeding on another. Predators have many mechanisms for feeding, but prey also
have many ways of avoiding predators. If prey have no way of hiding out, then eventually both
populations would die. If prey had easy hideouts, then the predator population would die out, if
prey can hide temporarily, then both populations will cycle.
• There are two types of hiding:
1. camouflage - they blend in with their background.
2. mimicry - they look like a different organism.
The resources that are available to the predators (A), so the predator population increases (B).
This leads to a reduction in the prey population (C), followed by a reduction in the predator
population (D). And the cycle continues.
Population estimates of snowshoe hare and Canada lynx show a pattern of 10-year cycles in
population size. The hare population usually peaks about a year before the lynx population
peaks.
F. Succession
• The way in which populations and communities change over time.
• Primary succession is when there was no previous life.
• Secondary succession is after partial destruction (eg forest fire, road building).
• Pioneer organisms take root first (moss, lichen, insects) and build up the soil layer.
• Transition communities take over and continue the process.
• Climax community is the stable end populations that develop.
Primary succession starts with rock and ends with a stable ecosystem (shown below). The first
organisms to grow on bare rock are lichens, likely carried there by wind or visiting birds.
Organisms that live in inhospitable places, without soil or shelter, are called pioneer species.
They slowly create conditions suitable for other organisms.
Secondary succession occurs in developed communities that have been disturbed and is usually
faster than primary succession. This is because a disturbance such as a forest fire does not
remove the soil or completely destroy all of the organic matter in the area, and conditions are
suitable for grasses and shrubs to become established quickly.
Thought Lab – Succession
On average, fires in the boreal forest of Alberta occur every 50 years. The life span of a
lodgepole pine is 220 years. Many lodgepole pines do not have a chance to live to “old age”
because of the frequency of these fires.
The classical model of succession came out of an explorer’s observations of a glacial valley in
the late 1800s. Because succession is such a long process, however, early ecologists had
difficulty testing this model of succession. In fact, no studies have lasted the hundreds of years
required to observe the entire life cycle of certain types of trees. Nevertheless, with the
development of new technologies and long-term studies of model forests, ecologists are able to
gather and assess new information.
Suppose that you are studying the impact of a wild land fi re in an area of Alberta’s boreal forest.
All the above-ground vegetation in the area was destroyed. Suppose that you visit the area 20
years after the fire and see a layer of small white spruce trees growing below a layer of tall
lodgepole pines. You hypothesize that this community is following the classical model of
succession. If your hypothesis is correct, then presumably the pine trees are being replaced by
the spruce trees, which are characteristic of climax communities in this area.
Procedure
Use the information above to answer the following Analysis questions.
Analysis
1. What type of succession—primary or secondary—is taking place in the area? Explain your
answer.
2. You hypothesized that the community is following the classical model of succession, with
one species replacing another. If your hypothesis is correct, what would you predict about the
ages of the pine trees relative to the spruce trees? Explain your answer.
3. How could you determine the ages of the trees in the area?
4. Analysis of the trees in the area indicates that both populations are about 20 years old. How
does this information affect your original hypothesis?
5. Scientists have studied the birth rate and death rate of each species of tree. They have used
their data to create the following survivorship curves, which show the proportion of
individuals in a population that survive over time. As shown in section A on the graphs, both
populations have a great decline in numbers after the seeds started germinating. List three
factors that might cause the young seedlings to die.
6. Compare the rate of death of lodgepole pine trees with the rate of death of spruce trees in
section A of the graphs.
7. Section B of the graphs represents a natural process called density thinning. It occurs in
dense populations, when resources are very limited. Some of the population dies, which
leaves more resources for the remaining population. Suggest a reason why density thinning
affects the lodgepole pine population more than the spruce population.
8. Lodgepole pines are shade intolerant. When their seeds germinate, the seedlings grow very
tall very quickly. In contrast, spruce trees are shade tolerant and grow more slowly than
lodgepole pines. Would you expect the taller or shorter lodgepole pines to die during density
thinning? Explain your answer.
9. Consider again your hypothesis that the community is following the classical model of
succession and, therefore, the spruce trees are replacing the lodgepole pine trees. Based on
your hypothesis, sketch a graph of the number of individual trees in each population versus
time. Compare your graph to the survivorship curves. Formulate an alternative hypothesis
about how succession is occurring in the community under study.
10. Which type of competition—interspecific or intraspecific—is more important to the pattern
of succession in the study area? Explain your answer.
Extensions
11. Explain how the trees came to grow in the study area in the first place.
12. Some plants need more light than others to survive. Knowing this, explain how the following
factors might affect the type of plants that will start the process of secondary succession after
an ecological disturbance. Then identify the factor that is probably the most important in
determining which species will be the first to repopulate an area after an ecological
disturbance. Explain your reasoning.
a) the type of ecological disturbance (for example, a forest fire versus a fallen tree)
b) the types of seeds left in the soil after the disturbance
c) the availability of moisture in the soil
d) the availability of nutrients in the soil
General Outcome D3: Students will explain, in quantitative terms, the change in
populations over time.
G. Chaos Theory
• States that ‘since randomness is a basic feature of many complex systems, long
term predictions may well be difficult to impossible’. Small uncertainties in short term
predictions of individual events may be magnified to such an extent over the long term that
expected behaviors in complex systems become unpredictable.
H. Dynamic Equilibrium or Steady State Theory
• In mature ecosystems populations tend to remain relatively stable over long periods of time
I. Populations
Populations are characterized by three criteria:
 Population size
 Population Density
 Rate of Change
a) Population size
• Can be determined in two different ways - either a total count (okay in small area with small
population), or representative sampling (sample a small area and multiply by total area). This
assumes the population is distributed randomly
Factors affecting population size:
1. natality
2. mortality
3. immigration
4. emigration
• open populations - where all four factors are functioning.
• closed populations - no immigration or emigration.
b) Population Density
• Populations are usually given in numbers per unit area.
• Dp = N/A
Dp = population density
N = number of individuals in a population
A = area (or V=volume)
• Density will change depending upon the area (eg; Canada vs. Vancouver).
• Population density may change over time: increase density means the population
is increasing.
• distribution may be:
1. clumped
2. random
3. uniform
• Type of distribution depends upon the resource availability - most common is a clumped
distribution
Thought Lab – Distribution Patterns and Population Size Estimates
Purpose: To see how transects (long, narrow areas of land used for ecological study) might be
used to sample different moose populations.
Procedure
1. Examine the three diagrams of hypothetical moose populations. What are the two
different distribution patterns shown?
2. The shaded parts of the diagrams represent the transects that were used to sample each
population. Calculate the area per transect. (In these diagrams, 1.0 cm represents 1.0 km.)
3. For each hypothetical population, count the moose within each transect.
4. For each hypothetical population, calculate the average number of moose per transect.
5. Calculate the average density of each hypothetical moose population.
6.Calculate the total study area that is inhabited by one moose population. Estimate the total
number of moose in each hypothetical population.
Analysis
1. The actual numbers of moose in the three populations are 60, 133, and 133, respectively.
How close were your estimates to the actual sizes of the populations?
2. Explain the difference, if any, between your estimate and the actual size of the first
population.
3. Explain any differences between your estimates and the actual sizes of the second and third
populations.
4. How would you design a sampling experiment on a real population of wild moose? (Note: In
real life, the time and expenses involved usually restricts the proportion sampled to between
10 and 20 percent of the total area of interest.)
Extension
5. There is concern that an introduced population of moose may deplete the resources in its
home range. Why would scientists want to know the density of this population? If you were
given the size of this population, how would you calculate its population density?
c) Rate of Change – Population Growth
• Change in population size, ∆N= [natality + immigration] – [mortality + emigration]
• Rate of change in a population refers to some factor such as density changing over time also
referred to as growth rate(gr).
rN = ∆N/∆t
∆N = change in population size
∆t = time interval
Problem
A collard pika (Ochotona collaris) population dropped from exactly 25 individuals in 1998 to 5
individuals in 2000. Calculate the growth rate of this population from 1998 to 2000.
What Is Required?
To determine the growth rate (gr) of the collard pika population from 1998 to 2000
What Is Given?
The values needed to calculate the change in population size (ΔN): The original number of
individuals is 25.0. The final number of individuals is 5.00.
The values needed to calculate the change in time (Δt): The beginning of the time frame is 1998.
The end of the time frame is 2000.
Step 1
ΔN = final number of individuals – original number of individuals
= 5.00 – 25.0
= –20.0 individuals
Step 2
Δt = final time – initial time
= 2000 – 1998
= 2 years
Step 3
N
t
20.0 individuals

2 years
 10 individuals/year
gr 
The growth rate of the collard pika population was –10 individuals per year. In other words, the
population dropped at a rate of 10 individuals per year.
Check Your Solution
N
t
 gr  t   N
gr 
 10 individuals/ year   2

years  20 individuals
20 individuals  20 individuals
• Growth rate is also referred to as a per capita growth rate (cpr), and represents
the change in population size ∆N, relative to the initial population size, N.
cgr= ∆N/N
Problem
A population of 26 caribou (Rangifer tarandus) was introduced onto a predator-free island in
Alaska in 1910. For the next 25 years, the per capita growth rate of the population was 75.9. In
about 1935, resources became limited and the population crashed. Calculate the number of
caribou on the island just before the population crashed.
What Is Required?
To determine the size of the island caribou population after the given time interval
What Is Given?
The value of the original number of individuals in the population (N): 26 caribou
The per capita growth rate (cgr) for the population over 25 years: 75.9
Step 1
N
N
N   cgr  N 
cgr 
Step 2
ΔN = (75.9)(26 caribou)
= 1973.4 caribou
Step 3
Final number of individuals in population = ΔN + N
= 1973.4 caribou + 26 caribou
= 1999.4 caribou
Step 4
1999.4 caribou ≈ 2.0 × 103 caribou
There were about 2000 caribou on the island just before the population crashed.
Check Your Solution
ΔN – N = 2000 caribou – 26 caribou
= 1974 caribou
N
N
 1974 caribou / 26 caribou
cgr 
 75.9
Is effective when comparing populations of different sizes i.e. school population vs. community
• Many factors affect the growth of populations.
• The capacity for reproduction is the biotic potential.
• The biotic potential is regulated by four factors:
1. maximum number of offspring per birth
2. chances that the offspring will reach reproductive age
3. number of times per year the organism reproduces
4. the age at which reproduction begins
• The ability of an environment to support a population is called its carrying capacity (changes
with availability of resources).
• Some factors affecting the growth of populations are density - dependent, some are density –
independent.
• Density - dependent work by increasing death and limiting reproduction as a population
increases: disease, food supply, predation.
• Density - independent work regardless of the population number: floods, drought, temperature
Thought Lab – What Limits the Growth of Grizzly Bear
Populations?
Procedure
Using the data in the first table, draw a graph that shows the change in
size of the Alberta grizzly bear population outside the National Parks over
time. Then complete the following Analysis questions.
Analysis
1.
2.
3.
To manage the grizzly bear population better, the government of
Alberta introduced a hunting lottery that awards a limited number of
grizzly bear hunting licenses. Predict the year that this regulation
was introduced.
The number of grizzly bear deaths in Alberta from 1976 to 1988 was
estimated to be 581. Only 281 deaths were recorded from 1988 to
2000. How does this information affect the prediction you made in
question 1? Explain your answer.
Determine the per capita growth rate (cgr) for each of the following
time intervals: 1991 to 1992, 1997 to 1998, and 1998 to 1999.
Suggest why the cgr has changed over time.
Number of Grizzly Bears
in Alberta,
Outside the National Parks
Year
Population
size
1988
575
1989
536
1990
547
1991
638
1992
669
1993
686
1994
700
1995
735
1996
765
1997
776
1998
807
1999
833
2000
841
4.
Population counts were made in several bear management regions around the province.
Some of the data are shown in following table.
Grizzly Bear Population Sizes in Alberta
Region
Area (km2)
Bear population
A
14 128
31
B
6 089
44
C
22 840
168
Source: Alberta Wildlife Status Reports, Alberta Sustainable Resource
Development, 2002
a) For each region, determine the number of grizzly bears per 1000 km2.
b) Compare the densities for the three regions. Suggest three reasons for the differences, if
any. Explain your thinking.
5.
Very few grizzly bears die of old age. What are two other possible causes of death, not
associated with human activities?
6.
Studies have shown that male grizzly bears will cross roads and use underpasses to forage
in a better environment. Females tend to remain in more restricted areas.
a) How might the movement of male and female grizzly bears in their habitat affect genetic
diversity in the population?
b) How would this behaviour influence the per capita growth rate of the population?
7.
Grizzly bears reach sexual maturity at five years of age. When food is abundant, females
average two cubs per litter every other year. With inadequate nutrition, females produce
fewer cubs.
a) Compared with mosquitoes, how would you describe the life strategy of grizzly bears?
b) Explain why the biotic potential of grizzly bears is relatively low.
c) How might grizzly bears’ low biotic potential present challenges for people who are
working to conserve the grizzly bear population?
8.
Near Lake Louise, Alberta, there is a road sign that asks drivers on the highway to reduce
their speed from 90 to 70 km/h along a 15 km stretch where grizzly bears are known to
forage for food, especially at dusk and dawn. Do you think that lowering the speed limit
along this stretch of highway is a reasonable action? Would the installation of underpasses
along this stretch of highway be a better alternative? Compare the advantages and
disadvantages of each option. What questions might you want answered before making a
decision about this issue?
9. One report concluded that people must “find a way” to prevent the Trans-Canada highway
from being a barrier to grizzly bear migration. List the stakeholders in this issue. Based on the
point of view of one of these stakeholders, suggest what actions could be taken to overcome the
fragmentation of the grizzly bear’s habitat. Share your ideas on this issue in a class discussion
J. Growth Curves


There is different shaped curves depending upon the type of population growth.
Exponential growth gives a J-shaped curve, where the speed of growth is determined by
maximum reproductive rate. However, organisms in nature cannot sustain unlimited
growth. Therefore, most populations show an S-shaped curve, which is characteristic of
sigmoidal or logistic growth.
J-shaped Curve
• Occurs in closed systems - aquarium
containing paramecium or bacteria,
yeast or other microorganisms which
have short life span and are easy to
handle and manipulate.
• 4 definite phases
1. lag phase - adjustment to new
environment.
2. growth phase - rapid increase in
population.
3. stationary phase - lack of space,
nutrients or accumulation of wastes
population growth ceases - natality = mortality.
4. death phase - mortality > natality.
 nutrients run out and wastes accumulate.
S-shaped Curve
• This curve is typical when a limiting factor is
introduced or increased or when an organism is placed
in a new environment.
• Reaches new equilibrium.
• Carrying capacity is the maximum number of
individuals the environment can support. The human
population is at the top of the J right now. Population
is almost due for a crash - 1/5 is malnourished - no
housing - no water.
Population Growth Curve Depicts Life Strategy
• K-selected
 Reach sexual maturity later in life.
 Spend a lot of time with their offspring.
 Large animals.
 Have few offspring.
 S-shaped growth curve.
 Long life span.
 Live in stable communities.
• r-selected
 Reach sexual maturity
quickly.
 Spend no time with their
offspring.
 Small organisms.
 Have many offspring.
 J-shaped growth curve.
 Short life span.
 Live in fluctuating, unstable environments.
Histograms
• Histograms are useful for depicting the percentages in age groups within a population. The
shape of the histogram tells if a population is growing, stabilized or declining.
Thought Lab – Population Growth Rates in Different Countries
Procedure
Use the table below to answer the following Analysis questions.
Human Demographic Information for Selected Countries in 2001
Country
Population size
(millions) (N)
Number of births (b)
per 1000 individuals
Number of deaths (d) per
1000 individuals
Canada
32.2
10
7
Ethiopia
77.4
41
16
Finland
5.2
11
9
Germany
82.5
9
10
Greece
11.1
9
10
India
1103.6
25
8
Nigeria
131.5
43
19
Analysis
1. Use the following data table to record the results of your calculations, or create a computer
spreadsheet with the following headings:
Predicted Population Growth from 2001 to 2011 in Selected Countries
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
Population size (N) at one-year intervals
2001
Countr Annu
y
al per
capita
growt
h rate
(cgr)
2. The table of demographic information on the previous page shows the total population size
and the number of births and deaths that occur annually per 1000 people in different
populations. In other words, the table shows birth and death rates for each population.
Subtract the deaths per 1000 individuals from the births per 1000 individuals each year to
calculate the annual per capita growth rate (cgr) for each population:
b
d
cgr 

1000 1000
Note that this estimate of cgr does not take into account emigration or immigration.
3. Use Canada’s 2001 population size and annual cgr to calculate the predicted population size
for 2002:
N(Canada in 2002) = N(Canada in 2001) + (cgr)(N(Canada in 2001))
= (1 + cgr)(N(Canada in 2001))
= (1 + cgr)(32.2 × 106)
Then use Canada’s 2002 population size and annual cgr to calculate the predicted population
size for 2003. Repeat this step for the rest of the years listed in your data table. (Show one
sample calculation.)
4. Repeat the calculations in step 3 for each country listed in your data table.
5. Using a full sheet of arithmetic graph paper (or a computer graphing program), graph the size
of Canada’s population from 2001 through 2011. This graph is a hypothetical population
growth curve for Canada for 2001 through 2011. Remember to label each axis and include a
title for your graph.
6. Graph population growth curves for the six other countries listed in your data table. You can
use the same piece of graph paper (or plot area) for all the growth curves, as long as you use
a different symbol or colour for each growth curve and provide a legend.
7. Compare the steepness of the different growth curves. Describe how annual cgr affects the
steepness of a growth curve.
8. Describe the effect of a population’s initial size on the steepness of its growth curve.
9. Why is the annual cgr negative for some populations? Describe the growth curve for a
population with a negative cgr.
10. Based on your graph, which populations are currently undergoing exponential growth?
11. Based on your graph, for which populations is the growth rate (gr) slowing? (Recall
N
that gr 
.)
t
12. Classify the countries in your data table into countries that you would consider to be more
industrialized and countries that you would consider to be less industrialized. Compare the
growth curves that are typical of each group. Explain the differences between the two types
of curves.