population dynamics -...
TRANSCRIPT
Population Dynamics
Population Dynamics
Population: all the individuals of a species that live together in an area
Demography: the statistical study of populations, make predictions about how a population will change
Population Dynamics
Key Features of Populations
•Size – age structure of individuals
•Density – total number per unit area
•Dispersion - (clumped, even/uniform, random)
PRE-
REPRODUCTIVE
REPRODUCTIVE
POST-
REPRODUCTIVE
Population of a Stable Country
Age- Structure Pyramids
Key Features of Populations
2. Density: measurement of
population per unit area or unit
volume
Formula: Dp= N
Dp - Pop. Density = # of individuals per unit of
space
S
Immigration- movement of individuals into a population
Emigration- movement of individuals out of a population
Factors that affect density
Density-dependent factors- Biotic factors in the environment that have an increasing effect as population size increases
Ex. disease
competition
parasites
Factors that affect density
Density-independent factors- Abiotic factors in the environment that affect populations regardless of their density
Ex. temperature
storms
habitat destruction
drought
Immigration
Emigration
Natality Mortality Population +
+
-
-
Factors That Affect Future
Population Growth
Dispersion : describes their spacing relative to each other
• clumped
• even or uniform
• random
Key Features of Populations
even
random
clumped
Population Dispersion
Other factors that affect population growth
Limiting factor- any biotic or abiotic factor that restricts the
existence of organisms in a specific environment.
EX.- Amount of water Amount of food Temperature
Many
organisms
present
Few
organisms
present
Few
organisms
present
None None
Limiting Factor- Zone of Tolerance
Population Growth
Biotic Potential- the amount a population would grow if there were unlimited resources- not a practical model because organisms are limited in nature by amount of food, space, light, air, water
The intrinsic rate of increase (r) is the rate at which a population would grow if it had unlimited resources.
Carrying Capacity- the maximum population size that can be supported by the
available resources
There can only be as many organisms as the environmental resources can support
Carrying Capacity
Carrying Capacity (k)
N
u
m
b
e
r
Time
J-shaped curve
(exponential growth)
S-shaped curve
(logistic growth)
Life History Patterns
. R Strategists
short life span
small body size
reproduce quickly
have many young offsprings
little parental care
Ex: cockroaches, weeds, microbes
K Strategists
long life span
large body size
reproduce slowly
have few young offsprings
provides parental care
Ex: humans, elephants, giraffes
Life History Patterns
Human Population Growth
Human Population Growth
Time unit
Births
Deaths
Natural
increase
Year
130,013,274
56,130,242
73,883,032
Month
10,834,440
4,677,520
6,156,919
Day 356,201 153,781 202,419
Hour 14,842 6,408 8,434
Minute 247 107 141
Second 4.1 1.8 2.3
Hardy-Weinberg Equilibrium
Population Genetics
Basic Understanding
The problem of genetic variation and natural selection
Why do allele frequencies stay constant for long periods ?
Hardy-Weinberg Principle
Population Genetics
The study of various properties of genes in populations
Genetic variation within natural populations was a puzzle to Darwin and his contemporaries
The way in which meiosis produces genetic segregation among the progeny of a hybrid had not yet been discovered
It was thought that Natural Selection should always favour the optimal form and eliminate variation
Hardy and Weinberg independently solved the puzzle of why
genetic variation exists
Background
Hardy & Weinberg showed that the frequency of
genotypes in a population will stay the same from
one generation to the next.
Dominant alleles do not, in fact, replace recessive
ones.
We call this a Hardy-Weinberg equilibrium
This means that if 23% of the population has the
genotype AaTTRR in a generation, 23% of the
following generation will also have that genotype.
There are, however, a number of conditions that must be met for a population to
exhibit the Hardy-Weinberg equilibrium.
These are:
1) A large population, to ensure no statistical flukes
2) Random mating (i.e. organisms with one genotype do not prefer to mate with organisms with a certain genotype)
3) No mutations, or mutational equilibrium
4) No migration between populations (i.e. the population remains static)
5) No natural selection (i.e. no genotype is more likely to survive than another)
In a population exhibiting the Hardy-Weinberg equilibrium, it is possible to determine the frequency of a genotype in the following generation without knowing the frequency in the current generation.
Hardy and Weinberg determined that the following equations can determine the frequency when p is the frequency of allele A and q the frequency of allele a
The Hardy-Weinberg equation can be expressed in terms of what is known as a binomial expansion:
p + q = 1
p2 + 2pq + q2 = 1
For the first equation, if allele A has a
frequency of say 46%, then allele a must
have a frequency of 54% to maintain 100%
in the population.
For the latter equation, a monohybrid
Punnett square will prove its validity.
Set up the Punnett square so that two
organisms with genotype pq (or Aa) are
mated.
The derivation of these equations is
simple
Punnett square
The Punnett square results in pp, pq, pq, and qq.
Because these are probabilities for genotypes, each square has a 25% chance.
This means that all four should equal 100%, or one.
To make things easier, convert pp and qq to p2 and q2 (elementary algebra, p*p = p2).
If the results are added, the equation p2 + pq + pq + q2 = 1 emerges.
By simplifying, it is p2 + 2pq + q2 = 1.
Sample problem
A population of cats can be either black or white, the black allele (B) has complete dominance over the white allele (b). Given a population of 1000 cats, 840 black and 160 white.
Determine the following :
a. Allele frequency for dominant and recessive trait
b. Frequency of individuals per genotype
c. Number of individuals per genotype
There are 2 equations to solve the Hardy Weinberg Equilibrium question -
p + q = 1
p2 + 2pq + q2 =1
Where, p = frequency of dominant allele
q = frequency of recessive allele
p2 = frequency of individuals with the homozygous dominant genotype
2pq = frequency of individuals with the heterozygous genotype
q2 = frequency of individuals with the homozygous recessive genotype
How to calculate the number of individuals with the
given genotype ?
p2 + 2pq + q2 =1
So
p2 x total population
2pq x total population
q2 x total population
Sample problem 02
Consider a population of 100 jaguars, with 84 spotted jaguars and 16 black jaguars. The frequencies are 0.84 and 0.16.
Based on these phenotypic frequencies, can we deduce the underlying frequencies of genotypes ?
If the black jaguars are homozygous recessive for b (i.e. are bb) and spotted jaguars are either homozygous dominant BB or heterozygous Bb, we can calculate allele frequencies of the 2 alleles.
Let p = frequency of B allele and q = frequency of b allele.
(p+q)2 = p2 + 2pq + q2
where p2 = individuals homozygous for B
pq = heterozygotes with Bb
q2 = bb homozygotes
If q2 = 0.16 (frequency of black jaguars),
then q = 0.4 (because0.16 = 0.4)
Therefore, p, the frequency of allele B,
would be 0.6 (because 1.0 – 0.4 = 0.6).
The genotype frequencies can be calculated:
There are p2 = (0.6)2 X 100 (number of
jaguars in population) = 36 homozygous
dominant (BB) individuals
The heterozygous individuals (Bb) = 2pq =
(2 * 0.6 * 0.4) * 100 = 48 heterozygous Bb
individuals
Why do allele frequencies change ?
According to the Hardy-Weinberg principle, allele and genotype frequencies will remain the same from generation to generation in a large, random mating population IF no mutation, no gene flow and no selection occur.
In fact, allele frequencies often change in natural populations, with some alleles increasing in frequency and others decreasing.
The Hardy-Weinberg principle establishes a convenient baseline against which to measure such changes
By examining how various factors alter the proportions of homozygotes and heterozygotes, we can identify the forces affecting the particular situation we study.
Significance of the Hardy-Weinberg Equation
By the outset of the 20th century, geneticists were able to use Punnett squares to predict the probability of offspring genotypes for particular traits based on the known genotypes of their two parents.
Numerical problems - HWE
1) A study on blood types in a population found the following
genotypic distribution among the people sampled: 1101 were
MM, 1496 were MN and 503 were NN. Calculate the allele
frequencies of M and N, the expected numbers of the three
genotypic classes (assuming random mating).
2) A scientist has studied the amount of polymorphism in the alleles
controlling the enzyme Lactate Dehydrogenase (LDH) in a species of
minnow. From one population, 1000 individuals were sampled. The
scientist found the following fequencies of genotypes: AA = .080, Aa
= .280; aa = .640. From these data calculate the allele frequencies of
the "A" and "a" alleles in this population. Use the appropriate
statistical test to help you decide whether or not this population was in
Hardy-Weinberg equilibrium (HWE).
Numerical problems - HWE
3) For a human blood, there are two alleles (called S and s) and three
distinct phenotypes that can be identified by means of the appropriate
reagents. The following data was taken from people in Himachal
Pradesh. Among the 1000 people sampled, the following genotype
frequencies were observed SS = 99, Ss = 418 and ss = 483.
Calculate the frequency of S and s in this population and justify either
to reject or accept the hypothesis of Hardy-Weinberg proportions in
this population?
Numerical problems - HWE