Population Dynamics -...

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