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)
POST- REPRODUCTIVE REPRODUCTIVE PRE- 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: D p = N D p - Pop. Density = # of individuals per unit of space S
Factors that affect density Immigration- movement of individuals into a population Emigration- movement of individuals out of a population
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 Density-dependent factors- Biotic factors in the environment that have an increasing effect as population size increases Ex. disease competition parasites
Factors That Affect Future Population Growth Immigration + Natality + Population - Mortality - Emigration
Key Features of Populations Dispersion : describes their spacing relative to each other clumped even or uniform random clumped even random
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
None Limiting Factor- Zone of Tolerance Few organisms present Many organisms present Few organisms present None
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 N u m b e J-shaped curve (exponential growth) Carrying Capacity (k) S-shaped curve (logistic growth) r Time
Life History Patterns. R Strategists short life span small body size reproduce quickly have many young offsprings little parental care Ex: cockroaches, weeds, microbes
Life History Patterns K Strategists long life span large body size reproduce slowly have few young offsprings provides parental care Ex: humans, elephants, giraffes
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
Population Genetics Hardy-Weinberg Equilibrium
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 p 2 + 2pq + q 2 = 1
The derivation of these equations is simple 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.
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 p 2 and q 2 (elementary algebra, p*p = p 2 ). If the results are added, the equation p 2 + pq + pq + q 2 = 1 emerges. By simplifying, it is p 2 + 2pq + q 2 = 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 p 2 + 2pq + q 2 =1 Where, p = frequency of dominant allele q = frequency of recessive allele p 2 = frequency of individuals with the homozygous dominant genotype 2pq = frequency of individuals with the heterozygous genotype q 2 = frequency of individuals with the homozygous recessive genotype
How to calculate the number of individuals with the given genotype? p 2 + 2pq + q 2 =1 So p 2 x total population 2pq x total population q 2 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 = p 2 + 2pq + q 2 where p 2 = individuals homozygous for B pq = heterozygotes with Bb q 2 = bb homozygotes
If q 2 = 0.16 (frequency of black jaguars), then q = 0.4 (because 0.16 = 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 p 2 = (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).
Numerical problems - HWE 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?