1. Limited space (limited area, limited movement between habitats, reduction of habitat, territoriality)

2. Limited resources

3. Disease

4. Environmental stochasticity (stochasticity = the inherent unpredictability of biological systems)

(floods, fires, droughts, any and all natural disasters, fluctuations in the environment seasonal changes, etc.)

In a restricted population size - the chance of alterations in allele frequencies may have a noticeable impact on the population.

LARGE population - chance effects have a small impact.

small population - chance effects have a LARGE impact.

GENETIC DRIFT (def.) = THE CHANCE EFFECT THAT RESULTS FROM THE RANDOM SAMPLING OF GAMETES FROM GENERATION TO GENERATION.

In other words…Genetic drift is a sampling phenomenon.

Consider yourself walking parallel to a boundary fence. At every step, you move either towards or away from the fence. You decide which direction to take after flipping a coin. If it's heads, you move towards the fence. If it's tails, you move away.

The chance of crossing the fence within the first 50 steps is greater if you begin close to the fence than if you begin very far away.

If you think about genetic drift in the same way as the random walk along the fence, you can see that zero is what's known as an 'absorbing boundary' -- in other words, there's no going up from zero (if you think of this absorbing boundary as a fence, you could probably climb over it -- if it means you have NO A2 alleles left, there's no getting them back!)

REMEMBER THIS: "The ultimate fate of any sexual population lacking mechanisms to restore genetic variation would be fixation of one allele at each genetic locus throughout the genome." (Lacy, 1987)

Experiment #1 - (example in book)

GIVEN: You have a diploid population of 5 individuals (10 gametes)

This is your population gene pool:

A1, A1, A1, A1, A1, A2, A2, A2, A2, A2

Step #1: Flip a coin 10 times.

Make heads = the probability of picking one of the A1 gametes

Make tails = the probability of picking one of the A2 gametes

Question : What is the frequency of your alleles after 10 flips?

(if you were lucky enough to get 0.5 A1s' and 0.5 A2s' the first time -- this is called 'beginner's luck' in gambling circles -- try it a few more times and see if you get it again!)

GIVEN: You have a diploid population of 100 individuals (200 gametes)

This is your population gene pool:

100 A1 alleles

100 A2 alleles

Step #1 : Flip a coin 200 times.

Make heads = the probability of picking one of the A1 alleles

Make tails = the probability of picking one of the A2 alleles

Question : What is the frequency of your alleles after 200 flips?

*(psst…I don't really expect you to try this…BUT if you did this experiment, your frequency for A1 or A2 should range between 0.45 and 0.55 -- frequencies that are much closer to the original 0.5 A1s and 0.5 A2 frequencies you had when you started )

COMPARE THE TWO EXPERIMENTS:

What conclusions can you draw about allele frequencies and chance effects?

The consequences of probability: A finite population will eventually become homozygous by chance -- (i.e. heterozygosity will approach ZER0).

HERE COMES THE MATH: (important formula to follow!)

H_t - this is your heterozygosity for generation t

N - this is the number of individuals in the population

H_o- this is your initial observed heterozygosity

What does the following part of the equation mean? (it is often helpful to think of a mathematical equation in verbal terms).

[1-1/2N]

By plugging any number in for N, you can see that the result will be a number less than one -- this means that expected heterozygosity will always decline and will approach zero over time at a rate dependent on the size of the population.

*IF YOU DON'T SEE THIS, GET OUT A CALCULATOR AND PLUG IN AN ASCENDING OR DESCENDING SERIES OF NUMBERS FOR N -- TRY THIS OUT AT HOME. I CANNOT ENCOURAGE YOU STRONGLY ENOUGH TO DO SO!

EXAMPLE FROM BOOK: Drosophila melanogaster and the frequency of two alleles at the brown locus.

This example uses the equation provided above and shows you how it works for a real population.

N = 10

H_o = 0.5

Following the heterozygosity within the population over 100 generations

H₂ = (1 - 1/2(10))²(0.5) = 0.451

H₃ = (1 - 1/2(10))³(0.5) = 0.428

H₄ = (1 - 1/2(10))⁴(0.5) = 0.407

H₅ = (1 - 1/2(10))⁵(0.5) = 0.387

H₆ = (1 - 1/2(10))⁶(0.5) = 0.368

H₇ = (1 - 1/2(10))⁷(0.5) = 0.349

H₈ = (1 - 1/2(10))⁸(0.5) = 0.332

H₉ = (1 - 1/2(10))⁹(0.5) = 0.315

H₁₀ = (1 - 1/2(10))¹⁰(0.5) = 0.299

H₁₀₀ = (1 - 1/2(10))¹⁰⁰(0.5) = 0.00296

H₁₀₀₀ = (1 - 1/2(10))¹⁰⁰⁰(0.5) = 0.0000000000000000000000265

In the example above…

Proportion of population that is heterozygous after 10 generations = 0.29

(0.29)10 = 2.9 individuals

Proportion of population that is heterozygous after 100 generations = 0.00296

(0.00296)10 = .0296 individuals (QUESTION: Is this possible? ANSWER: No!)

Therefore, heterozygosity in the population will probably be gone by this point…

if you try numbers until you figure out when you will lose heterozygosity because of having too few heterozygous individuals, the solution is probably somewhere around…

H₃₁ = (1 - 1/2(10))³¹(0.5) = 0.1019

(.1019)10 = 1.019 individuals

…ah, one lonely heterozygote…there's still hope…

H₃₂ = (1 - 1/2(10))³²(0.5) = 0.0968

(.0968)10 = 0.968 individuals

**you will probably lose the heterozygosity in your population somewhere around 32 or more generations, although if you look at the numbers above, there is still some heterozygosity (i.e. 2.65 x 10²³) in the population after 1000 generations.

SEE Example 6.3 in text (page 97 -- the Northern Elephant Seal)

The concept of the VARIABILITY and RANDOMNESS: what this means when thinking about genetic diversity:

TRY THIS AT HOME:

Experiment #1 : flip a coin ten times, record # heads and # tails

Experiment #2 : flip a coin ten times, record # heads and # tails

Experiment #3 : flip a coin ten times, record # heads and # tails

Experiment #4 : flip a coin ten times, record # heads and # tails

Experiment #5 : flip a coin ten times, record # heads and # tails

Experiment #6 : flip a coin ten times, record # heads and # tails

Experiment #7 : flip a coin ten times, record # heads and # tails

Experiment #8 : flip a coin ten times, record # heads and # tails

Experiment #9 : flip a coin ten times, record # heads and # tails

Experiment #10 : flip a coin ten times, record # heads and # tails

QUESTION: How many times did you get the same proportions?

In any given population, only a proportion of the individuals will contribute offspring to the next generation.

Additionally, some individuals may produce more offspring than others.

1. Mating strategies

2. Health of Individuals
3. Spatial Distribution through habitat

3. other (see your notes)

HERE COMES THE MATH AGAIN! (important formula to follow…)

N_e - Effective population Size (i.e. the number of individuals that are actually reproducing as opposed to the total population)

N_m - this is the number of breeding males in the population

N_f - this is the number of breeding females in the population

PLEASE TRY THE ABOVE BY PLUGGING NUMBERS INTO THE ABOVE FORMULA AND PROVE IT TO YOURSELF -- also, STUDY THE FOLLOWING EXAMPLES!!!

EXAMPLE: A population of Mute swans

Say that;

N = 10 individuals in the population

N_m = 5 and

N_f = 5

then N_e = 4(5)(5)/5+5 = 100/10 = 10

(there are 10 individuals in the breeding population -- 5 males and 5 females.)

However…

For example, in some social vertebrate populations, one male may mate with many females…let's consider a group of Red Deer;

N = 11 individuals

**however…there is 1 male and 10 females -- this male breeds with all of the females.

Effective Population Size then becomes the following;

N_m = 1 and

N_f = 10

then N_e = 4(1)(10)/5+1 = 40/6 = 6.66 (this is the size of the breeding population !)

(do you notice the N_e in place of the N that used to be there in the above formula?

It's that simple!)

1. How important are changes in allele frequencies over time?

2. How important is variability within a population?

*Think about these questions…