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8/6/2020 Week 4 Assignment I: Growth Phase Calculations

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Week 4 Assignment I: Growth Phase Calculations

Due Sunday by 11:59pm Points 20 Submitting a file upload

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2020 has been a rough year to say the least, and the world is desperately in

need of some good news. Nay, not just good news, we need a hero. Enter

Diego (https://www.cnn.com/2020/06/16/americas/diego-tortoise-retires-homescli-intl/index.html) , who fathered 800 offspring to save his species (the

Española Galapagos tortoise). The population now sits at 2,000 tortoises and

Diego is going home.

As we saw last week, population size is important. Ideally, this means you

started with a lot of genetically diverse founders, but of course that isn’t always

the case. In the case of the Española Galapagos tortoises it was 12 females

and 2 males. So, often you have to grow your population to stabilize it and

ensure there isn’t an unacceptable loss of genetic diversity over time, even if

that genetic diversity is low. If you think back to the math from last week and do

a little not so fancy algebra, you can see that genetic deterioration occurs at a

rate that is the inverse of genetic retention, which you probably remember is

1- (1/2Ne)

8/6/2020 Week 4 Assignment I: Growth Phase Calculations

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The above equation basically states that after 1 generation, you will keep XX%

of genetic diversity. For example, if you have an Ne of 5, you will retain 90% of

genetic diversity after one generation. That’s not good! Of course, it also

means that at a very large captive population size of 100, after one generation

you have only retained 99.5% of genetic diversity. Which seems not too bad,

but think about that long term.

Answer the following questions. Submit you answers via Canvas.

1. How does the Ne/N ratio affect the above equation?

What are the real-world implications of a low or high Ne/N ratio?

Assume that the Española Galapagos tortoise captive population started

with an Ne/N ratio of 0.7. Calculate their rate of loss of genetic diversity

given their original population size.

Now let’s work on growing the population. Generally, you will see growth rate

represented in SSPs as lambda (λ). A λ of 1.08 denotes a population that is

increasing at 8% a year, and likewise a λ of 0.92 denotes a population that is

decreasing at 8% a year. Or, a λ >1 is always population growth and a λ < 1 is

always population decline.

λ can be calculated by dividing the population size currently by what it was

during the last generation. Or

λ = Nt/Nt-1

We won’t go into it here too deeply, but λ has a huge impact on genetic

projections. Below you can see the projections for the aye aye (Daubentonia

madagascariensis) from a 2019 SSP for the species. Notice that growth rate

differences of 1% (seemingly negligible) has large repercussions for the

species.

2. Calculate the λ for the Española Galapagos tortoise. Because the math

gets complicated when you have 50 generations, use this calculator

(http://www.endmemo.com/algebra/populationgrowth.php)

Now, take that rate and do the back calculations to try to predict your

population in 50 years. Was this the same number?

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Total Points: 20.0

Week 4 Assignment I: Growth Phase Calculations

Criteria Ratings Pts

6.0 pts

6.0 pts

8.0 pts

Why do you think this happens? What are the biological realities that can

influence this type of growth? Think about fluctuations in yearly breeding

success.

3. Now let’s work on growing your fictional captive population.

Identify a starting population size (both male and female)

Decide on a realistic target population size for 5 years in the future.

Calculate the lambda value you will need and how many individuals need

to be produced each year to achieve this goal.

Calculate the number of breeding pairs needed. Run the calculations for

the following breeding pair success rates: 0.3, 0.5, 0.85.

Briefly describe what the implications are for the different breeding pair

success rates.

Correctly interpreted the impacts of the Ne/N ratio, both theoretically and in real world

situations and calculated the rate of loss of genetic diversity.

Correctly interpreted the λ and expanded on the implications of this rate and the biological

realities that might affect it.

Created a full set of growth phase calculations for your fictional captive population.

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