Growth Phase Calculations

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
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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.