Exercise 4. The first lake trout was caught in Yellowstone Lake in 1994. Somehow
ID: 117280 • Letter: E
Question
Exercise 4. The first lake trout was caught in Yellowstone Lake in 1994. Somehow this non-native species found its way into Yellowstone Lake where it has undermined the native Cutthroat trout population. The lake trout are bottom dwellers, so they are not easily caught by anglers (you need to use 100-m nets to catch the lake trout); they do not enter the streams so they are not a food source for birds or bears; and with a lifespan of 50 years, they out-compete the native Cutthroat trout. Without predation, the lake trout population has sky-rocketed. In 2011, 224,000 lake trout were killed and removed from the lake; in 2012and 2013, 300,000 lake trout were removed from the ecosystem. If left unchecked the lake trout would totally consume the native Cutthroat trout, leaving dependent species without a food resource. The figure below shows the number of lake trout removed from Yellowstone. Typically the number of fish taken is directly related to the total population available in the lake. The catch of 2012-2013 nearly matches the catch from the previous decade.
Some researchers suggest that the population growth rates (r) for lake trout where no management occurs is about 1.35 trout per year for an increasing population. Current population estimates suggest that 500,000 lake trout are in Yellowstone Lake.
Using the equation for "Doubling Time for Population Growth," how long would it take for the lake trout population to double if no management practice was in place?
(Write out the equation, make appropriate substitutions, and show all work.)
A. about 6 months
B. about 6 years
C. 51.3 years
Number of Lake Trout Removed by Mesh Size Small Large 9.0 8.0S 7.0 400000 350000 300000 250000 200000 E 150000 100000 50000 4.0- 3,0 2.0 1.0 5 0.0 20012003 2005 2007 2009 20112013 2015Explanation / Answer
In the problem mentioned above the initial polpulation of lake trout is 500,000 and since the population is increasing compoundly that i.e. the increase accrues on the initial number and the accumulated number produced by the previous periods.
Initial number of lake trout is 500,000
Final no of lake trout is 2x 500,000= 1,000,000
Initial number of lake trout/Final number of lake trout =1000000/500000=2
log(2)= 0.6931= 69.31%
By using Doubling Time for Population Growth, which states that log Initial number /Final number) gives us a value which is when devided by population growth rates (r), will give us the approximate number of years to double up the population.
Therefor 69.31/1.35= 51.34 years or 51.3 years
That means option "c" is correct
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.