Logarithm functions are one way of expressing diminishing returns. Many biological phenomena exhibit this property where increased ‘effort’ x-axis becomes less and less efficient at increasing ‘output’ y-axes. For example, consider a population of the green algae Chlamydomonas collected from a pond adapting to the conditions of a laboratory. Each new mutation that increases the evolutionary fitness of the algae to the lab has a smaller effect than the previous one. In other words, as the population becomes more and more well adapted its harder and harder to increase fitness. This form of diminishing returns is shown in the plot in the first image attached. w(m) = 0.178 + 0.846 log(m) m = # mutations w = rel. fitness See the 2nd attached image for the two green poll questions that need to be answered please!
Logarithm functions are one way of expressing diminishing returns. Many biological phenomena exhibit this property where increased ‘effort’ x-axis becomes less and less efficient at increasing ‘output’ y-axes. For example, consider a population of the green algae Chlamydomonas collected from a pond adapting to the conditions of a laboratory. Each new mutation that increases the evolutionary fitness of the algae to the lab has a smaller effect than the previous one. In other words, as the population becomes more and more well adapted its harder and harder to increase fitness. This form of diminishing returns is shown in the plot in the first image attached. w(m) = 0.178 + 0.846 log(m) m = # mutations w = rel. fitness See the 2nd attached image for the two green poll questions that need to be answered please!
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Logarithm functions are one way of expressing diminishing returns. Many biological phenomena exhibit this property where increased ‘effort’ x-axis becomes less and less efficient at increasing ‘output’ y-axes. For example, consider a population of the green algae Chlamydomonas collected from a pond adapting to the conditions of a laboratory. Each new mutation that increases the evolutionary fitness of the algae to the lab has a smaller effect than the previous one. In other words, as the population becomes more and more well adapted its harder and harder to increase fitness. This form of diminishing returns is shown in the plot in the first image attached.
w(m) = 0.178 + 0.846 log(m)
m = # mutations w = rel. fitness
See the 2nd attached image for the two green poll questions that need to be answered please!
Transcribed Image Text:Relative Increase in Fitness
3
2
0
0
20
40
60
#mutations
80
100
Transcribed Image Text:B. Plot w(m) on a log-linear plot.
5
4
3
2
1
5
10
50
100
Poll 3: The
on a log scale
A. x-axis
B. y-axis
C. both axes
of a log-linear plot is
Poll 4: The domain of w(m) is
A. R+
B. Z+
C. N
Relabel the x-axis on the log-scale.
C. What is the equation for the line in the above plot?
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