PPt Island Biogeography (Ex 9)

Question 1

Island Biogeography

Answer 1

1. Concept: There are often less species on islands than on mainland. Why?
2. Function: Size of island + distance from mainland

Question 2

Number of Species on Islands

Answer 2

1. More herbivore species = fewer plant species
2. More predator species = fewer prey species
3. Fewer food species = fewer consumer species
4. Only 10% of energy is harnessed at each level
5. COMPETITIVE EXCLUSION = 1 niche, 1 species
6. More niches = more species
7. More species but same niches = higher extinction rates

Question 3

Logs

Answer 3

1. General rules:
   Log (xy) = logx + logy log(x/y) = logx-logy
   Logxy = ylogx
2. Specific log10 values of note:
   Log(1) = Log(100) = 0
   Log(10) = log(101) = 1
   Log(100) = log(102) = 2
   Log(0.1) = log(10-1) = -1
3. 210 = 1024 which is approximately 1000 = 103 log(210) = log(103)
4. Thus, 10log(2) is approximately 3 therefore log(2) =3/10 or 0.3(actually, to be accurate log(2) = 0.30103)

Question 4

S = CAz

Answer 4

Where
S = number of species
A = area of the island
C = the value of S at A = 1
z = the slope of the line
To graph the data, take the log of both sides
LogS = logC + zlogA

Question 5

Compare to slope-intercept of a straight line

Answer 5

LogS = logC + zlogA
Y = b + mx
LogS = y coordinate
logC = b (y-intercept)
z = m (slope)
LogA = x coordinate

Question 6

Calculating Z

Answer 6

1. “Z” is the slope of the best fit line on a log graph, so it is the same as calculating “m” in a linear graph, but with some modifications:
2. M = (y2-y1) / (x2-x1)
3. z = (log S2 - log S1) / (log A2 - log A1)

Question 7

Why use log-log graphs

Answer 7

1. Scale (fit more data on the same graph)
   1.5 need to chart exponential relationships
2. Best fit lines help us estimate relative species diversity

Question 8

Best Fit Lines…

Answer 8

1. … do not connect all the dots. They do not even connect the first dot with the last
2. … are lines drawn such that there are approximately an equal amount of data points both above and below the line
3. Basically, you want to illustrate the general direction that a group goes

Question 9

Applications

Answer 9

1. Conservation
2. Restoration
3. Translocation
4. Resource management
5. Small introduction to mathematical modeling
   5.5 What is the use in modeling?
   Weather, Polls, Investment/economy, Biology