Table 14.8 contains the l(x)b(x)
schedule for the plant Rhododendron
maximum. Like many plant species, R. maximum can reproduce asexually via
shoots and sexually via seeds. The b(x) values
in Table 14.8 are for shoot production.
a. Calculate g(x), R0, G, and r.
(NOTE: You may bring a sheet of paper with
the values you calculated to the exam.)
b. What is the probability of surviving between
6- and 7-years old?
c. What is the probability of dying between 1-
and 2-years old?
d. Based on these data, can the population
maintain itself solely through asexual reproduction? Explain your reasoning.
e. Discuss at least two possible causes for the
variations seen in fecundity.
f. How many shoots would be produced by a cohort
of 80 individuals over their lifetimes? Show your work.
a.
|
x |
l(x) |
b(x) |
g(x) |
L(x) |
T(x) |
e(x) |
l(x)b(x) |
xl(x)b(x) |
|
0 |
1.000 |
0.012 |
1.000 |
1.000 |
5.600 |
5.600 |
0.012 |
0.000 |
|
1 |
1.000 |
0.032 |
0.984 |
0.992 |
4.600 |
4.600 |
0.032 |
0.032 |
|
2 |
0.984 |
0.000 |
1.000 |
0.984 |
3.608 |
3.667 |
0.000 |
0.000 |
|
3 |
0.984 |
0.115 |
0.924 |
0.947 |
2.624 |
2.667 |
0.113 |
0.339 |
|
4 |
0.909 |
0.037 |
0.796 |
0.817 |
1.678 |
1.845 |
0.034 |
0.135 |
|
5 |
0.724 |
0.046 |
0.522 |
0.551 |
0.861 |
1.189 |
0.033 |
0.167 |
|
6 |
0.378 |
0.000 |
0.286 |
0.243 |
0.310 |
0.820 |
0.000 |
0.000 |
|
7 |
0.108 |
0.000 |
0.120 |
0.061 |
0.067 |
0.620 |
0.000 |
0.000 |
|
8 |
0.013 |
0.077 |
0.000 |
0.007 |
0.007 |
0.500 |
0.001 |
0.008 |
|
9 |
0 |
|
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R0 = |
0.225 |
|
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G = |
3.023 |
|
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r = |
-0.493 |
b. g(6) = 0.286
c. 1 - g(1) = 1- 0.984 = 0.026
d. no; and r < 0; plants cannot replace
themselves fully with new plants from shoots
e. many possible answers—environmental
fluctuations in water, temperature, etc.; variable pest/herbivore populations;
shoots produced only when sufficient energy is available
f. 80 x R0 = 80 x 0.255 = 18