Appendix C. A table showing statistical analyses of spatiotemporal variation in stage class transitions.
TABLE C1. Log-linear analyses of the effects of population, P, and year, Y, on fate, F, for each stage class, S. Summing the effects of each stage class gives the four-way model of the effects of population and year on the state-by-fate transition table, conditional on the differences in states among populations and years. Notation follows convention for hierarchical models, such that the presence of an interaction implies the presence of all lower-order interactions and single factor terms contained in the interaction. Values in boldface remain significant after sequential Bonferroni correction to maintain a table-wide Type I error rate of 0.05 for each species.
G2 |
||||||
Species |
Three-way models |
df |
Small non-reproductive |
Large non-reproductive |
Reproductive |
Sum (df) four-way model |
M. cardinalis |
Test 1: marginal effect of year on fate |
|||||
LY, F‡ |
33 |
318.65 |
167.75 |
123.10 |
609.50 (99) |
|
LY, YF§ |
27 |
260.17 |
107.55 |
112.91 |
480.63 (81) |
|
YF |
6 |
58.48**** |
60.20**** |
10.19NS |
128.87 (18)**** |
|
Test 2: marginal effect of population on fate |
||||||
LY, F‡ |
33 |
318.65 |
167.75 |
123.10 |
609.50 (99) |
|
LY, LF|| |
24 |
164.64 |
118.45 |
26.78 |
309.87 (72) |
|
LF |
9 |
154.01**** |
49.30**** |
96.32**** |
299.63 (27)**** |
|
Test 3: conditional effect of year on fate |
||||||
LY, LF|| |
24 |
164.64 |
118.45 |
26.78 |
309.87 (72) |
|
LY, YF, LF¶ |
18 |
127.42 |
44.78 |
19.10 |
191.30 (54) |
|
YF (given L) |
6 |
37.22**** |
73.67**** |
7.68 NS |
118.57 (18)**** |
|
Test 4: conditional effect of population on fate |
||||||
LY, YF§ |
27 |
260.17 |
107.55 |
112.91 |
480.63 (81) |
|
LY, YF, LF¶ |
18 |
127.42 |
44.78 |
19.10 |
191.30 (54) |
|
LF (given Y) |
9 |
132.75**** |
62.77**** |
93.81**** |
289.33 (27)**** |
|
Test 5: three-way interaction of year, population and fate |
||||||
LY, YF, LF |
18 |
127.42 |
44.78 |
19.10 |
191.30 (54) |
|
LYF |
0 |
0 |
0 |
0 |
0 |
|
LYF (given all two-ways) |
18 |
127.42**** |
44.78*** |
19.10 NS |
191.30 (54)**** |
|
M. lewisii |
Test 1: marginal effect of year on fate |
|||||
LY, F‡ |
33 |
218.35 |
178.38 |
129.43 |
526.16 (99) |
|
LY, YF§ |
27 |
109.83 |
165.54 |
120.43 |
395.80 (81) |
|
YF |
6 |
108.52**** |
12.84* |
9.00NS |
130.36 (18)**** |
|
Test 2: marginal effect of population on fate |
||||||
LY, F‡ |
33 |
218.35 |
178.38 |
129.43 |
526.16 (99) |
|
LY, LF|| |
24 |
120.49 |
70.34 |
31.93 |
222.76 (72) |
|
LF |
9 |
97.86**** |
108.04**** |
97.50**** |
303.40 (27)**** |
|
Test 3: conditional effect of year on fate |
||||||
LY, LF|| |
24 |
120.49 |
70.34 |
31.93 |
222.76 (72) |
|
LY, YF, LF¶ |
18 |
54.97 |
38.83 |
20.32 |
114.12 (54) |
|
YF (given L) |
6 |
65.52**** |
31.51**** |
11.61† |
108.64 (18)**** |
|
Test 4: conditional effect of population on fate |
||||||
LY, YF§ |
27 |
109.83 |
165.54 |
120.43 |
395.80 (81) |
|
LY, YF, LF¶ |
18 |
54.97 |
38.83 |
20.32 |
114.12 (54) |
|
LF (given Y) |
9 |
54.86**** |
126.71**** |
100.11**** |
281.68 (27)**** |
|
Test 5: three-way interaction of year, population and fate |
||||||
LY, YF, LF |
18 |
54.97 |
38.83 |
20.32 |
114.12 (54) |
|
LYF |
0 |
0 |
0 |
0 |
0 |
|
LYF (given all two-ways) |
18 |
54.97**** |
38.83** |
20.32NS |
114.12 (54)**** |
|
NS P > 0.10, † 0.05 < P < 0.10, * P < 0.05, ** P < 0.01, *** P < 0.001, **** P < 0.0001
‡ When summed over all stages, gives the four-way model SLY, SF.
§ When summed over all stages, gives the four-way model SLY, SYF.
|| When summed over all stages, gives the four-way model SLY, SLF.
¶When summed over all stages, gives the four-way model SLY, SYF, SLF.