Appendix I. Site summary matrices A^{(CR15)}, A^{(CR20)}, A^{(CR30)}, and A^{(PR15)} and additional results.
TABLE I1. Site summary matrices A^{(CR15)}, A^{(CR20)}, A^{(CR30)}, and A^{(PR15)} for 15, 20, and 30 m Conch Reef and 15 m Pickles Reef sites, respectively. Transition probabilities for each site were calculated by pooling transitions over 2000–2003 and 2003–2006. qx = stagespecific mortality rate, n = sample size, λ = dominant eigenvalue describing rate of population depletion, ρ = damping ratio and CI = 95% confidence intervals.
size class 
Size class 

Base 
I 
II 
III 
IV 
V 

Base 
0.667 
0 
0 
0.053 
0.067 
0 
I 
0.056 
0.36 
0.032 
0 
0 
0 
II 
0.028 
0.4 
0.516 
0 
0 
0 
III 
0 
0 
0.323 
0.684 
0 
0 
IV 
0.056 
0 
0 
0.263 
0.633 
0 
V 
0.028 
0 
0 
0 
0.233 
0.829 







qx 
0.167 
0.24 
0.129 
0 
0.067 
0.171 
n 
36 
25 
31 
19 
30 
35 
λ (CI) 
0.829 (0.704, 0.892) 
ρ (CI) 
1.027 (1.0, 1.092) 

20 m Conch 






Base 
0.737 
0 
0.057 
0.033 
0.021 
0 
I 
0.053 
0.487 
0 
0 
0 
0 
II 
0 
0.282 
0.543 
0.083 
0 
0 
III 
0.053 
0 
0.4 
0.517 
0.042 
0 
IV 
0.053 
0 
0 
0.3 
0.563 
0.022 
V 
0 
0 
0 
0 
0.229 
0.870 







qx 
0.105 
0.231 
0 
0.067 
0.146 
0.109 
n 
19 
39 
35 
60 
48 
46 
λ (CI) 
0.890 (0.809, 0.955) 
ρ (CI) 
1.093 (1.011, 1.247) 

30 m Conch 






Base 
0.571 
0 
0.05 
0 
0 
0.059 
I 
0 
0.5 
0 
0 
0 
0 
II 
0.143 
0.167 
0.5 
0.038 
0 
0 
III 
0 
0 
0.3 
0.538 
0.071 
0 
IV 
0 
0 
0 
0.346 
0.857 
0.118 
V 
0 
0 
0 
0 
0.071 
0.706 







qx 
0.286 
0.333 
0.15 
0.077 
0 
0.118 
n 
7 
12 
20 
26 
14 
17 
λ (CI) 
0.957 (0.837, 1.0) 
ρ (CI) 
1.415 (1.248, 1.884) 

15 m Pickles 






Base 
0.652 
0 
0 
0 
0 
0 
I 
0.043 
0.5 
0.115 
0 
0 
0 
II 
0.043 
0.278 
0.538 
0 
0 
0 
III 
0.087 
0.014 
0.308 
0.581 
0.023 
0.029 
IV 
0 
0 
0 
0.355 
0.75 
0.029 
V 
0 
0 
0 
0.032 
0.205 
0.857 







qx 
0.174 
0.208 
0.038 
0.032 
0.023 
0.086 
n 
23 
72 
52 
31 
44 
35 
λ (CI) 
0.933 (0.844, 0.991) 
ρ (CI) 
1.335 (1.235, 1.635) 
Not all transitions were observed at each site for a given time interval. For the lowest density site, CR30, there were initially no sponges present in size class I, and no mortality was observed for the two largest size classes. To allow for analytical comparisons between sites, transitions over each time interval were pooled to parameterize site summary matrices (Table I1).
For the site summary matrices, A^{(CR15)}, A^{(CR20)}, A^{(CR30)}, and A^{(PR15)}, sponge stasis was generally found to increase with increasing size (Table I1). One exception to this trend was A^{(CR30)}, where 12 and 6 % of size class V sponges were found to shrink to the next smallest size class or transition to the Base stage, respectively. Sponge mortality was greatest for size class I for all matrices and greatest mortality of size class V occurred for A^{(CR15)} (Table I1). Growth was more variable between sites compared to A^{(0003)} and A^{(0306)} and an inverse relationship between growth and size did not hold for all site summary matrices. In particular, growth of size class I for A^{(CR20)} and A^{(CR30)} was low compared to growth of size classes II and III for these matrices. Sponge shrinkage and partial mortality was variable among and between sites with transitions to the next smallest size class or the Base stage observed for size classes II through V. Interestingly, no sponges were observed to transition to the Base stage at Pickles Reef (Table I1).
Spatially, there was a direct relationship between population decline and depth on Conch Reef, with the deepest site having the slowest rate of depletion (Table I1). Randomization tests indicated that population depletion was significantly faster at CR15 compared to CR30 (P = 0.044). Comparisons between all other sites were nonsignificant. The damping ratio increased with increasing depth on Conch Reef (Table I1). A^{(CR30)} had a significantly greater ρ compared to A^{(CR15)} (P = 0.007) and A^{(CR20)} (P = 0.016). A^{(PR15)} also had a significantly greater ρ compared to A^{(CR15)} (P = 0.041) and A^{(CR20)} (P = 0.05).