Appendix D. A figure depicting the projected population structure under the conditions of A^{(03-06)}; and projections of the site summary matrices A^{(CR15)}, A^{(CR20)}, A^{(CR30)}, and A^{(PR15)}.

Figure D1 shows the projected population structure under the conditions of A^{(03-06)}. In this projection, size class V composes 20.1% of the initial population while 9.6% of the population is in size class I. Through time, the population becomes increasingly positively skewed, with 13.6 and 23.8% of the population composed of individuals in size classes V and I, respectively.

FIG. D1. Projection as in Fig. 2B for A^{(03-06)} illustrating changes in the population structure of Xestospongia muta through time. |

PROJECTIONS OF SITE SUMMARY MATRICES

For each site summary matrices, A^{(CR15)}, A^{(CR20)}, A^{(CR30)}, and A^{(PR15)}, two projections were completed. For the first projection, depletion of the population was examined by assuming zero recruitment. For the second projection, a recruitment vector, **r**, was added to the population vector at each projection interval. The mean number of sponges that recruited to each site over 2000-2003 and 2003-2006 and survived to the end of each interval was used as **r** for projections.

Projections of the site summary matrices indicate that populations behaved differently over spatial scales. Population depletion slowed with increasing depth on Conch Reef (Fig. D2A). The rate of population depletion at PR15 was more similar to CR20 and CR30 than CR15. Projections indicate that, without recruitment, populations at CR15, CR20, CR30 and PR15 would be depleted in 87, 123, 207, and 195 years, respectively, under 2000-2006 conditions.

Populations increased under the conditions experienced at all sites (Fig. D2B). Recruitment vectors added to the population at each iteration were 14 size class I and 3 size class II for A^{(CR15)}, 27 size class I, 8.5 size class II, 1 size class III, and 0.5 Base stage for A^{(CR20)}, 16.5 size class I, 7.5 size class II, 1 size class III, and, 0.5 Base stage for A^{(CR30)}, and 26 size class I, 3.5 size class II and 0.5 Base stage for A^{(PR15)}. The fastest rates of population growth were exhibited at CR20 and PR15. In addition, higher recruitment at CR20 offset the faster population depletion at this site compared to PR15 and the population was found to increase at a faster rate (Fig. D2B). Of all sites, CR15 had both the fastest population depletion and lowest recruitment, and projections indicate that population increases were slowest at this site.

FIG. D2. Projections of the site summary matrices A^{(CR15)}, A^{(CR20)}, A^{(CR30)}, and A^{(PR15)} over 51 years (A) without recruitment of Xestospongia muta to observe the rate of population decline, and (B) with the addition of a recruitment vector, r, at each iteration to observe the importance of recruitment on population growth. r^{(CR15)}= 14 size class I and 3 size class II, r^{(CR20)}= 27 size class I, 8.5 size class II, 1 size class III, and 0.5 Base, r^{(CR30)}= 16.5 size class I, 7.5 size class II, 1 size class III, and, 0.5 Base, and A^{(PR15)}= 26 size class I, 3.5 size class II and 0.5 Base. |