Bounding the Equilibrium Distribution of Markov Population Models

Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its function as a biological switch. Unfortunately, the state space of these systems is infinite in most cases, preventing the use of traditional steady state solution techniques. In this paper we develop a new approach to tackle this problem by first retrieving geometric bounds enclosing a major part of the steady state probability mass, followed by a more detailed analysis revealing state-wise bounds.Comment: 4 page

Site-Dependent Differences in Artificial Reef Function: Implications for Coral Reef Restoration

There is an increasing use of artificial structure in coral reef restoration (for references, see Spieler et al., this volume). Often artificial reef structures are chosen for a restoration project simply because they were used elsewhere. However, it is questionable whether the results obtained at one restoration site can be extrapolated to another. In recent years, several studies have examined the effect of artificial reef site selection on formation of associated fish, algae, and/or invertebrate assemblages (Alevizon et al., 1985; Blinova et al., 1994; Bombace et al., 1994; Caley and St. John, 1996; Chang, 1985; Haughton and Aiken, 1989; Hixon and Beets, 1989; Jara and Cespedes, 1994; Kruer and Causey, 1992; Lozano-Alvarez et al., 1994; Moffitt et al., 1989; Relini et al., 1994; Sherman et al., 2000; Sherman et al., 1999; Sogard, 1989; Spieler, 1998; Tomascik, 1991). Although not designed specifically as coral reef restoration projects, the results of these studies lend insight into the problems of restoration. This paper is an overview of recent literature on site selection intended for resource managers interested in using artificial reefs in coral reef restoration. To that end, we re-examined the data from several studies comparing similar artificial reef structures at different sites

Artificial Substrate and Coral Reef Restoration: What Do We Need to Know to Know What We Need

To use artificial substrate effectively in coral reef restoration certain basic knowledge is required: (1) what is the artificial substrate expected to accomplish relative to the goals of the restoration effort and (2) what are the expected interactions of the selected substrate’s composition, texture, orientation, and design with the damaged environment and the biota of interest. Whereas the first point is usually clear, at least in general terms, the second is not. In this review, we examine: the functions of artificial substrate in restoration and some of the physical (i.e., composition; surface texture; color and chemistry; and design in terms of profile, shelter, shading, size and configuration, settlement attractants, and stability) and environmental factors (i.e., temperature, light sedimentation, surround biota, hydrodynamics, depth, and temporal effects) affecting these functions. We conclude that until substantial additional research is accomplished, the use of artificial substrate in coral reef restoration will remain a ‘best guess’ endeavor. Areas requiring additional research are identified and some potentially promising lines of inquiry are suggested

Reef Fish Assemblage Structure Affected by Small-Scale Spacing and Size Variations of Artificial Patch Reefs

To examine how varying the distance between patch reefs affects reef fish assemblage structure, replicate concrete reef modules (∼ 1 m3 each) were deployed on sand bottom at 8 m depth off Ft. Lauderdale, Florida, USA (26°07N, 80°05W). Modules were positioned at the apices of one of four differently sized equilateral triangles. Triangular configurations had side lengths of: 25 m, 15 m, 5 m, and 0.33 m; each treatment with two replicates. Two additional configurations: (1) a solitary module (Single) and (2) two modules side by side (Double), also with two replicates, were deployed in order to examine the interaction of reef size with fish assemblages. SCUBA divers censused fishes monthly, for 2 years, recording the species present, their abundance and sizes (TL). Fishes were assigned to one of five length categories: \u3c 2 cm, \u3e 2–5 cm, \u3e 5–10 cm, \u3e 10–20 cm, and \u3e 20 cm. In general and excluding the smallest three-module spacing treatment (0.33 m treatment), which may have provided unique treatment-specific refuge, total fish abundance and richness were shown to increase when isolation distance increased. However, there were also species-specific and size class differences in response to isolation distance. The second part of this study indicated varying reef size, by doubling and tripling the number of reef modules, increased total fish abundance and species richness. Nevertheless, fish abundance and species richness did not change by an identical multiplier (e.g., doubling modules ≠ double abundance). These results suggest that scientists and marine managers alike should consider reef size and isolation as habitat attributes capable of altering the structure and dynamics of reef fish assemblages

A Comparison of Reef Fish Assemblages on the East and West Sides of Central Eleuthera, Bahamas

Eleuthera is a long, narrow crescent-shaped Atlantic margin island on the eastern extremity of the Great Bahama Bank in the central Bahamas. It is 144 km long and less than 5 km at its greatest width. Fringing reefs with substantial vertical relief (to 5 m in depths of 6 m) are found approximately 500 m offshore on the eastern side of the island facing the Atlantic Ocean. The western side of the island has stretches of rock cliffs and large fallen boulders providing substrate with similar vertical relief. No open passes exist between the two sides of the island and thus no direct larval transport from one side to the other appears possible. We compared post-settlement fish assemblages and larval supply on either side of central Eleuthera near Governor’s Harbour quarterly from July 2003 until July 2004. Twelve point-counts were performed at two replicate sites on both sides of the island to census juveniles and adults. Abundance, as well as average, maximum and minimum lengths of species present were recorded. Three light traps were moored at each of the same sites 40-50 m from the reef for three to five nights around the new moon to examine larval supply. Fish collected in the light traps were preserved and transported to the lab. They were identified, enumerated, and standard length was measured. Preliminary analyses of point-count and light trap data indicate dissimilar assemblage structure between the two sides of the island, with significantly greater fish abundance and species richness on the eastern side

Marine Biological Monitoring in Broward County, Florida: Year 2 Annual Report

A study has been undertaken to monitor Broward County, Florida (southeast Florida) coral communities, reef fish assemblages and sedimentation rates in relation to possible effects from a proposed extensive beach renourishment (restoration) project. Coral communities and reef fish assemblages will be monitored at a total of 23 stations distributed offshore Broward County. This monitoring effort will characterize and quantify populations of scleractinian (stony) corals, octocorallian (gorgonian) corals, sponges, and reef fishes. In addition, sediment traps located at each station will be sampled and analyzed. This document reports the data collected during the second year of this project. Coral communities and fish assemblages were monitored at each of the 23 sites between September and October 2001. In addition, sedimentation analysis for the January, March, May, July and September 2001 collections were conducted. For September/October 2001, mean (± 1 S.D.) stony coral density for the 23 sites was 2.62 ± 1.85 colonies/m2. Mean stony coral coverage was 2.39 ± 3.96%. Mean gorgonian density was 7.91 ± 8.01 colonies/m2 and mean sponge density was 14.09 ± 6.93 colonies/m2. First Reef sites had greater mean stony coral coverage but lower gorgonian and sponge density than Second and Third Reef sites. First Reef coral cover was much lower than the Third Reef when the First reef site, FTL4, was removed from the analysis. FTL4 had much greater stony coral cover than the mean cover for the remaining First Reef sites (19.95% compared to 1.45%). Shannon-Weaver Diversity Indices performed on the overall transect data resulted in values of 1.45 ± 0.53 and 1.72 ± 0.44 for cover and number of species respectively. Overall evenness was 0.77 ± 0.14 for number of species and 0.64 ± 0.21 for cover. There was no significant difference determined between the January/February 2001 site visit data and the September/October 2001 site visit data for mean stony coral density and cover. Mean octocoral density also did not differ significantly between these site visits, but mean sponge density was significantly less in September/October 2001 than in January/February 2001. Stony coral density, stony coral coverage, gorgonian density and sponge density data collected from the 18 monitoring sites established in 1997 and visited yearly from 1997 to 1999 were analyzed. No significant difference in yearly mean stony coral density, mean stony coral cover and mean gorgonian density was determined. Mean sponge density did show significant differences with 1998 sponge density greater than 1997. Trends in fish density were similar to those trends identified within the coral community transects. The greatest density of fishes occurs on the Third Reef followed by the First and Second. A difference in richness was seen amongst the three Reefs with the First Reef having the lowest number of species. The differences noted in abundance, density, and richness between the data collected in January/February 2001 and in September/October 2001 confirm previous reports of temporal differences in the fish assemblage offshore Broward County (Spieler 1998). The First Reef had a statistically higher rate of sedimentation than both the Second and Third Reefs when data from January-September 2001 were pooled. Pooled site data showed that January 2001 and May 2001 samples had the greatest sedimentation rates. The grain size for sites on the Third Reef was significantly smaller than both the First and Second Reefs. When site data were pooled, January 2001 had a significantly larger mean grain size than the other four sampling intervals in 2001. Data collected and analyses completed during this monitoring project will be used to help evaluate effects from the proposed beach renourishment project