Mass Energy and Flow in closed ecosystems

The general equations of biomass and energy transfer for an n-species, closed ecosystem are written. It is demonstrated how in "ecological time" the parameters describing the dynamics of biomass transfer are related to the parameters of energy transfer, such as respiration, fixation, and energy content. This relationship is determinate for the straight-chain ecosystem, and a simple example is worked out. The results show how the density dependent terms in population dynamics arise naturally, and how the stable system exhibits a hierarchy in energy per unit biomass. A procedure is proposed for extending the theory to include webbed systems, and the particular difficulties involved in the extension are brought before the scientific community for discussion.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

A comparison of seafloor habitats and associated benthic fauna in areas open and closed to bottom trawling along the central California Continental Shelf

Executive Summary: A number of studies have shown that mobile, bottom-contact fishing gear (such as otter trawls) can alter seafloor habitats and associated biota. Considerably less is known about the recovery of these resources following such disturbances, though this information is critical for successful management. In part, this paucity of information can be attributed to the lack of access to adequate control sites – areas of the seafloor that are closed to fishing activity. Recent closures along the coast of central California provide an excellent opportunity to track the recovery of historically trawled areas and to compare recovery rates to adjacent areas that continue to be trawled. In June 2006 we initiated a multi-year study of the recovery of seafloor microhabitats and associated benthic fauna inside and outside two new Essential Fish Habitat (EFH) closures within the Cordell Bank and Gulf of the Farallones National Marine Sanctuaries. Study sites inside the EFH closure at Cordell Bank were located in historically active areas of fishing effort, which had not been trawled since 2003. Sites outside the EFH closure in the Gulf of Farallones were located in an area that continues to be actively trawled. All sites were located in unconsolidated sands at equivalent water depths. Video and still photographic data collected via a remotely operated vehicle (ROV) were used to quantify the abundance, richness, and diversity of microhabitats and epifaunal macro-invertebrates at recovering and actively trawled sites, while bottom grabs and conductivity/temperature/depth (CTD) casts were used to quantify infaunal diversity and to characterize local environmental conditions. Analysis of still photos found differences in common seafloor microhabitats between the recovering and actively trawled areas, while analysis of videographic data indicated that biogenic mound and biogenic depression microhabitats were significantly less abundant at trawled sites. Each of these features provides structure with which demersal fishes, across a wide range of size classes, have been observed to associate. Epifaunal macro-invertebrates were sparsely distributed and occurred in low numbers in both treatments. However, their total abundance was significantly different between treatments, which was attributable to lower densities at trawled sites. In addition, the dominant taxa were different between the two sites. Patchily-distributed buried brittle stars dominated the recovering site, and sea whips (Halipteris cf. willemoesi) were most numerous at the trawled site though they occurred in only five of ten transects. Numerical classification (cluster analysis) of the infaunal samples also revealed a clear difference between benthic assemblages in the recovering vs. trawled areas due to differences in the relative abundances of component species. There were no major differences in infaunal species richness, H′ diversity, or J′ evenness between recovering vs. trawled site groups. However, total infaunal abundance showed a significant difference attributable to much lower densities at trawled sites. This pattern was driven largely by the small oweniid polychaete Myriochele gracilis, which was the most abundant species in the overall study region though significantly less abundant at trawled sites. Other taxa that were significantly less abundant at trawled sites included the polychaete M. olgae and the polychaete family Terebellidae. In contrast, the thyasirid bivalve Axinopsida serricata and the polychaetes Spiophanes spp. (mostly S. duplex), Prionospio spp., and Scoloplos armiger all had significantly to near significantly higher abundances at trawled sites. As a result of such contrasting species patterns, there also was a significant difference in the overall dominance structure of infaunal assemblages between the two treatments. It is suggested that the observed biological patterns were the result of trawling impacts and varying levels of recovery due to the difference in trawling status between the two areas. The EFH closure was established in June 2006, within a month of when sampling was conducted for the present study, however, the stations within this closure area are at sites that actually have experienced little trawling since 2003, based on National Marine Fishery Service trawl records. Thus, the three-year period would be sufficient time for some post-trawling changes to have occurred. Other results from this study (e.g., similarly moderate numbers of infaunal species in both areas that are lower than values recorded elsewhere in comparable habitats along the California continental shelf) also indicate that recovery within the closure area is not yet complete. Additional sampling is needed to evaluate subsequent recovery trends and persistence of effects. Furthermore, to date, the study has been limited to unconsolidated substrates. Ultimately, the goal of this project is to characterize the recovery trajectories of a wide spectrum of seafloor habitats and communities and to link that recovery to the dynamics of exploited marine fishes. (PDF has 48 pages.)

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Phase-dependent properties for absorption and dispersion in a closed equispaced three-level ladder system

It is shown that in a closed equispaced three-level ladder system, by controlling the relative phase of two applied coherent fields, the conversion from absorption with inversion to lasing without inversion (LWI) can be realized; a large index of the refraction with zero absorption can be gotten; considerable increasing of the spectrum region and value of the LWI gain can be achieved. Our study also reveals that the incoherent pumping will produce a remarkable effect oil the phase-dependent properties of the system. Modifying value of the incoherent pumping can change the property of the system from absorption to amplification and enhance significantly LWI gain. If the incoherent pumping is absent, we cannot get any gain for any value of the relative phase. (c) 2007 Elsevier GmbH. All rights reserved.