ALBERT

Description: Community structure is defined as the mathematical statistical distribution of the relative species abundance vector. Consideration of the decomposition equation for species richness, S, evenness, E, and the Shannon estimate of entropy or information, H, plus their respective regressions on the accumulation of the number of individuals, N, in a sample leads to the establishment of three structural types. Each type is defined by the slope, {beta}1H, of the regression H versus lnN and depends on the accumulation rate of species between samples (beta-diversity) in a community. These types are designated as 1) Type 0, where H is constant with the accumulation of lnN denoting equilibrium or stability (Log series is a special case); 2) Type 1, where the slope of H is positive with the accumulation of lnN denoting growth or expansion (Log normal is a special case); and 3) Type -1, where the slope of H is negative with the accumulation of lnN denoting decline, instability or stress. In this study, 72 communities were analyzed from environments ranging from marginal marine to the abyss. Only 10 communities are identified as type -1 with the majority of these at lower bathyal and abyssal depths. At abyssal depths the average {beta}1H is -0.057 and data from fossil communities in the Arctic indicate that this unstable, stressed situation has persisted for at least 50 ka. In the Gulf of Mexico at shelf depths, low values for {beta}1H are registered near the Mississippi delta. In contrast, the open-ocean east of New Zealand has an average {beta}1H of 0.227, the highest recorded. Among marginal marine environments an average {beta}1H of -0.030 was recorded in Long Island Sound before the collapse of that community. In contrast, the Indian River Lagoon, Florida had the highest {beta}1H for a marginal marine environment with an average value of 0.195. No simple invariant pattern between type 0 and type 1 communities is prevalent in any environment. Overall 31 communities are type 0 and 31 are type 1. In marginal marine environments (22 communities) the average value of {beta}1H is 0.092. In the open-ocean (50 communities) the average value of {beta}1H is 0.093. Evidently, for any group to remain highly successful on the average a slightly positive value of {beta}1H is required.

Description: The mixed siliciclastic/carbonate sediments of Baffin Bay, Texas, provide a record of the evolution of the Bay for the last 10 ka. Flooding surfaces at 8 ka and 5.5 ka provided an a priori separation of sediments in a core into three groups. Discriminant analysis and interpretation of species composition of the foraminifera from these groups indicated a progression from deltaic to open-bay to hypersaline environments. This traditional paleoecological analysis, however, does not utilize the information available in the relative abundance distribution (RAD) within each community. An approach capable of assessing within community change is provided by S (species richness), H (Shannon information function) and E (evenness) analysis. Using this approach not only can communities be designated without a priori assumptions and environments identified easily, but also the RAD within each community can be evaluated, providing a record of community growth, decline or stasis with time. Stasis, or the ecological balance of nature, is mathematically defined as an equilibrium between S and E such that diversity (H) remains constant with time. This stasis requires that, as the number of individuals (N) gets larger with time, the value of H remains constant. Thus, at stasis a regression between H versus lnN will have a 0 value for the regression coefficient (β 1H ), here termed the Relative Abundance Distribution Index, RADI. A positive value of RADI indicates community growth, a negative value indicates community decline. In the Baffin Bay core 6, communities were identified from 46 samples using SHE analysis. At ~9 ka the RADI was positive, indicating the growth of a normal marine community with a high S. A second community, still largely normal marine but with a slightly negative RADI, formed at ~8 ka. Beginning at ~6.4 ka, the 3 rd and 4 th marginal marine communities with highly negative RADIs formed, indicating a sharp decline for ~1 ka during the formation of Padre Island, which may have taken ~1000 years. At ~5 ka the 5 th and 6 th marginal marine communities were established with RADIs indicating a prolonged period of stasis. The 5 th community was dominated by Elphidium with a high percentage of miliolids. The 6 th community, established at ~2 ka, was dominated by Ammonia and a moderate percentage of miliolids. These last two communities, both at stasis, were apparently responding to changes in salinity brought on by changes in rainfall.

Description: It is common to find that authors use more than one diversity measure in published research without providing interpretation or explanation. We use a survey of the last three years of articles published in this journal along with a classic data set of Parker from the Gulf of Mexico to show that the familiar practice of citing multiple indices, e.g., Shannon’s and Simpson’s diversity indices and/or Fisher’s α, each calculated for the same samples, is redundant and singularly uninformative. In addition, authors often register surprise at the performance of indices when describing diversity over gradients such as depth or time. We show that there is no requirement that the values of the indices be concordant over any gradient and the behavior of a measure can be mathematically determined by the distribution of the observed species. The measures we found to be the most common in current use were S, α, H, , and max p i . The mathematical equivalence of measures is shown through simple plots and description and a standard set of non-redundant measures on a log scale, lnS, H, and ln (1/max p i ) is recommended. Use of standardized analytical approaches to the study of problems of change in biodiversity removes limitations on the potential for inference concerning local as well as regional and global scales.