Authorship credit for multi-authored scientific publications is routinely allocated either by issuing full publication credit repeatedly to all coauthors, or by dividing one credit equally among all coauthors. The ensuing inflationary and equalizing biases distort derived bibliometric measures of merit by systematically benefiting secondary authors at the expense of primary authors. Here I show how harmonic counting, which allocates credit according to authorship rank and the number of coauthors, provides simultaneous source-level correction for both biases as well as accommodating further decoding of byline information. I also demonstrate large and erratic effects of counting bias on the original h-index, and show how the harmonic version of the h-index provides unbiased bibliometric ranking of scientific merit while retaining the original's essential simplicity, transparency and intended fairness. Harmonic decoding of byline information resolves the conundrum of authorship credit allocation by providing a simple recipe for source-level correction of inflationary and equalizing bias. Harmonic counting could also offer unrivalled accuracy in automated assessments of scientific productivity, impact and achievement.
Bibliometric counting methods need to be validated against perceived notions of authorship credit allocation, and standardized by rejecting methods with poor fit or questionable ethical implications. Harmonic counting meets these concerns by exhibiting a robust fit to previously published empirical data from medicine, psychology and chemistry, and by complying with three basic ethical criteria for the equitable sharing of authorship credit. Harmonic counting can also incorporate additional byline information about equal contribution, or the elevated status of a corresponding last author. By contrast, several previously proposed counting schemes from the bibliometric literature including arithmetic, geometric and fractional counting, do not fit the empirical data as well and do not consistently meet the ethical criteria. In conclusion, harmonic counting would seem to provide unrivalled accuracy, fairness and flexibility to the long overdue task of standardizing bibliometric allocation of publication and citation credit.
Outbreak populations of the green sea urchin Strongylocentrotus droebachiensis Miiller caused widespread decimation of the original Laminaria hyperborea (Gunn.) Fosl. kelp forest in Vestflorden, Northern Norway, during the early 1980s. In the follow~ng decade, some of the resulting urch~n-dominated barren grounds reverted to kelp forest, which, after persisting for more than 5 yr, began to be eliminated yet again. Age analysis of annual growth rings in kelp stipes from field sites at V~r a y Island i n l c a t e that the time of initial kelp recovery varied from site to site but took place between 1984 and 1987. The earliest independent observations of localized macrophyte recovery were made in 1984 at the Harbour Pier site, where, by August 1992, the new kelp forest had already been eliminated by recurrent destructive grazing. Sea urchin density inside re-established kelp forests at 3 other sites on Vaer~y Island was 45 to 75 ind. m-2 in 1992. These urchin populations had significantly aggregated spatial patterns, and recurrent destructive grazing appeared to be mrmnent. This prediction was verified in 1993 when barren grounds reappeared at all study sltes. The threshold conditions for initiation of destructive grazing have been approximated by a curve in the aggregation-density plane. Sea urchins in the Vestfjorden area are infected by the recently discovered epizootic endoparasitic nematode Echinornermella matsi. In 1992, the prevalence of E. matsiat Varay Island ranged from 8.8% in the barren ground at the Harbour Pier site, to between 13.6 and 21.6% in the successionally immature kelp forest at the 3 other sites. The observed kelp forest recovery at Vceray Island was predicted by the macroparasite hypothesis which states that E. matsi may function as a terminator of sea urchin outbreaks in Northern Norway. However, the succession towards an ecologically mature kelp forest community has been interrupted by the unexpected recurrence of destructive grazing, and the macroparasite hypothesis must therefore be rejected in its present form. Furthermore, these local events may, on the larger time and spatial scales of the current outbreak phenomenon, indicate that the euphotic hard bottom component of the coastal ecosystem in Northern Norway has entered a cyclical domain.
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