To assess bacterioplankton production in the sea, we have developed a procedure for measuring growth based on incorporation of tritiated thymidine into DNA; the accuracy of this procedure was tested under a variety of laboratory and field conditions. By autoradiography, we have found that for all practical purposes our technique is specific for the nonphotosynthetic bacteria and that virtually all of the “active” bacteria (one-third or more of the total countable bacteria) take up thymidine. We also measured (1) the intracellular isotope dilution of thymidine assessed by parallel experiments with labeled phosphorus, and (2) DNA content of natural marine bacteria (0.2 to 0.6 μm size fraction); a conversion factor derived from these data permitted estimation of production from thymidine incorporation results. A very similar conversion factor was independently derived from the empirical relationship between thymidine incorporation and growth of natural bacterioplankton under controlled conditions. Combined results show that this technique, which can be performed rapidly and easily at sea, provides good estimates of production. Data from Southern California Bight waters, which contain oligotrophic as well as moderately eutrophic regions, show that average bacterioplankton doubling times, like those of the phytoplankton, are on the order of a few days, with fastest growth at depths just below those of greatest phytoplankton abundance. Offshore bacterial production is roughly 5 to 25% of the primary production; thus, at a 50% assimilation efficiency, the bacterioplankton would consume 10 to 50% of the total fixed carbon.

Thymidine incorporation as a measure of heterotrophic bacterioplankton production in marine surface waters : Evaluation and field results

This paper provides a formal statistical basis for the efficiency evaluation techniques of data envelopment analysis (DEA). DEA estimators of the best practice monotone increasing and concave production function are shown to be also maximum likelihood estimators if the deviation of actual output from the efficient output is regarded as a stochastic variable with a monotone decreasing probability density function. While the best practice frontier estimator is biased below the theoretical frontier for a finite sample size, the bias approaches zero for large samples. The DEA estimators exhibit the desirable asymptotic property of consistency, and the asymptotic distribution of the DEA estimators of inefficiency deviations is identical to the true distribution of these deviations. This result is then employed to suggest possible statistical tests of hypotheses based on asymptotic distributions.

Maximum likelihood, consistency and data envelopment analysis: a statistical foundation

Interest in the passive dispersal of organisms has been associated primarily with the problems concerning the colonization of oceanic islands. See for example: Darwin (1845), Wallace (1892), Guppy (1917), Ridley (1930), Guilick (1932), Darlington (1938), Gibson-Hill (1950), and Zimmerman (1948). Because of the great distances between oceanic islands and sources of terrestrial plants or animals, events of successful colonization of such an island by new species are rare. The result is that workers in this field have been limited virtually to the enumeration of the species found on a given island and to speculation as to how each organism may have reached that island. The most probable mode of transport in each case has been suggested on the basis of what may be known (or suspected) of the ecology of the species. Little advantage was taken of what was possibly the greatest opportunity in modern times to observe the recolonization of an island. This was following the tremendous explosion of Krakatau in 1883, when much of the island was blown into the air and the remainder was covered by many feet of glowing volcanic ash. Much of the original flora and fauna of this island was undoubtedly destroyed (Dammerman 1948) although there is question as to whether it was all wiped out (Backer 1929). Dammerman summarized the results of occasional brief collecting trips to the island during the years following the explosion. His data show that the colonization of this island (which is only about 19 miles from Sebesi Island and about 40 miles from Java and from Sumatra) was a slow process. An analogous situation, and one which is much more amenable to study, concerns the invasion and colonization of isolated bodies of water bv small aquatic organisms. Many of the dispersal mechanisms which operate to colonize oceanic islands operate here, but because isolating distances are much smaller, events of successful colonization are much Organism Associations . . .. ...... ...... 177 Transport by Birds .. 180 Transport by Insects ........ 180

https://www.jstor.org/stable/pdfplus/1948560.pdf

The Passive Dispersal of Small Aquatic Organisms and Their Colonization of Isolated Bodies of Water

Existing and new approaches for the analysis of CATA data

The small-sample properties of three goodness-of-fit statistics for the analysis of categorical data are examined with respect to the adequacy of the asymptotic chi-squared approximation. The approximate tests based on the likelihood ratio and Freeman-Tukey statistics yield exact levels that are typically in excess of the nominal levels for moderate expected values. In contrast, the Pearson statistic attains exact levels that are quite close to the nominal values. The reason for the large number of rejections for the likelihood ratio and Freeman-Tukey statistics is related to their handling of small observed counts.

Small-Sample Comparisons of Exact Levels for Chi-Squared Goodness-of-Fit Statistics

Nonparametric and Shortcut Statistics.

Nonparametric and shortcut statistics in the social, biological, and medical sciences

In applied statistics there is an increasing tendency toward leniency regarding minimum expectation prerequisite to Pearson's X 2 test for goodness of fit, based on various empirical studies of the distribution of X2 in sampling from multinomial populations with given parameters. In this study it is shown that the chi-square probabilities of X 2 may differ markedly from the exact cumulative multinomial probabilities. Contrary to prevailing opinion, the approximation did not improve, when samples were small, as expectation increased nor as the number of categories or degrees of freedom increased.

Inaccuracy of the x2 Test of Goodness of Fit When Expected Frequencies Are Small

Cochran's Q test for differences between related-sample percentages or proportions has generally been incorrectly presented in secondary sources. The most common mistake results from failure to recognize that rows containing only 1's or only 0's, i.e., only successes or only failures, do not affect the value of Q. The F test, however, is affected by such rows. The probabilities from the χ2 and F approximations are compared with the exact probabilities in three sets of data. A rule of thumb, based on extensive study of the distribution of 0 in small samples, is given as an aid in judging when the χ2 approximation is satisfactory for practical purposes.

Note on the Cochran Q Test

/pdf/significance-values-for-an-exact-multinomial-test-and-4sydfjrrca.pdf

Merle W. Tate

Papers

Nonparametric and Shortcut Statistics.

Nonparametric and shortcut statistics in the social, biological, and medical sciences

Inaccuracy of the x2 Test of Goodness of Fit When Expected Frequencies Are Small

Note on the Cochran Q Test

Significance Values for an Exact Multinomial Test and Accuracy of the Chi-Square Approximation, Final Report.