This paper presents a fully specified model of long-run growth in which knowledge is assumed to be an input in production that has increasing marginal productivity. It is essentially a competitive equilibrium model with endogenous technological change. In contrast to models based on diminishing returns, growth rates can be increasing over time, the effects of small disturbances can be amplified by the actions of private agents, and large countries may always grow faster than small countries. Long-run evidence is offered in support of the empirical relevance of these possibilities.

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Increasing Returns and Long-Run Growth

In the early 1980s, a strategy for graphical representation of multivariate (multi-species) abundance data was introduced into marine ecology by, among others, Field, et al. (1982). A decade on, it is instructive to: (i) identify which elements of this often-quoted strategy have proved most useful in practical assessment of community change resulting from pollution impact; and (ii) ask to what extent evolution of techniques in the intervening years has added self-consistency and comprehensiveness to the approach. The pivotal concept has proved to be that of a biologically-relevant definition of similarity of two samples, and its utilization mainly in simple rank form, for example ‘sample A is more similar to sample B than it is to sample C’. Statistical assumptions about the data are thus minimized and the resulting non-parametric techniques will be of very general applicability. From such a starting point, a unified framework needs to encompass: (i) the display of community patterns through clustering and ordination of samples; (ii) identification of species principally responsible for determining sample groupings; (iii) statistical tests for differences in space and time (multivariate analogues of analysis of variance, based on rank similarities); and (iv) the linking of community differences to patterns in the physical and chemical environment (the latter also dictated by rank similarities between samples). Techniques are described that bring such a framework into place, and areas in which problems remain are identified. Accumulated practical experience with these methods is discussed, in particular applications to marine benthos, and it is concluded that they have much to offer practitioners of environmental impact studies on communities.

Non-parametric multivariate analyses of changes in community structure

Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test.

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Techniques of trend analysis for monthly water quality data

We studied whether microalbuminuria (30 to 140 micrograms of albumin per milliliter) would predict the later development of increased proteinuria and early mortality in Type II diabetics. During 1973, morning urine specimens of diabetic clinic patients 50 to 75 years of age whose disease had been diagnosed the age of 45 were examined for albumin level by radioimmunoassay. Seventy-six patients with albumin concentrations of 30 to 140 micrograms per milliliter were identified for long-term follow-up. They were compared with normal controls, diabetic patients with lower albumin concentrations (75 patients with concentrations less than 15 micrograms per milliliter and 53 with concentrations of 16 to 29 micrograms per milliliter), and 28 diabetic patients with higher concentrations (greater than 140). Age, duration of diabetes, treatment method, fasting blood glucose level, blood pressure, height, and weight were determined for the four diabetic groups. After nine years the group with albumin concentrations of 30 to 140 micrograms per milliliter was more likely to have clinically detectable proteinuria (greater than 400 micrograms per milliliter) than were the groups with lower concentrations. Mortality was 148 per cent higher in this group than in normal controls--comparable to the increase (116 per cent) in the group with heavy proteinuria (albumin levels greater than 140 micrograms per milliliter). In addition, mortality was increased 76 per cent in the group with albumin levels of 16 to 29 micrograms per milliliter and 37 per cent in the group with levels below 15. We conclude that microalbuminuria in patients with Type II diabetes is predictive of clinical proteinuria and increased mortality.

P. A. P. Moran

Papers

Rank Correlation Methods