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Models based on transformed Gaussian curves are described and used to summarise the seasonal variations in the surface temperature, dissolved reactive phosphorus concentration and phytoplankton biomass of three lakes in the English Lake District. The models are then used to quantify the effects of reducing the frequency of sampling on the detection of long-term (decadal-scale) change in the selected lakes. Three case studies are presented to demonstrate the effect of local changes in the catchment and regional-scale changes in the weather. The results demonstrate that the fitted models typically explained more than 70 percent of the recorded variation and can be used to quantify systematic changes in the timing and magnitude of the inter-annual variations. Tests where these time-series were systematically degraded showed that relatively little information was lost by fortnightly sampling but there was a marked reduction in the proportion of the variance explained when the sampling frequency was reduced from monthly to bi-monthly. Further tests on sub-sets of the acquired data showed that the capacity to detect change was not strongly influenced by the period of observation. When the length of record was reduced from 30 to 9 years the temperature and phosphorus models still explained a high proportion of the recorded variance but the results with the chlorophyll model were more time-dependent.

This report documents the initial phases (model development) of a DoD Challenge project investigating the interactions of organophosphorus compounds with acetylcholinesterase. This project entails characterization of the structural features, which lie al the heart of the interaction between novel organophosphorus compounds (or other more reversible inhibitors) and the enzyme acetylcholinesterase. Large biological systems present inherent difficulties to the modeling community. We are using quantum chemical and mixed quantum/classical techniques, QM/MM, to examine structural effects of reactions involving novel organophosphorus compound in the active site of the enzyme, as well as the role of surrounding residues. This investigation will provide highly accurate and reliable characterizations of the biochemical processes responsible for both activity and inhibition of novel organophosphorus compounds. It is expected that the results should prove relevant to toxicological endeavors within the medical and non-medical community alike., The original document contains color images. All DTIC reproductions will be in black and white.

1. A growth model, originally developed for brown trout (Salmo trutta), has now been fitted to data for Atlantic salmon (S. salar) and stone-loach (Barbatula barbatula) from English populations, and Arctic charr (Salvelinus alpinus) from Sweden. The model relates growth rate to temperature for a fish of standard size and the functional relationship has a triangular shape with a sharp peak at the optimal temperature for growth and zero growth at the base of the triangle. It was unsuitable for growth data for Norwegian salmon, and a curvilinear Ratkowsky model provided a better fit, though the experimental protocol was different in the Norwegian and English experiments. 2. The Norwegian salmon were kept in groups in each tank, had to compete for food, and had to be divided into slow, moderate and fast growers before the Ratkowsky model could be fitted. Each English salmon was kept in its own tank and fed individually. For replicate experiments, fish of similar size were selected. Variation among fish kept under similar conditions was therefore small, and the triangular model was essentially for individual fish, not groups of fish. 3. The present simulation study tests the hypothesis that individual differences in the growth response could account for the curvilinear growth-temperature relationship for the Norwegian salmon. The triangular model was used to generate the growth response to temperature for a group of salmon, each fish having a slightly different temperature preference and growth rate. The result was a curvilinear response, well approximated by the Ratkowsky model (adjusted R2 = 0.96). When the variability in individual temperature preference was increased, the Ratkowsky model was an even better fit (adjusted R2 = 0.98). Therefore, the apparent discrepancy between the two models was reconciled by allowing for individual differences in temperature preference and growth rate within groups of fish.

Declining sulphur deposition since the late 1970s has led to increases in pH in lakes and streams of the English Lake District (Cumbria, UK). To determine whether there have been biological responses to the chemical changes, we carried out surveys of stream macroinvertebrates and lake surface sediment diatoms, and compared the results with those from earlier surveys. Macroinvertebrate taxa in five streams (current average pH range 5.1–7.0) sampled in 1999 showed clear changes from those found during 1965/1966 and 1972. For three of the streams, more taxa were present in 1999 than recorded using comparable sampling methods in the 1960s and 1970s, despite lower numbers of individuals being recovered in 1999. Values of the Margalef diversity index could be calculated for both 1965–1972 and 1999 for four of the streams; the index was significantly greater in 1999 (P<0.001) in three streams, and unchanged in one stream (the most acid). The 1999 survey revealed the presence of acid-sensitive taxa that had been absent in the earlier surveys, notably the three stoneflies Leuctra fusca, L. moselyi and Chloroperla tripunctata. Some taxa that had been present during 1965–1972 were absent in 1999, but few of these were acid-sensitive. Diatoms from the surface sediments of six lakes were classified according to their acid sensitivities. In three of the lakes sampled in 1999 there were more diatoms characteristic of circumneutral waters, and less acidophilic species than had been found in 1983–1985. In the remaining three lakes, no noticeable changes had occurred. Overall, the observed biological changes are qualitatively as expected for the observed increases in pH, and there have been no instances of biological change in the opposite direction. The results support the expectation that changes in freshwater ecological status can be reversed by decreasing the remote emissions of acidifying pollutants.

A gravity model, frequently used to explain trade patterns, is used to explain stock market correlations. The main relult of the trade literature is that geography matters for goods markets. Physical location and traading costs should be less of an issue in asset markets. However we find that geographical variables still matter when examining equity market linkages. In particular, the number of overlapping opening hours and sharing a common border tends to increase cross-country stock market correlation. These relults may stem from asymmetrical information and investor sentiment, lending some empirical support for these elplanations of the international diversification puzzle.

1. The chief objectives were to analyse and model experimental data for maximum growth and food consumption of Atlantic salmon parr (Salmo salar) collected from a cold glacier fed river in western Norway. The growth and feeding models were also applied to groups of Atlantic salmon growing and feeding at rates below the maximum. The growth models were validated by comparing their predictions with observed growth in the river supplying the experimental fish. 2. Two different models were fitted, one originally developed for British salmon and the other based on a model for bacterial growth. Both gave estimates for optimum temperature for growth at 18–19 °C, somewhat higher than for Atlantic salmon from Britain. Higher optimal temperature for growth in salmon from a cold Norwegian river than from British rivers does not concur with predictions from the thermal adaptation hypothesis. 3. Model parameter estimates differed among growth groups in that the lower critical temperature for growth increased from fast to slow growing individuals. In contrast to findings for brown trout (Salmo trutta), the optimum temperature for growth did not decrease with decreasing levels of food consumption. 4. A new and simple model showed that food consumption (expressed in energy terms) peaked at 19.5–19.8 °C, which is similar to the optimal temperature for growth. Feeding began at a temperature 1.5 °C below the lower temperature for growth and ended about 1 °C above the maximum temperature for growth. Model parameter estimates for consumption differed among growth groups in a manner similar to the growth models. Maximum consumption was lower for Atlantic salmon than for brown trout, except at temperatures above 18 °C. 5. By combining the growth and food consumption models, growth efficiency was estimated and reached a maximum at about 14 °C for fast growing individuals, increasing to nearly 17 °C for slow growing ones, although it was lower overall for the latter group. Efficiency also de

1. The chief objectives were: (i) to compare two growth models, one based on weight and the other on energy, using the same data set for the analyses; (ii) to discover if weight and energy units can be simply interchanged for growth assessment. The data set was for 183 brown trout, Salmo trutta (live weight 1–300 g), fed to satiation on shrimps, Gammarus pulex, and grown individually over 42 days at constant temperatures (range 3.8–20.4 °C). 2. Rates of change in weight or energy content, and final weight or energy content at the end of 42 days growth, were estimated from the models and were excellent fits to the experimental data (P < 0.001). The shape of the temperature relationship for rates of change or final values was triangular for the weight model and curvilinear for the energetics model. Optimum temperatures for growth according to the weight and energetics models were 13.1 and 13.9 °C, respectively, for rates of change and 13.1 and 13.5 °C, respectively, for final values. When the growth period was extended to 100 and then 300 days, the triangular relationship and optimum temperature remained the same for the weight model, but the curvilinear relationship became more triangular for the energetics model and the optimum temperature identical to that in the weight model. The relationship between gross efficiency and temperature also differed in shape between the two models but maximum efficiencies occurred at a similar value of 9 ± 0.1 °C (18 and 32% for weight and energetics models). As fish weight increased, gross efficiency remained constant in terms of energy units, but decreased markedly in terms of weight. 3. These comparisons showed that different conclusions can be drawn from the two models, even if the same data set was analysed. There was a close relationship between initial wet weight and energy content for stock trout used in the experiments, but the relationship was not so close at the end of the experiments, and interchangeability of units could

Long-term changes in stream water chemistry in the upper Duddon catchment (southwest Lake District, UK) were investigated. Ten streams were sampled and analysed weekly during 1998, and the results compared with data for the early 1970s and 1986. The waters exhibited a range of pH, average values for 1998 being 5.04–7.04. For all the streams, the average pH in 1998 was greater than that during 1971–73. Statistical analysis was carried out, using the 1970s data to estimate the magnitude of inter-annual variation, and taking discharge into account on the basis of antecedent rainfall. The results showed that for two of the streams the pH increase was significant at the 2.5% level, while for a further three it was significant at the 10% level. Comparison of the 1998 concentrations of nitrate and non-marine sulphate with data obtained for five streams in 1973–74 showed that average nitrate concentration had increased from 11 to 20 μeq dm−3 while that of non-marine sulphate had decreased from 94 to 50 μeq dm−3. For four of the streams, comparisons were also made between the 1998 data and those for 1986. In three cases, pH in 1998 was generally higher, and Al generally lower, than the values for 1986, but in the fourth case little difference was evident. The present results support observations for five nearby standing waters, strengthening the evidence for a general reversal of acidification in the southwest part of Lake District, due to a decline in the deposition of pollutant sulphur.

1 The chief objectives were to determine the daily energy intake and growth of piscivorous brown trout (Salmo trutta), and to compare the observed values with those expected from models developed previously for brown trout feeding on freshwater invertebrates. Energy budgets for individual fish were obtained from experiments with 40 trout (initial live weight 250–318 g) bred from wild parents, and kept at five constant temperatures (5, 10, 13, 15, 18 °C) and 100% oxygen saturation. Each trout was fed to satiation on freshly killed sticklebacks (Gasterosteus aculeatus) over a period of 42 days. 2 Energy intake (CIN cal day-1) and growth (CG cal day-1) were measured directly and energy losses (CQ cal day-1) were estimated by difference (CQ = CIN - CG). All three variables increased with temperature. A model previously used to predict the daily energy intake (CIN(INV)) of trout feeding to satiation on invertebrates was adapted, by changing only one parameter, to provide an excellent model (R2 = 0.998) for predicting the mean daily energy intake (CIN(ST)) for the piscivorous trout. Values of CIN(ST) were 58% (range 48–67%) higher than those for CIN(INV). A simple model was also developed to estimate mean daily energy losses for piscivorous trout (R2 = 0.999). Both models were combined to provide excellent estimates of the daily energy gain (growth) of the piscivorous trout, and this was about three times that for trout feeding on invertebrates. The optimum temperature for maximum growth in energy terms increased from 13.9 °C for trout feeding on invertebrates to 17.0 °C (range 16.6–17.4 °C) for piscivorous trout. 3 The models are basically an extension of those developed for trout feeding on invertebrates. They show clearly how energy intake, growth, and the optimum temperature for growth increase markedly when trout change their diet from invertebrates to fish. The implications of this are discussed and it is shown that, in theory, these increases should continue if a m

The date of fry emergence over 30 years in a sea trout nursery stream, predicted by an individual-based model, correlated significantly (r=0·660, P<0·001) with an index of the North Atlantic Oscillation. Water temperature is the main driving variable in the model and stream temperature also correlated significantly (r=0·662, P<0·001) with the index, providing a probable causal link. Therefore, the inter-annual variations in emergence may not be unique to this one stream, but may be typical of other trout streams with similar climatic conditions.

1. The chief objectives were to determine the daily optimum energy intake (COPT cal day−1) for growth and the gross efficiency (KG%) for converting energy intake into growth for brown trout, Salmo trutta. Energy budgets for individual fish were obtained from experiments with 292 trout (initial live weight 1–318 g) bred from wild parents, and kept at five constant temperatures (5, 10, 13, 15, 18 °C) and 100% oxygen saturation. Most trout (252) were fed over a period of 42 days on a fixed ration of shrimps, Gammarus pulex, the ration levels varying between zero and maximum, but 40 of the larger trout were fed to satiation on freshly-killed sticklebacks (Gasterosteus aculeatus). 2. Energetics models developed in earlier studies on the same data were summarized briefly and were used to predict the relationship between the change in the total energy content of a trout (CG cal day−1) and its energy intake (CIN cal day−1), and hence to estimate COPT. The models were also used to predict the relationship between KG and CIN. In both comparisons, there was good agreement between observed values from the experiments and expected mean values predicted from the models. For trout feeding on invertebrates, COPT lay closer to the maximum, rather than the maintenance, energy intake. When the diet changed from invertebrates to fish, there was a marked increase in CIN, CG and KG. 3. For trout feeding on invertebrates, KG exceeded 30% within 7–11 °C, with a maximum KG of 31.8% at 8.9 °C. For piscivorous trout, KG exceeded 30% within 4–16 °C and 40% within 6.5–12 °C, with a maximum KG of 41.8% at 9.3 °C. These differences were discussed in relation to the results of previous workers, and the models used in the present study provided a method of exploring the limitations of the ‘K-line’ hypothesis for the relationship between KG and CIN.

1. The chief objective of the present study was to develop a functional model for the daily change in the total energy content of a brown trout, Salmo trutta , (equivalent to growth when positive) in relation to the difference between energy intake (energy content of food) and energy losses (metabolism + losses in faeces and excretory products). Energy budgets for individual fish were obtained in earlier experiments with 210 hatchery trout (live weight = 11–270 g) kept at fairly constant temperatures (mean values ranging from 3.6 to 20.4 °C), but without strict control of temperature or oxygen, and in later experiments, with 252 trout (1–300 g) bred from wild parents and kept at five constant temperatures (5, 10, 13, 15 and 18 °C) and 100% oxygen saturation. Each trout was fed a fixed ration of shrimps, Gammarus pulex, the ration level varying between zero and maximum. 2. Energy intake (CIN, cal day−−1) was measured directly and expressed as a proportion (p) of the maximum energy intake (C, cal day−−1), the latter being estimated from a model developed earlier. In a new model, energy losses (CQ, cal day−−1) were expressed as a function of temperature, fish weight and ration level. This model was continuous over the 3.6–20.4 °C range, had twelve fitted parameters and was an excellent fit to the data for the 462 trout (P < 0.001, R2 = 0.9970). In an extended model, the weight exponent for energy losses was not assumed equal to that for energy intake, the difference between the two exponents being very small, but significant, with a slight improvement in the fit of the model (R2 increased to 0.9972). 3. The limits of model use were discussed. An example of its utility was to elucidate the complex relationships between both positive (growth) and negative daily changes in the total energy content of the trout, and temperature, fish size and variable energy intake. The model has raised several questions for future work, including the effect of increasing energy intake by

Water chemistry data are reported for five high-altitude standing waters in the English Lake District, with current average pH values in the range 5–7. The waters show long-term increases in pH, ranging from 0.3 to 0.8 pH units, between 1974 and 1997. The pH of Devoke Water, which was acidified only mildly, has returned to values estimated for the pre-industrial period (1850 and earlier). Alkalinity in Devoke Water increased from ca 20 μeq litre−1 in the early 1980s to ca 70 μeq litre−1 in the 1990s, and alkalinities in three of the other waters have increased by ca 20 μeq litre−1 since the 1970s. For the two intensively monitored sites (Devoke Water and Levers Water), significant decreases in the concentration of non-marine sulphate are demonstrated, which have taken place concurrently with decreases in the atmospheric deposition of pollutant sulphur. Approximate calculations suggest that the catchment of Levers Water was a sink for sulphur in the 1970s, and that the catchment of Devoke Water may currently be a source of sulphate. For neither Devoke Water nor Levers Water is there evidence of a long-term decrease in the concentration of non-marine base cations.

1. A model developed over 20 years ago has been used to estimate daily food intake in brown trout living in streams and lakes over a wide geographical range. The chief disadvantages of this early model are that it is not continuous and requires twelve parameters, not all of which can be interpreted biologically. A new model, using a larger data set, was therefore developed to overcome these problems and estimate the mean daily energy intake. 2. The two data sets used to develop the original model were also used to develop the general form of the new one, but a third data set was used to specify the model more precisely and to estimate the parameters. This third data set originated from experiments in which 185 trout (live weight range 1–350 g) were kept individually at 19 constant temperatures (range 3.8–21.7 °C) usually for 5–6 weeks. They were fed freshly killed shrimps (Gammarus pulex) and their food consumption was recorded throughout each experiment. 3. Five, six and eight parameter versions of the new model were all excellent fits to the data (P < 0.001, R2 > 0.99), with the eight parameter version being slightly the best. All parameters can be interpreted in biological terms; three define threshold temperatures, three define the curvilinear slopes in the model over different temperature ranges, one is a weight exponent and one is the maximum daily energy intake of a 1 g trout. The simpler six parameter model was adequate at temperatures above 7 °C. 4. An additional experiment with twenty-eight trout feeding on six different invertebrate foods provided estimates of energy intake that were very similar to those predicted from the model. However, when daily intake was converted to dry weight, agreement with values from the model (also as dry weight) was poor. Possible reasons for this are discussed, as are other studies using the earlier model, and it is shown that different conclusions can be reached depending upon whether comparisons are based on units of ener

1. Unlike a neighbouring sea-trout population that showed strong density-dependent survival, a resident trout population (Salmo trutta L.) showed simple proportionate survival in the early life-stages. However, this persistent population fluctuated within narrow limits. Mature adults, especially during spawning, were the only possible life-stage left in which regulation might occur.2. An October census, just prior to spawning, was made at five sites (total area 300 m2) from 1965 to 1983. Gravel nests (redds) associated with females of known size were excavated outside these sites to obtain a power-function relationship between egg density per redd and female length (range 181–280 mm, n = 26). This relationship and the census data for females (range 186–284 mm) were used to estimate egg densities in each year-class.3. The census data for the early life-stages (0+, 1+, 2+ trout) confirmed proportionate survival with no evidence for density-dependent regulation. In contrast, the number of spawning females produced in each year-class was strongly density dependent on the initial number of females that laid eggs at the start of the year-class. Similarly, total egg production in each year-class was density dependent on initial egg density.4 Both relationships were well described by the Ricker and Beverton-Holt stock-recruitment models (P < 0.001) and the goodness-of-fit was similar for both models. This study is probably the first to provide clear evidence for fish population regulation in the adult, rather than the juvenile, stage.

The objective of this study was to predict interannual fluctuations in the emergence period of sea trout fry, using models developed from field data for 70 excavated redds, and laboratory data on egg and alevin development at 30 constant temperatures (range 1·5–10·5° C with 100 naturally fertilized eggs at each temperature). Egg weight and numbers per redd both increased with female length; a power function described the relationship. Early spawners were the largest females laying the largest and most numerous eggs, whilst late spawners were the smallest females laying the smallest and least numerous eggs; middle spawners being intermediate between these two extremes. Mean values for egg weight and numbers of eggs per redd were obtained for these three groups. Hatching and emergence times in the laboratory decreased with increasing temperature. Of five models tested for hatching time, the best fit was provided by a three-parameter hyperbolic model which formed the asis of the individual-based model used to predict egg hatching and fry emergence. Model development was described in detail and the final equations predicted the times taken for 5, 50 and 95% of the fry to emerge, and hence the period over which 90% of the fry emerged. Analogous models were obtained for egg hatching. All models were excellent fits to the laboratory data. Hatching times for eggs kept in perforated boxes in the stream were almost identical to those kept at similar mean temperatures in the laboratory. Model predictions of fry emergence times were validated by field data for 8 years (1967–1971, 1974, 1975, 1980). The chief objective was therefore fulfilled, and predictions for the 30-year study (1967–1996) revealed a large variation in the timing of emergence (extremes: 11 March–4 April 1989, 15–20 May 1979). Most of the variation in median emergence date was due to variations in water temperature, with spawning dates as a secondary factor; the latter, however, had a greater effect on the len

The objective was to predict interannual fluctuations in the size of sea-trout fry when they emerged from the redd, using models developed from field data for 70 excavated redds (≥three per year), and from experimental data on egg and alevin development at 30 constant temperatures in the laboratory (range 1·5—10·5) C with 100 naturally fertilized eggs at each temperature). Egg weight increased with female length and also with the number of eggs laid in a redd, both relationships being well described by a power function. Early spawners were the largest females laying the largest and most numerous eggs, whilst late spawners were the smallest females laying the smallest and least numerous eggs, with middle spawners being intermediate between these two extremes. Mean values for egg weight and number of eggs per redd were obtained for these three groups. The numbers of early, middle and late spawners for each year of a 30-year study and the mean values from the excavated redds were used to estimate weighted means for the number of eggs per unit area and egg weight. Mean values varied considerably between years (30-year ranges: 518–7964 eggs per 60 m2; 112–138 mg wet weight). In the laboratory, mean weights of newly hatched alevins and newly emerged fry were both related positively to mean egg weights. Alevin and fry mean weights were independent of the number of days required for 50% of the eggs to hatch or fry to emerge. Models described in a previous paper formed the basis of those used to predict fry weights over the emergence period. Model predictions were validated by field data for the whole emergence period in 8 years (1967–1971, 1974, 1975, 1980), and by pre-fry weights on single dates in 21 years (1967–1987). As pre-fry densities on these single dates were very similar to egg densities for the same year class, mortality in the egg and alevin stages was very low. The chief objective was therefore fulfilled, and the extent of interannual fluctuations for the 30-ye

Placing limits on the movement of economic fundamentals in order to maintain an exchange rate within a target zone also puts a target zone around interest rate differentials. The bandwidth of exchange rate and interest rate differentials target zones will be different except at one point; it is suggested that this point gives a useful partitioning of target zones into broad and narrow categories. For realistic parameter values, this occurs at an exchange rate target zone of plus or minus 3.2%.

A statistical method is described which identifies whether survival patterns of culturable microbes over time are significantly different when compared to natural within replicate microcosm variability. The method is likelihood based and assumes that counts of numbers of microbes are Poisson or Poisson-like distributed. An example is presented to illustrate the methodology.

1 The changes in abundance of Asterionella formosa in the South Basin of Windermere between 1946 and 1990 are described and analysed. The average seasonal cycle for the 45-year period shows an overwintering population of about 10 cell ml−1 which increases with an exponential rate of 0.09 loge day−1 to an annual maximum of 4000 cell ml−1 by about Day 124. There is then a rapid decline at an exponential rate of loss of 0.29 loge day−1 to values which typically are less than 0.01 cell ml−1 in mid-summer. By about Day 240 a second period of rapid increase occurs with an exponential rate of increase of 0.18 loge. day−1 to a plateau of about 7 cell ml−1 in late autumn and early winter. 2 This average pattern is subject to considerable year-to-year variation. The timing and extent of the increase in the autumn was particularly variable. The rate of increase in the spring was strongly positively correlated, and that in the autumn strongly negatively correlated, with the day at which the exponential phase started. Rates for these two phases of increase were not statistically different when expressed in terms of time from mid-summer, which reinforces earlier conclusions that light availability is the main factor governing the rate of spring increase and suggests that this is also the case for the autumn increase. 3 Eight descriptors of seasonal development showed statistically significant changes over the 45 years. Early winter populations declined from 27 to 4 cell ml−1, and linked to this the day at which cell concentrations exceeded 50 cell ml−1 occurred later by 24 days from Day 54 in 1946 to 78 in 1990. The lower early winter population appears to be linked to a lower end of year population as this decreased between 1946 and 1968 from 46 to 2 cell ml−1, and then increased slightly to 7 cell ml−1 in 1990. The start of the spring exponential increase occurred on Day 57 in 1946 and started earlier by 19 days in 1968 but then occurred later, at Day 76, in 1990. The duration

Post-stress plasma cortisol levels, following a standardized confinement stress, were monitored on a monthly basis for 5 months in 240 individually marked rainbow trout from each of two strains. At the end of this period individuals showing a consistent high or low response to stress were segregated. Post-stress plasma cortisol levels in selected high- and low-responding fish were similar for each strain (high 148.6 ± 3.2, 144.7 ± 2.4 ng ml−1; low 80.3 ± 2.3, 72.9 ± 2.7 ng ml−1). The difference in magnitude of response between the two selected groups was maintained for at least 28 months, post-stress plasma cortisol values in strain 1 at this point being, high responders 404.1 ± 28.2 ng ml−1, low responders 172.8 ± 20.0 ng ml−1. Despite this stability of response within the selected fish, analysis of the complete data set (480 fish ) failed to demonstrate unequivocally whether a stable response level to stress is characteristic of all individuals. The implications of these results are discussed with reference to the potential benefits of producing strains of fish with a reduced sensitivity or responsiveness to common forms of aquacultural stress.

Model V describes the binding of ions by humic substances in terms of complexation at discrete sites, modified by electrostatic attraction and/or repulsion, and also takes account of nonspecific binding due to counterion accumulation. The model operates over wide ranges of pH (3–11) and ionic strength (0.001-1 M). Electrostatic effects on specific binding are described with an empirical relationship involving net humic charge and an electrostatic interaction factor. Accumulation of counterions is described by Donnan-type expressions. The model assumes the presence of eight proton-dissociating groups in the humic material, distinguished by intrinsic pK values. In general, the description of proton dissociation requires seven parameters, but for fulvic-type material only six are needed. The proton-dissociating groups may interact individually with other ions, or pairs of them may form bidentate sites. Binding at the monodentate and bidentate sites is characterized by intrinsic equilibrium constants for cation-proton exchange; there are two such constants (pKMHA and pKMHB) for each cation. Model parameters are derived from published data for fulvic-type material on proton dissociation (eight data sets) and metal binding (twenty-six data sets, eleven metals). In the case of proton dissociation, the greatest variability among samples is in site densities, while intrinsic dissociation constants and electrostatic interaction factors are relatively consistent. With parameters for proton dissociation fixed, adjustments of pKMHA and pKMHB permit reasonable fitting of metal binding data, including pH dependence. There are insufficient available data to evaluate properly ionic strength and competition effects on metal binding, but correct trends are reproduced by the model. Values of pKMHA for metals indicate that binding strength increases in the order Mg2+ < Ca2+ < Mn2+ < Cd2+ < Co2+ < Ni2+ ~ Zn2+ < Pb2+ < Cu2+ < VO2+. The strong correlation between pKMHA and the analogous co

Monitored sequences of bedload transport events in two small gravel-bedded trout streams are described. To model the event timings, the inhomogeneous gamma process, with the special case of the Poisson process, are introduced, in which the baseline intensity is related to a linear regression combination of covariates. These may be time-varying covariates, such as seasonal cycles, covariates specific to an individual process or covariates common to more than one process. It is shown that the maximum likelihood estimates of the regression parameters may be obtained by an iterative least-squares procedure. The procedure is demonstrated by application to the bedload transport event sequences.

A discrete-site model of ion-binding by humic substances (HS), incorporating a description of electrostatic effects, is evaluated with analytical data for surface waters of acid pH (3.5–6.5). After optimization of the model by adjustment of the binding-site content of the HS, the root-mean-square deviation (RMSD) between measured and calculated concentrations of organically-complexed monomeric aluminium—[Alm-org]—is 1 μM for a range of measured values of 0.1–9.0 μM (108 samples from 12 different locations). The optimization indicates that the dissolved organic matter of natural waters is only about 50% as ‘active’ (in the sense of ion-binding) as isolated HS. The model, optimized for Al-binding, also accounts for the contribution of HS to ionic balance; for 139 samples (from 8 locations) with dissolved organic carbon concentrations in the range 4.6–43.0 mg 1−1, and using measured pH as input for the computations, the mean calculated ratio of cations to anions was 1.03, with a standard deviation of 0.11. A similar result was obtained with an optimized version of the model of B. G. Oliver, E. M. Thurman and R. L. Malcolm (Geochim. cosmochim. Acta47, 2031–2035, 1983). For the same 139 samples, pH values were also calculated, using total measured anion concentration as inputs. The RMSD in pH was 0.35 for all samples, but only 0.18 for the 56 samples of pH ⩽ 4.5. Statistical analyses indicate that inadequacies in model assumptions, including the estimation of concentrations of HS in water samples, account for about one-third of the discrepancy between measured and calculated [Alm-org]; the remaining two-thirds is explained by errors in input data and measured [Alm-org]. In the case of pH prediction, no model inadequacy is apparent, because of the high sensitivity of the calculations to errors in input data.

Four experimental stream channels were used to study instantaneous downstream dispersal rates of young trout, Salmo trutta L., and salmon, S. salur L., relative to four different water velocities. Young salmon showed a high rate of dispersal at a low velocity of 7.5 cm s−1 and lower rates at higher velocities of 25 to 70cm s−1. Trout showed their lowest rate at 25cm s−1 with a slightly higher rate at 7.5 cm s−1 and increasingly higher rates at velocities in excess of 25 cm s−1. These results are consistent with field observations on the velocity preferences of young trout and salmon.

SUMMARY. 1, Windermere is a glacial valley lake with two basins separated by shallows and a total area of 14.8 km2. Perch, pike and charr are the dominant fish species and have been studied on a continuous basis for over 45 years. 2. The initial slow-growing stocks of numerous small perch and moderate numbers of large pike were subjected to a heavy initial fishing pressure that was subsequently relaxed for perch but not for larger (>550 mm) pike. The number of charr in the lake has increased 6–8-fold during the study, probably due to the sustained reduction in the abundance of the larger pike that heavily predate the autumn spawning race of charr when it enters the shallow littoral areas to spawn. 3. The biomass of perch did not recover from the initial fishery until the late 1950s when strong year-classes occurred in warm summers. However, it was now composed of larger and faster growing individuals. In 1976, disease killed over 98% of all adult perch in the lake and the subsequent recovery has again been slow. 4. Existing models have explained the variation in perch year-class strength for the years 1959–74 in terms of adult perch biomass, pike cohort strength and temperature in the year of hatch. A new. more generally applicable model, incorporating a stock-recruitment expression, gives a better fit to the earlier data, particularly from the North Basin, where there have been periods of extremely low adult biomass. 5. The importance of continuing to extend these long-term data sets and the scope for future modelling work are discussed.