Presentation and analysis of a model simulating epilimnetic and hypolimnetic temperatures in lakes

An important factor in aquatic modelling is water temperature. This is especially true for dimictic lakes where stratification and mixing influence many processes and variables, such as oxygen conditions, lake water retention time, etc. This paper evaluates and improves an existing method to predict water temperatures developed by Håkanson ,1996 (Ecol. Model., 88:157–181). The method is incorporated in a model simulating water temperatures in epilimnion and hypolimnion. The model is calibrated and validated against an extensive set of empirical data. It is driven by readily available parameters, e.g. latitude, continentality and altitude. The predictive power, especially for the epilimnetic temperature, is such that the model could be used as a sub-model in many models concerning lake ecosystems. However, the model has only been tested for Swedish lakes covering a relatively narrow range in terms of latitude, longitude and altitude and it would be interesting to investigate if this approach also holds for other parts of the world. As an example of how the model can be used in practise, a simulation of retention of caesium in lake water, using the temperature model as a sub-model, is presented.     

A practical approach to predict the duration of the growing season for European lakes

This work presents the first practically useful models to estimate the duration of the growing season (GS in days) for European lakes. GS is a fundamental parameter in limnology, where it is used, e.g., to calculate lake characteristic annual primary production (in g ww/m²·yr) from measurement data in g C/l·day. We have presented two simple empirical regression equations where GS is estimated from latitude. We have also introduced a more comprehensive model. It is derived from a previously presented well calibrated and validated model predicting lake epilimnetic temperatures from readily available data on latitude, altitude, continentality (distance from the Sea) and lake volume. Operationally, the duration of the growing season (GS in days) is defined from the predicted number of days when epilimentic water temperatures are higher than 9°C. The two modelling approaches are based on different presuppositions and they have been derived and tested from different data-sets. A model comparison has shown that the overall correspondence in predicted GS-values between the methods is very good. Evidently, the more comprehensive model can provide more relevant GS-predictions for many lakes since it also accounts for differences among lakes in altitude, continentality and volume.     

An atmospheric—terrestrial heavy metal transport model. I. model theory

A general model TOHM was developed to predict the terrestrial fate of zinc, cadmium, chromium, lead and mercury emitted by the operation of a coal-fired electric generating facility. The general model consisted of interfacing submodels describing atmospheric dispersion, precipitation, soil chemistry, and soil erosion. The models were developed from input data from a semi-arid region of the southwest United States, and except for the climatic and topographic constraints, are not site specific. TOHM was found to predict no substantial increase in indigenous levels of zinc, chromium and lead in the impact (deposition) area. However, both mercury and cadmium were predicted to be emitted and eroded to the environmental sink (receiving lake) in concentrations exceeding that naturally present in the system. TOHM is currently unvalidated, though comparison of soil erosion predictions with erosion quantities measured in the impact area gives good agreement.     

A three-layer aquatic ecosystem model: sediment submodel tests and some simulations

Some recent simulations using a model given in a previous paper are presented. The model includes the phosphorus, algae and zooplankton levels in each of three layers of a lake: i.e., in the epilimnion, in the hypolimnion, and in sediment. Special emphasis is laid on testing the sediment submodel. Comparison with laboratory exoperiments conducted by Tessenow gives good agreement. The effects of some parameter variations are discussed.     

Habitat specialization and the exploitation of allochthonous carbon by zooplankton

The significance of spatial subsidies depends on consumer resource interactions in the recipient habitat. Lakes are subsidized by terrestrial carbon sources, but the pathways of allochthonous carbon through lake food webs are complex and not well understood. Zooplankton vertically partition resources within stratified lakes in response to life history trade-offs that are governed by predators, the quantity and quality of food, and abiotic conditions (e.g., UV, temperature, and viscosity). We measured habitat specialization of zooplankton in an oligotrophic lake where allochthonous and autochthonous resources varied with depth. During stratification, the quantity and quality of zooplankton food was highest in the hypolimnion. We used a yearlong time series of the delta13C of zooplankton and particulate organic matter (POM) to determine which zooplankton species exploited hypolimnetic rather than epilimnetic resources. Because the delta13C of POM decreased with depth, we used the delta13C of zooplankton to detect inter- and intraspecific variation in habitat selection. We incubated Daphnia pulex at discrete depths in the water column to confirm that the delta13C of zooplankton can indicate habitat specialization. Zooplankton that specialized in the epilimnion relied more on allochthonous carbon sources than those that specialized in the hypolimnion. Therefore, the fate of allochthonous carbon subsidies to lakes depends on spatially explicit consumer-resource interactions.     

A model of phosphorus cycling in the epilimnion of oligotrophic and mesotrophic lakes

A dynamic size-based model describing phosphorus (P) cycling in the epilimnion of lakes is established and validated against published data, and some influences of epilimnetic community structure and function on phosphorus cycling are investigated. We used literature values where possible and calibration otherwise to obtain parameter values. The simulation results show good agreement with empirical and experimental data. The model-derived turnover times of nanoplankton and mesoplankton exhibited a positive relationship with total phosphorus (TP), but the turnover times of larger size-functional groups did not. Nanoplankton and picoplankton became similar in their turnover times with increasing TP. Addition of fish altered the size of particulate P pools and turnover rates, decreased phosphate turnover times and decreased phosphorus sedimentation rates as expected from empirical studies. The model predictions appear to be robust and reasonably successful in reproducing the known behaviour of the P-cycle in the epilimnia of oligotrophic and mesotrophic lakes.     

A model of mercury contamination in a woodland stream

A model for the accumulation of mercury in four compartments of woodland stream has been set up. The four components considered are sediments, detritus, invertebrates and fish. The model inputs are concentrations of dissolved monomethyl mercury and dissolved inorganic mercury (Hg²⁺) in the water. The model predicts that some reevaluation of current safe mercury concentrations in water may be needed in order to keep mercury concentrations in fish below current actions levels.     

Population differences in predation on Batesian mimics in allopatry with their model: selection against mimics is strongest when they are common

Batesian mimicry evolves when a palatable species, the “mimic,” resembles a dangerous species, the “model,” because both receive protection from predation. Yet, this protection should break down where the model is absent, because predators in such areas would not be under selection to avoid the model. Here, we test this prediction in a coral snake mimicry complex. We exposed plasticine replicas of milk snakes that closely mimic coral snakes to natural predators to determine if good mimetic milk snakes are preferentially attacked in allopatry with their model. Moreover, we evaluated whether attack rates on these replicas varied among three different allopatric regions that differed in the type of mimic found locally (i.e., good mimic, poor mimic, or no mimic). When all three regions were considered together, mimics were not preferentially attacked. When regions were analyzed separately, however, attacks on mimics were significantly greater than randomness only where good mimics were found. These variable levels of predation on good mimics might reflect frequency-dependent (i.e., apostatic) predation. In allopatric regions where good mimics are present, predators might have learned or evolved preferences for conspicuous, palatable prey that they encounter frequently. By contrast, in allopatric regions where good mimics are absent, predators might not have learned or evolved preferences for novel phenotypes. Thus, when predation is frequency-dependent, as long as good mimics are rare, they might not experience elevated levels of predation in allopatry with their model as predicted by the Batesian mimicry hypothesis.     

Large scale parameter study of an individual-based model of clonal plant with volunteer computing

Understanding clonal strategies (i.e. the ability of plants to reproduce vegetatively) is particularly important to explain species persistence. A clonal individual may be considered as a network of interconnected ramets that colonizes space. Resources in this network can be shared and/or stored. We developed an individual-based model (IBM) to simulate the growth of an individual clonal plant. Typically a realistic IBM requires a large set of parameters to adequately represent the complexity of the clonal plant growth. Simulations in the literature are often limited to small subsets of the parameter space and are guided by the a priori knowledge and with heuristic aims of the researcher. The aim of this paper was to demonstrate the benefit of volunteer computing in computational ecology to systematically browse the parameter space and analyze the simulation results in order to draw rigorous conclusions. To be specific, we simulated clonal plant growth using nine growth rules related to the metabolic process, plant architecture, resource sharing and storage and nineteen input parameters. We chose 2-4 values per input parameter which corresponded to 20 millions of combinations tested through volunteer computing. We used three criteria to evaluate plant performance: plant total resource, ramet production and maximum length of one branch. The 1% top-performing plants were sorted according to these criteria. Plant total resource and ramet production were correlated while considering the top-performing plants. The maximum length of one branch was independent from the other two performance traits. We detected two processes promoting at least one of the plant performance traits: (i) a relatively high metabolic gain (high photosynthetic activity and low production cost for new growth units), a low resource storage and long integration distance for resource sharing; (ii) short spacer lengths and the predominance of elongation of existing branches over branching. Interactive effects between parameter values were demonstrated for more than half of the input parameters. Best performance was reached for plants with slightly different combinations of values for these parameters (i.e. different strategies) rather than a single one (i.e. unique strategy). This modeling approach with volunteer computing enabled us to proceed to large-scale virtual experiments which provided a new quality of insight into ecological processes linked with clonal plant growth.     

Inorganic and methyl-mercury speciation in sediments of the Swarzędzkie Lake

Sediment samples were analysed for mercury and methylmercury content in different parts of the bottom sediment of Swarz ?dzkie Lake, which were influenced by different external pollution sources. The results of determination with two methods of mineralization using two separate media (HNO₃/H₂O₂ and HF) were compared. The accuracy of the studied methods was analysed using certified reference material IAEA 405 of river sediment. The recovery of mercury was satisfactory and ranged from 97.5 to 98.8%. Methylmercury compounds in the studied sediments were found in limited concentrations. Their concentrations ranged from 0.26 to 58.1 μg kg^?1, i.e. 1.0–7.4% of the total mercury content. The depth profile displayed high values of both total and methylmercury content at a depth of 10–20 cm, related to the heavy pollution of the lake in the 1980s. Canonical analysis displayed the relationship of both total mercury and methylmercury concentrations with organic matter and phosphorus content in bottom sediments.     

Data assimilation in a simple marine ecosystem model based on spatial biological parameterizations

Assuming that a set of constant parameters fits for marine ecosystem modeling and parameter estimation studies on large space scales is questionable since ecosystem types spanning long distances are quite different. In this study, SeaWiFS chlorophyll-a data are assimilated into a simple NPZD model by the adjoint method in a climatological physical environment provided by FOAM. To improve the assimilation results, different spatial parameterization schemes are utilized. The results show that the values of the selected sensitive parameters are spatially variable and the application of spatial parameterizations can improve the assimilation results significantly.     

Using a model selection criterion to identify appropriate complexity in aquatic biogeochemical models

Aquatic biogeochemical models are widely used as tools for understanding aquatic ecosystems and predicting their response to various stimuli (e.g., nutrient loading, toxic substances, climate change). Due to the complexity of these systems, such models are often elaborate and include a large number of estimated parameters. However, correspondingly large data sets are rarely available for calibration purposes, leading to models that may be overfit and possess reduced predictive capabilities. We apply, for the first time, information-theoretic model-selection techniques to a set of spatially explicit (1D) algal dynamics models of varying parameter dimension. We demonstrate that increases in complexity tend to produce a better model fit to calibration data, but beyond a certain degree of complexity the benefits of adding parameters are diminished (the risk of overfitting becomes greater). The particular approach taken here is computationally expensive, but several suggestions are made as to how multimodel methods may practically be extended to more sophisticated models.     

Geostatistical model averaging based on conditional information criteria

Variable selection in geostatistical regression is an important problem, but has not been well studied in the literature. In this paper, we focus on spatial prediction and consider a class of conditional information criteria indexed by a penalty parameter. Instead of applying a fixed criterion, which leads to an unstable predictor in the sense that it is discontinuous with respect to the response variables due to that a small change in the response may cause a different model to be selected, we further stabilize the predictor by local model averaging, resulting in a predictor that is not only continuous but also differentiable even after plugging-in estimated model parameters. Then Stein’s unbiased risk estimate is applied to select the penalty parameter, leading to a data-dependent penalty that is adaptive to the underlying model. Some numerical experiments show superiority of the proposed model averaging method over some commonly used variable selection methods. In addition, the proposed method is applied to a mercury data set for lakes in Maine.     

Inorganic mercury pharmacokinetics in man: a two-compartment model

Excreta data obtained from five human subjects and previously analyzed as part of a multicompartment model (Hall, L.L., P.V. Allen, H.L. Fisher, and B. Most. 1995. The kinetics of intravenously administered inorganic mercury in humans. In Kinetic models of trace element and mineral metabolism, ed. K.N.S. Subramanian and M.E. Wastney, 1-21. Boca Raton: CRC Press) were reanalyzed by means of a two-compartment model. The mobile compartment represents mercury of any form that is available for transport throughout the body. The immobile compartment represents mercury in forms that are not available for transport. The model simulates time profiles for body inorganic mercury and for fecal and urinary excretion. According to the model, intravenously administered mercury enters the body in the mobile form. Following administration, two distinct kinetic profiles were observed. In four of five subjects, mobile mercury in the body declined rapidly and the immobile form became dominant within 6 days. In these subjects, fecal excretion profiles were characterized by an initial phase dominated by excretion of mobile mercury lasting up to 6 days. This was followed by a slower phase during which mobile and immobile mercury were excreted in varying amounts. A similar pattern was seen in urinary profiles, but the initial phase is shorter and less pronounced. In each of these subjects, immobile mercury accounted for 84–94% of the total cumulative urinary excretion. The fifth subject showed a unique kinetic profile. Conversion of mobile to immobile mercury was slow and the two forms did not reach equivalence until approximately 70 days after dosing. Despite this fact, approximately 99% of fecally excreted mercury and 100% of urinary mercury originated in the immobile compartment. Possible explanations for the different profiles are discussed within the context of the model.     

Whole-lake dissolved inorganic 13C additions reveal seasonal shifts in zooplankton diet

Sustained whole-lake additions of 13C-enriched dissolved inorganic carbon (DIC), intended to increase experimentally the delta13C of DIC in the epilimnion of a small lake with high dissolved organic carbon (DOC), were made during three seasonal periods (spring, summer, and autumn). Coupled with carbon and nitrogen stable isotope analysis of zooplankton and several of their putative food sources, these additions were used to investigate seasonal changes in the relative contributions of different food sources to zooplankton diet in the lake. Four main potential food sources were considered: phytoplankton, heterotrophic bacteria (HB), methanotrophic bacteria (MOB), and green sulfur bacteria (GSB). Because the number of potential food sources exceeded the number of isotopes analyzed, a computer program (IsoSource) was used to estimate the range of possible contributions of the various food sources. During all three periods the added inorganic 13C quickly increased the epilimnetic DIC delta13C by between 18 per thousand and 21 per thousand above the initial value of approximately -21 per thousand. This 13C enrichment of DIC was rapidly transmitted to the particulate organic matter (POM), which included photosynthetic phytoplankton. In spring and summer, delta13C of both adult and juvenile Daphnia increased by approximately 10 per thousand, indicating that Daphnia utilized autochthonous carbon. However, this 13C labeling of Daphnia was not so obvious during the autumn period, when their delta13C generally decreased. According to the IsoSource model outputs based on both delta13C and delta15N values, Daphnia utilized all four potential food source types during spring, summer, and autumn, but in different proportions. The possible contribution of phytoplankton to Daphnia diet was substantial (25-71%) in all seasons. The possible contributions of the bacterial food sources were more variable. The possible contribution of GSB was minor (0-20%) at all times and negligible in autumn. The possible contribution of HB was higher but very variable. Methanotrophic bacteria always made a significant contribution to Daphnia diet and were likely the single most important food source in autumn. Since both HB and MOB in this high-DOC lake probably depend largely on allochthonous organic carbon, our results highlight the seasonal variability in the potential importance of ecosystem subsidies in lake food webs.     

Using a 1-D mixing model to simulate the vertical flux of heat and oxygen in a lake subject to episodic mixing

A one-dimensional, two-layer lake model is used to simulate the daily temperature and oxygen profile of an English Lake in response to changes in wind, air temperature and radiation. The thermal model component derives from the TEMIX lake model originally developed by the Institute of Limnology in St. Petersburg [Mironov, D.V., Golosov, S.D., Zilitinkevitch, S.S., Kreiman, K.D., Terzhevik, A.Y., 1991. Seasonal changes of temperature and mixing conditions in a lake. In: Zilitinkevitch, S.S. (Ed.), Modelling Air–Lake Interactions. Springer-Verlag, pp. 74–90]. This paper describes the model's adaptation and its extension to incorporate dissolved oxygen to simulate periods of anoxia of short duration during summer stratification. The new oxygen model component, which is based on mass-balance principles, divides the lake into two layers in a similar way to the thermal model. Its primary purpose is to model periods of anoxia for use in studies of fish survival. The model has been tested over a 10-year period from 1991 to 1999 using daily weather data and fortnightly observations of chlorophyll a and secchi depth. Ten years of fortnightly oxygen measurements, together with 2 years of more detailed (hourly) oxygen data, indicate that simulated and observed oxygen levels are in reasonable agreement considering the sparseness of the chlorophyll observations. The balance between the relative effects of temperature and BOD on oxygen depletion is of particular importance to model accuracy.     

Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

● A hydrodynamic-Bayesian inference model was developed for water pollution tracking. ● Model is not stuck in local optimal solutions for high-dimensional problem. ● Model can estimate source parameters accurately with known river water levels. ● Both sudden spill incident and normal sewage inputs into the river can be tracked. ● Model is superior to the traditional approaches based on the test cases. Water quality restoration in rivers requires identification of the locations and discharges of pollution sources, and a reliable mathematical model to accomplish this identification is essential. In this paper, an innovative framework is presented to inversely estimate pollution sources for both accident preparedness and normal management of the allowable pollutant discharge. The proposed model integrates the concepts of the hydrodynamic diffusion wave equation and an improved Bayesian-Markov chain Monte Carlo method (MCMC). The methodological framework is tested using a designed case of a sudden wastewater spill incident (i.e., source location, flow rate, and starting and ending times of the discharge) and a real case of multiple sewage inputs into a river (i.e., locations and daily flows of sewage sources). The proposed modeling based on the improved Bayesian-MCMC method can effectively solve high-dimensional search and optimization problems according to known river water levels at pre-set monitoring sites. It can adequately provide accurate source estimation parameters using only one simulation through exploration of the full parameter space. In comparison, the inverse models based on the popular random walk Metropolis (RWM) algorithm and microbial genetic algorithm (MGA) do not produce reliable estimates for the two scenarios even after multiple simulation runs, and they fall into locally optimal solutions. Since much more water level data are available than water quality data, the proposed approach also provides a cost-effective solution for identifying pollution sources in rivers with the support of high-frequency water level data, especially for rivers receiving significant sewage discharges.     

Does the metal content in soil around a pregnant woman’s home increase the risk of low birth weight for her infant?

Low birth weight (LBW) is associated with a number of maternal environmental exposures during pregnancy. This study explored the association between soil metal concentrations around the home where the mother lived during pregnancy and the outcome of LBW. We used a retrospective cohort of 9,920 mother–child pairs who were insured by Medicaid during pregnancy and lived in ten residential areas, where we conducted soil sampling. We used a grid that overlaid the residential areas and collected soil samples at the grid intersections. The soil was analyzed for the concentration of eight metals [arsenic (As), barium (Ba), chromium (Cr), copper (Cu), lead (Pb), manganese (Mn), nickel (Ni), and mercury (Hg)], and we then used Bayesian Kriging to estimate the concentration at the actual maternal addresses, since we had the GIS coordinates of the homes. We used generalized additive modeling, because the metal concentrations had nonlinear associations with LBW, to develop the best fitting multivariable model for estimating the risk of LBW. The final model showed significant associations for female infants, maternal smoking during pregnancy, non-white mothers, Cu, and As with LBW. The As variable was nonlinear in relation to LBW, and the association between higher concentrations of As with LBW was strong (p = 0.002). We identified a statistically significant association between soil concentrations of arsenic around the home of pregnant women and an increased risk of LBW for her infant.     

Using a mathematical model to test the null hypothesis of optimal shell construction by four marine gastropods

A previous analysis (Heath 1985; Biol J Linn Soc 24: 165–174) tested and rejected the null hypothesis that gastropods construct their shells with optimal efficiency. The ratio volume of material used to volume of space enclosed (V _shell:V _space) was used as a measure of inefficiency of construction and shown to exhibit smooth parabolic curves if plotted as a function of whorl overlap. In the present analysis, in contrast, it is demonstrated that inefficiency of a particular combination of mode and rate of shell construction, consisting of variable interapertural areas and rapidly expanding whorl cross sections, is described by polynomial curves with inflection points. As an empirical test of this theoretically derived observation, V _shell:V _space of shells of four species of marine gastropods [Architectonica perspectiva (L., 1758), Cittarium pica (L., 1758), Euspira heros (Say, 1822), and Telescopium telescopium (L., 1758)] was calculated, using a mathematical model. By varying the vertical component of aperture trajectories [i.e. translation (T )] in the mathematical model, hypothetical forms representing a range of possible whorl overlap were simulated graphically and, for each form, V _shell:V _space was calculated. Plots of V _shell:V _space as a function of whorl overlap were described accurately by polynomial curves with inflection points, and each real shell yielded a nonoptimal V _shell:V _space, exhibiting approximately 75% less whorl overlap than its most efficiently constructed, hypothetical form. Inflection points of inefficiency curves represent critical points at which the reduction of space provided begins to exceed significantly the amount of material saved with increasing whorl overlap, and nonoptimal shell forms might represent compromises between efficient construction and function. Received: 26 June 1998 / Accepted: 17 March 1999