A stochastic computer model for simulating population growth

A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model's behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka's Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values or r_m and K. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetle Tribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

ON THE MECHANISM OF ADAPTATION TO PROTEIN SYNTHESIS INHIBITORS BY TETRAHYMENA : Facilitation, Cross Adaptation, and Resensitization

Tetrahymena is able to adapt to the presence of sublethal concentrations of many drugs which inhibit a wide variety of cellular functions. In spite of the generality of this phenomenon in Tetrahymena, the mechanism of adaptation at the cellular and molecular levels is unknown. This study deals mainly with adaptation to the protein synthesis inhibitors, cycloheximide and emetine. The physiological response of Tetrahymena to sublethal concentrations of these drugs is an immediate cessation of cell division for a period of time dependent on the drug concentration, followed by an abrupt resumption of exponential growth at a constant rate. By measuring the length of the growth lags under a variety of experimental conditions, we have confirmed several observations made by Frankel and coworkers, and provide evidence for two new phenomena associated with adaptation to cycloheximide: (a) adaptation to cycloheximide also results in adaptation of cells to emetine, another protein synthesis inhibitor not closely related structurally to cycloheximide. We have termed this phenomenon cross adaptation, (b) exposure to concentrations of cycloheximide too low to cause any growth lags or inhibition of protein synthesis significantly shortens the time required by cells to adapt to higher concentrations of cycloheximide. We have termed this phenomenon facilitation. Facilitation shows some degree of specificity in that facilitation with cycloheximide has no effect on adaptation to emetine. From this, we infer the existence of two distinct systems involved in adaptation to cycloheximide, one of which shows a higher degree of specificity towards cycloheximide than the other. We also show that transfer of adapted or facilitated cells to drug-free medium results in a gradual but complete resensitization. The kinetics of resensitization suggest that the cellular machinery responsible for adaptation and facilitation does not leave the cell, but is simply diluted out during cell division.     

Effect of competition on the demography of planktonic cladocerans — Daphnia and Diaphanosoma

Summary Isolated and mixed continuous cultures of Daphnia hyalina and Diaphanosoma brachyurum in lake water were maintained under laboratory conditions to elucidate demographic effects of competition. Population dynamics curves were obtained. Interspecific competition was revealed by the decrease in the average density of animals in the mixed versus isolated cultures and by the extinction of one species in the presence of the other. Within the first 50 days either Diaphanosoma (4 cases) or Daphnia (1 case) was the superior competitor, depending on the initial conditions. Further cultivation resulted in the extinction of Diaphanosoma in the mixed cultures. There were no statistically significant differences between the maximum rates of population increase (r _m ) in Daphnia and Diaphanosoma at the concentration of edible algae about 2·10⁵ m³ml^-1(0.293 and 0.286 days^-1, respectively). Time lags for density-dependent parameters of the populations were evaluated by means of rank cross-correlations. Regardless of the species identity the time lags of fecundity, birth rate, and the rate of population growth were significantly higher in the superior competitor. The initial conditions of culturing affected the time lags which in their turn influenced the outcome of the interaction. Enhanced competitive ability due to the maximized time lags in Daphnia was not associated with the loss of population stability. Conversely, it brought about destabilization of Diaphanosoma populations which seemed to be the ultimate cause of its extinction observed in the end of the experiment. Time lag of the population growth rate was well predicted based on the half-sum of time lags in birth and death rates (r²=0.80, P<0.001). Daphnia responded to competition with a sharp shortening of the time lags of fecundity, birth rate, and the population growth rate. It increased clutch size and showed inverse relationship between the fecundity time lag and average fecundity even though it was strongly suppressed by Diaphanosoma. The competitive ability was not related to the percentage of adults in the populations. In contrast to the current belief the major result of interspecific competition in the experiment was not a decrease in the rate of population growth but was a reduction in population time lags.     

DEBtox theory and matrix population models as helpful tools in understanding the interaction between toxic cyanobacteria and zooplankton

Bioassays were performed to find out how field samples of the toxic cyanobacteria Microcystis aeruginosa affect Moina micrura, a cladoceran found in the tropical Jacarepagua Lagoon (Rio de Janeiro, Brazil). The DEBtox (Dynamic Energy Budget theory applied to toxicity data) approach has been proposed for use in analysing chronic toxicity tests as an alternative to calculating the usual safety parameters (NOEC, ECx). DEBtox theory deals with the energy balance between physiological processes (assimilation, maintenance, growth and reproduction), and it can be used to investigate and compare various hypotheses concerning the mechanism of action of a toxicant. Even though the DEBtox framework was designed for standard toxicity bioassays carried out with standard species (fish, daphnids), we applied the growth and reproduction models to M. micrura, by adapting the data available using a weight-length allometric relationship. Our modelling approach appeared to be very relevant at the individual level, and confirmed previous conclusions about the toxic mechanism. In our study we also wanted to assess the toxic effects at the population level, which is a more relevant endpoint in risk assessment. We therefore incorporated both lethal and sublethal toxic effects in a matrix population model used to calculate the finite rate of population change as a continuous function of the exposure concentration. Alongside this calculation, we constructed a confidence band to predict the critical exposure concentration for population health. Finally, we discuss our findings with regard to the prospects for further refining the analysis of ecotoxicological data.     

Model simulations of continuous rotifer cultures

Derived from the Monod-model and regulating principles a regulation model of the rotifer development in chemostats was developed. The model was validated in continuous cultures of Brachionus angularis both in steady-states, when undisturbed, and in transient-states after perturbations by step changes of dilution rate or input substrate concentration. Simulations of the simple model monotonically approached steady-states, but cultures show overshoots and damped oscillations before reaching this state. After introducing time-lags into the model it depends on the size of the time lag if model rotifer densities reach stable steady-state values (at low time lags) or stable limit cycles with periodic oscillations (at high time lags). At even higher time lags chaotic conditions occur in the model with final extinction of the rotifers.     

Application of micro-segmented flow for two-dimensional characterization of the combinatorial effect of zinc and copper ions on metal-tolerant Streptomyces strains

The cultivation and growth behavior of metal-tolerant strains of Streptomyce acidiscabies E13 and Streptomyces sp. F4 were studied under droplet-based microfluidics conditions. It was shown that the technique of micro segmented flow is well suited for the investigation of dependence of bacterial growth on different concentrations of either single metal ions or combinations of them. This study confirms higher tolerance to Zn than to Cu by our test organism. The highly resolved dose–response curves reflect two transitions between the different growth behaviors, separating initial responses to Cu concentration ranges into those with (a) intense growth, (b) moderate growth, and (c) growth inhibition. For Streptomyces sp. F4, an initial stimulation was shown in the sublethal range of zinc sulfate. Two-dimensional screenings using computer-controlled fluid actuation and in situ micro flow-through fluorimetry reflected a strong growth stimulation of strain F4 by zinc sulfate in the presence of sublethal Cu concentrations. This stimulatory effect on binary mixtures may be useful in providing optimal growth conditions in bioremediation procedures.     

Population growth lags in introduced species

When introduced to new ecosystems, species'' populations often grow immediately postrelease. Some introduced species, however, maintain a low population size for years or decades before sudden, rapid population growth is observed. Because exponential population growth always starts slowly, it can be difficult to distinguish species experiencing the early phases of slow exponential population growth (inherent lags) from those with actively delayed growth rates (prolonged lags). Introduced ungulates provide an excellent system in which to examine lags, because some introduced ungulate populations have demonstrated rapid population growth immediately postintroduction, while others have not. Using studies from the literature, we investigated which exotic ungulate species and populations (n = 36) showed prolonged population growth lags by comparing the doubling time of real ungulate populations to those predicted from exponential growth models for theoretical populations. Having identified the specific populations that displayed prolonged lags, we examined the impacts of several environmental and biological variables likely to influence the length of lag period. We found that seventeen populations (47%) showed significant prolonged population growth lags. We could not, however, determine the specific factors that contributed to the length of these lag phases, suggesting that these ungulate populations'' growth is idiosyncratic and difficult to predict. Introduced species that exhibit delayed growth should be closely monitored by managers, who must be proactive in controlling their growth to minimize the impact such populations may have on their environment.     

Time lags in ecological systems.

A model representing ten species in a four trophic level community is constructed by using Volterra's equations including time lags, and is solved numerically for some values of the parameters. Classical discrete and continuous time lags yield similar results; simulating with discrete time lags thus appears useful. Parasitic versus predatory structures are compared by measuring the amplitudes of oscillations and the time taken to settle down to equilibrium, and give the following qualitative conclusions for the model.An increase in the carrying capacity of a trophic level increases the destabilizing influence of time lag in that level, this increase is more marked in predatory structures. Time lags appear to cause more violent oscillations in species strongly linked to a predatory system than in weakly linked species. The oscillatory period increases in predatory systems as the time lag is moved to higher levels, while it decreases in parasitic systems.     

Modeling the Non-Stationary Climate Dependent Temporal Dynamics of Aedes aegypti

Background

Temperature and humidity strongly affect the physiology, longevity, fecundity and dispersal behavior of Aedes aegypti, vector of dengue fever. Contrastingly, the statistical associations measured between time series of mosquito abundance and meteorological variables are often weak and contradictory. Here, we investigated the significance of these relationships at different time scales.

Methods and Findings

A time series of the adult mosquito abundance from a medium-sized city in Brazil, lasting 109 weeks was analyzed. Meteorological variables included temperature, precipitation, wind velocity and humidity. As analytical tools, generalized linear models (GLM) with time lags and interaction terms were used to identify average effects while the wavelet analysis was complementarily used to identify transient associations. The fitted GLM showed that mosquito abundance is significantly affected by the interaction between lagged temperature and humidity, and also by the mosquito abundance a week earlier. Extreme meteorological variables were the best predictors, and the mosquito population tended to increase at values above and 54% humidity. The wavelet analysis identified non-stationary local effects of these meteorological variables on abundance throughout the study period, with peaks in the spring-summer period. The wavelet detected weak but significant effects for precipitation and wind velocity.

Conclusion

Our results support the presence of transient relationships between meteorological variables and mosquito abundance. Such transient association may be explained by the ability of Ae. aegypti to buffer part of its response to climate, for example, by choosing sites with proper microclimate. We also observed enough coupling between the abundance and meteorological variables to develop a model with good predictive power. Extreme values of meteorological variables with time lags, interaction terms and previous mosquito abundance are strong predictors and should be considered when understanding the climate effect on mosquito abundance and population growth.     

Combined Non-Target Effects of Insecticide and High Temperature on the Parasitoid Bracon nigricans

We studied the acute toxicity and the sublethal effects, on reproduction and host-killing activity, of four widely used insecticides on the generalist parasitoid Bracon nigricans (Hymenoptera: Braconidae), a natural enemy of the invasive tomato pest, Tuta absoluta (Lepidoptera: Gelechiidae). Laboratory bioassays were conducted applying maximum insecticide label rates at three constant temperatures, 25, 35 and 40°C, considered as regular, high and very high, respectively. Data on female survival and offspring production were used to calculate population growth indexes as a measure of population recovery after pesticide exposure. Spinetoram caused 80% mortality at 25°C and 100% at higher temperatures, while spinosad caused 100% mortality under all temperature regimes. Cyantraniliprole was slightly toxic to B. nigricans adults in terms of acute toxicity at the three temperatures, while it did not cause any sublethal effects in egg-laying and host-killing activities. The interaction between the two tested factors (insecticide and temperature) significantly influenced the number of eggs laid by the parasitoid, which was the lowest in the case of females exposed to chlorantraniliprole at 35°C. Furthermore, significantly lower B. nigricans demographic growth indexes were estimated for all the insecticides under all temperature conditions, with the exception of chlorantraniliprole at 25°C. Our findings highlight an interaction between high temperatures and insecticide exposure, which suggests a need for including natural stressors, such as temperature, in pesticide risk assessments procedures.     

Subpopulations of sensorless bacteria drive fitness in fluctuating environments

Populations of bacteria often undergo a lag in growth when switching conditions. Because growth lags can be large compared to typical doubling times, variations in growth lag are an important but often overlooked component of bacterial fitness in fluctuating environments. We here explore how growth lag variation is determined for the archetypical switch from glucose to lactose as a carbon source in Escherichia coli. First, we show that single-cell lags are bimodally distributed and controlled by a single-molecule trigger. That is, gene expression noise causes the population before the switch to divide into subpopulations with zero and nonzero lac operon expression. While “sensorless” cells with zero preexisting lac expression at the switch have long lags because they are unable to sense the lactose signal, any nonzero lac operon expression suffices to ensure a short lag. Second, we show that the growth lag at the population level depends crucially on the fraction of sensorless cells and that this fraction in turn depends sensitively on the growth condition before the switch. Consequently, even small changes in basal expression can significantly affect the fraction of sensorless cells, thereby population lags and fitness under switching conditions, and may thus be subject to significant natural selection. Indeed, we show that condition-dependent population lags vary across wild E. coli isolates. Since many sensory genes are naturally low expressed in conditions where their inducer is not present, bimodal responses due to subpopulations of sensorless cells may be a general mechanism inducing phenotypic heterogeneity and controlling population lags in switching environments. This mechanism also illustrates how gene expression noise can turn even a simple sensory gene circuit into a bet hedging module and underlines the profound role of gene expression noise in regulatory responses.

Is ignorance bliss for some bacterial cells? Single-cell analysis of the archetypical switch from glucose to lactose as a carbon source in E. coli shows that bacteria can exhibit stochastic bimodal responses to external stimuli because the corresponding sensory circuit is so lowly expressed that some cells are effectively blind to the stimulus.     

Growth of newly established alien populations: comparison of North American gypsy moth colonies with invasion theory

A common characteristic observed in many biological invasions is the existence of a lag between the time of arrival by the alien population and the time when established populations are noticed. Considerable advances have been made in modeling the expansion of invading species, and there is often remarkable congruence between the behavior of these models with spread of actual populations. While these models have been used to characterize expansion of very newly founded colonies, there have been few attempts to compare the behavior predicted from theory with spread in actual newly founded populations, largely due to the difficulty of sampling sparse populations. Models predict that time lags in the radial expansion of newly invaded populations may be due to time requirements for the population to grow from founding to detectable levels. Models also indicate that these time lags can be predicted based upon population parameters such as the intrinsic rate of population growth and diffusion coefficient. In this paper, we compared the behavior of these models with historical data on gypsy moth, Lymantria dispar, establishment and spread to show similarities between model predictions and observed population spread, both of which exhibited temporal lags of expansion. However, actual populations exhibited certain behaviors that were not predicted, and this could be due, in part, to the existence of Allee effects and stochasticity. Further work that incorporates these effects is needed to more fully understand the growth of incipient colonies of invading species. Ultimately, this information can be of critical importance in the selection of effective strategies for their detection and eradication.     

Sensitive biomarker of polycyclic aromatic hydrocarbons (PAHs): urinary 1-hydroxyprene glucuronide in relation to smoking and low ambient levels of exposure

The lysosomal neutral red retention time (NRRT) assay, a biomarker for lysosomal membrane stability, and the total immune activity (TIA) assay, a measure of non-specific immune system activity, were used in laboratory studies to assess the toxic effects of 2,4,6-trinitrotoluene (TNT) on earthworms (Eisenia andrei) in vivo. The results were compared with the concentration of TNT and its metabolites in earthworm tissue, as well as standard sublethal toxicity endpoints including growth (i.e. weight change) and reproduction effects from previously published studies. Filter paper experiments indicated a significant decrease in NRRT at ≥1.8 μg TNT cm^-2, whereas sublethal (weight loss) and lethal effects to earthworms were detected at ≥3.5 and 7.1 μg TNT cm^-2, respectively. Experiments in artificial soil showed that NRRT effects could be detected at lower TNT concentrations (≥55 mg TNT kg^-1 soil dry weight) compared with other sublethal endpoints (effects on growth and reproduction). The TIA biomarker did not significantly respond to TNT. Copper (as CuSO₄, filter paper contact tests) and 2-chloroacetamide (soil tests), which were used as reference toxicants, also decreased the NRRT. The use of the NRRT assay linked with tissue concentrations of TNT metabolites in earthworms was identified as a potentially appropriate biomarker approach for TNT exposure assessment under laboratory conditions and a novel tool for effects-based risk assessment.     

Side effects of diflubenzuron on a pear psylla predator:Forficula auricularia

A series of laboratory, semi-field and field tests showed the high toxicity of diflubenzuron toForficula auricularia L. nymphs, at concentrations of 15 and 20 g a.i./hl registered in various European countries and the United States to controlCydia pomonella L. Diflubenzuron proved more selective using the 10 g/hl concentration registered in France, but several sublethal effects have been observed: morphological abnormalities, reduced weight increase and mobility. Unexpectedly for a chitin-deposit inhibitor, intake was reduced, which became apparent from the beginning of exposure to the insecticide, before the onset of the moulting process. In the semi-field tests, and despite diflubenzuron's slowing down effect on psylla nymphs, the earwig's reduced predatory activity due to the product resulted in greater growth of the psylla populations than without treatment. The field-test confirmed the efficacy ofF. auricularia as a psylla predator, and the relative selectivity of diflubenzuron at the lowest concentration.     

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or “spikes” nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons’ fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron’s firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.     

Evaluation of tissue and cellular biomarkers to assess 2,4,6-trinitrotoluene (TNT) exposure in earthworms: effects-based assessment in laboratory studies using Eisenia andrei

The lysosomal neutral red retention time (NRRT) assay, a biomarker for lysosomal membrane stability, and the total immune activity (TIA) assay, a measure of non-specific immune system activity, were used in laboratory studies to assess the toxic effects of 2,4,6-trinitrotoluene (TNT) on earthworms (Eisenia andrei) in vivo. The results were compared with the concentration of TNT and its metabolites in earthworm tissue, as well as standard sublethal toxicity endpoints including growth (i.e. weight change) and reproduction effects from previously published studies. Filter paper experiments indicated a significant decrease in NRRT at ≥1.8 µg TNT cm^-2, whereas sublethal (weight loss) and lethal effects to earthworms were detected at ≥3.5 and 7.1 µg TNT cm^-2, respectively. Experiments in artificial soil showed that NRRT effects could be detected at lower TNT concentrations ( ≥55 mg TNT kg^-1 soil dry weight) compared with other sublethal endpoints (effects on growth and reproduction). The TIA biomarker did not significantly respond to TNT. Copper (as CuSO₄, filter paper contact tests) and 2-chloroacetamide (soil tests), which were used as reference toxicants, also decreased the NRRT. The use of the NRRT assay linked with tissue concentrations of TNT metabolites in earthworms was identified as a potentially appropriate biomarker approach for TNT exposure assessment under laboratory conditions and a novel tool for effects-based risk assessment.     

Lethal and sublethal effects of abamectin, spinosad, methoxyfenozide and acetamiprid on the predaceous plant bug Deraeocoris brevis in the laboratory

Deraeocoris brevis (Uhler) (Hemiptera: Miridae), an important generalist predator in pome fruits in the western United States, was reared in the laboratory on frozen Ephestia kuehniella (Zeller) (Lepidoptera: Pyralidae) eggs and treated in a Potter spray tower to assess acute toxicity and chronic sublethal effects of abamectin, spinosad, methoxyfenozide, and acetamiprid. Acute toxicity was assessed using topical application. Sublethal effects were examined as the combined result of topical, residual and oral exposure. Two different dose rates, the full field rate and 10% rate of the full field rate, were compared to distilled water as the untreated check. Methoxyfenozide and spinosad had no acute toxicity to nymphs and adults at the 10% and full field rate, and no effect on egg hatch and nymph survival just after hatch. Acetamiprid and abamectin at the full field rate did not affect egg hatch, but the residue had moderate to high toxicity to hatched nymphs. Also, topically applied acetamiprid and abamectin had moderate to high acute toxicity to nymphs and adults at the full field rate, but moderate toxicity at the 10% rate. In sublethal bioassays, abamectin-treated adults (10% field rate) laid 80% fewer and less viable eggs compared with the untreated check. Spinosad-treated (full field rate) adults laid fewer and less viable eggs. Also, egg hatch in the subsequent generation was lower. Methoxyfenozide had no sublethal effects on adults at the full rate, but slowed development of 4th instars following treatment of 2nd instar nymphs, and lowered fecundity by 30% in the subsequent generation compared with the untreated check. Acetamiprid (10% rate) applied to nymphs or adults had no effects on development or reproduction. Results from this study suggest that the newer reduced risk insecticides, which have begun to replace organophosphate insecticides in pome fruits in the United States, are not as selective to natural enemies as initially thought. Their impact on D. brevis varied with chemistry and mode of action from primarily acute toxicity (i.e., acetamiprid) to reproductive and other sublethal effects (i.e., methoxyfenozide, spinosad) or a combination of both (i.e., abamectin). In addition to acute toxicity, sublethal effects need to be quantified in order to accurately predict the total impact of a pesticide on a natural enemy in the field.     

Use of Stochastic Models To Assess the Effect of Environmental Factors on Microbial Growth

We present a novel application of a stochastic ecological model to the study and analysis of microbial growth dynamics as influenced by environmental conditions in an extensive experimental data set. The model proved to be useful in bridging the gap between theoretical ideas in ecology and an applied problem in microbiology. The data consisted of recorded growth curves of Escherichia coli grown in triplicate in a base medium with all 32 possible combinations of five supplements: glucose, NH₄Cl, HCl, EDTA, and NaCl. The potential complexity of 2⁵ experimental treatments and their effects was reduced to 2² as just the metal chelator EDTA, the presumed osmotic pressure imposed by NaCl, and the interaction between these two factors were enough to explain the variability seen in the data. The statistical analysis showed that the positive and negative effects of the five chemical supplements and their combinations were directly translated into an increase or decrease in time required to attain stationary phase and the population size at which the stationary phase started. The stochastic ecological model proved to be useful, as it effectively explained and summarized the uncertainty seen in the recorded growth curves. Our findings have broad implications for both basic and applied research and illustrate how stochastic mathematical modeling coupled with rigorous statistical methods can be of great assistance in understanding basic processes in microbial ecology.     

THE TOXIC ACTION OF COPPER ON NITELLA

1. Using the loss of turgidity of the cells as a criterion it is found that the toxicity curve of copper chloride with Nitella is sigmoid. An empirical equation can be constructed which will approximately fit the curve. 2. When the concentration of the copper chloride is varied the toxic effect varies as a constant, fractional, power of the concentration. This relation holds when the concentration is plotted against either (1) the time necessary to reach a given point on the ordinate of the survivor curve, (2) the maximum speed of toxic action as shown by the tangent to the survivor curve or (3) the first derivative of the equation which fits the survivor curve. 3. When the temperature is varied and the logarithm of the reciprocal of the time necessary to reach a given point on the survivor curves is plotted against the reciprocal of the absolute temperature the resulting figure consists of several intersecting curves. A hypothetical system is described which will give straight lines under normal conditions and curves when acted upon by a toxic agent.     

Amphibian survival,growth and development in response to mineral nitrogen exposure and predator cues in the field: an experimental approach

Mineral nitrogen (N) has been suggested as a potential factor causing declines in amphibian populations, especially in agricultural landscapes; however, there is a question as to whether it remains in the water column long enough to be toxic. We explored the hypothesis that mineral N can cause both lethal and sublethal toxic effects in amphibian embryos and larvae in a manipulative field experiment. We sampled 12 ponds, fertilizing half with ammonium nitrate fertilizer early in the spring, and measured hatching, survival, development, growth, and the incidence of deformities in native populations of wood frog (Rana sylvatica) and eastern tiger salamander (Ambystoma tigrinum tigrinum) embryos and larvae held in in situ enclosures. We found that higher ammonium concentrations negatively affect R. sylvatica more strongly than A. tigrinum. R. sylvatica tended to have lower survival as embryos and young tadpoles, slowed embryonic development, and an increased proportion of hatchlings with deformities at experimentally elevated ammonium. A. tigrinum did not experience significantly reduced survival, but their larval development was slowed in response to elevated ammonium and the abundance of large invertebrate predators. Variable species susceptibility, such as that shown by R sylvatica and A. tigrinum, could have large indirect effects on aquatic community structure through modification of competitive or predator-prey relationships. Ammonium and nitrate + nitrite concentrations were not correlated with other measures that might have affected amphibians, such as pH, pond area, depth, or vegetation. Our results highlight the potential importance of elevated ammonium on the growth, development and survival of amphibians, especially those that breed in surface waters receiving anthropogenic N inputs. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.