A reliability index for models

Since the prediction of environmental changes depends heavily on mathematical models, environmental planners have a definite need for a general test that can be easily applied to determine the reliability of a model or to choose between available models. In this paper a ‘reliability index’ for a model is defined. This index is a number k ? 1 which is determined from a set x₁,x₂,…,x_n of model predictions and a corresponding set y₁,y₂,…,y_n of observations. One interpretation of the index k is that the model predictions agree with observations, in some sense, within a factor of k. The index k is defined using an intuitive, geometric approach and is justified through agreement with another index developed using statistical techniques. Examples are given for a model which predicts the atmospheric movement of radon-222 originating from a concentrated source of radium-226, such as a uranium tailings pile.     

A stochastic forest fire growth model

We consider a stochastic fire growth model, with the aim of predicting the behaviour of large forest fires. Such a model can describe not only average growth, but also the variability of the growth. Implementing such a model in a computing environment allows one to obtain probability contour plots, burn size distributions, and distributions of time to specified events. Such a model also allows the incorporation of a stochastic spotting mechanism.

Development of a hydrothermal time seed germination model which uses the Weibull distribution to describe base water potential

Seed germination has been modelled extensively using hydrothermal time (HTT) models, that predict time to germination as a function of the extent to which seedbed temperature, T, and water potential, Ψ, exceed the base temperature, T_b, and base water potential, Ψ_b, of each seed percentile, g. Within a seed population the variation in time to germination arises from variation in Ψ_b(g) modelled by a normal distribution. We tested the assumption of normality in the distribution of Ψ_b(g) by germinating seed of two unrelated species with non-dormant seed (Buddleja davidii (Franch.) and Pinus radiata D. Don) across a range of constant Ψ at sub-optimal T. When incorporated into a HTT model the Weibull distribution more accurately described both the right skewed distribution of Ψ_b(g) and germination time course over sub-optimal T than the HTT based on the normal distribution, for both species. Given the flexibility of the Weibull distribution this model not only provides a useful method for predicting germination but also a means of determining the distribution of Ψ_b(g).     

Present-day genetic composition suggests contrasting demographic histories of two dominant chaetognaths of the North-East Atlantic, <Emphasis Type="Italic">Sagitta elegans</Emphasis> and <Emphasis Type="Italic">S. setosa</Emphasis>

Sagitta elegans and S. setosa are the two dominant chaetognaths in the North-East (NE) Atlantic. They are closely related and have a similar ecology and life history, but differ in distributional ranges. Sagitta setosa is a typical neritic species occurring exclusively above shelf regions, whereas S. elegans is a more oceanic species with a widespread distribution. We hypothesised that neritic species, because of smaller and more fragmented populations, would have been more vulnerable to population bottlenecks resulting from range contractions during Pleistocene glaciations than oceanic species. To test this hypothesis we compared mitochondrial Cytochrome Oxidase II DNA sequences of S. elegans and S. setosa from sampling locations across the NE Atlantic. Both species displayed very high levels of genetic diversity with unique haplotypes for every sequenced individual and an approximately three times higher level of nucleotide diversity in S. elegans (0.061) compared to S. setosa (0.021). Sagitta setosa mitochondrial DNA (mtDNA) haplotypes produced a star-like phylogeny and a uni-modal mismatch distribution indicative of a bottleneck followed by population expansion. In contrast, S. elegans had a deeper mtDNA phylogeny and a multi-modal mismatch distribution as would be expected from a more stable population. Neutrality tests indicated that assumptions of the standard neutral model were violated for both species and results from the McDonald-Kreitman test suggested that selection played a role in the evolution of their mitochondrial DNA. Congruent with these results, both species had much smaller effective population sizes estimated from genetic data when compared to census population sizes estimated from abundance data, with a factor of ~10⁸–10⁹ difference. Assuming that selective effects are comparable for the two species, we conclude that the difference in genetic signature can only be explained by contrasting demographic histories. Our data are consistent with the hypothesis that in the NE Atlantic, the neritic S. setosa has been more severely affected by population bottlenecks resulting from Pleistocene range shifts than the more oceanic S. elegans.     

Spatial distribution of the infaunal benthic communities of the Ría de Muros,north-west Spain

Benthic samples were collected at 13 stations in the Ría de Muros, north-west Spain. There are three major communities: (1) in the southern and outer part of the ría, an Amphiura filiformis—Thyone fusus community, inhabiting sandy sediments with low organic content; (2) in the middle part of the ría, and Amphiura chiajei—Maldane glebifex community, inhabiting muddy sediments that are not anoxic (sulphide not detected); (3) in Muros Bay and the inner part of the ría, a Spiochaetopterus costarum community, inhabiting anoxic sediments with high organic content. Biomass is very high (up to 46.2 g ash-free dry wt) in the first two communities. In the Spiochaetopterus costarum community, biomass and diversity are much lower, probably because of oxygen deficiency.     

Photodegradation of the organophosphorus insecticide ‘Phorate’

The photolysis of Phorate(I) (0,0‐diethyl S‐ethyl thiomethyl phosphordithioate) has been studied as a thin film on a glass surface and in a solution of methanol‐water (60:40) by ultraviolet light (λ > 290 nm). The rate of disappearance of Phorate in the solution show first order Kinetics with a rate constant of 4.9 × 10^–5 S ^–1. The half‐life of (I) exposed on a glass surface is found to be 5 hours. The structure of the major photoproducts were characterised by ¹H NMR and mass spectroscopy.     

Male mating speed promote hybridization in the Rana lessonae–Rana esculenta waterfrog system

Hybridization is a widespread phenomenon in many vertebrate groups. Prezygotic isolating mechanisms, probably caused by selection against hybrids with reduced fitness, reduce the likelihood of such events. Although hybrid-reduced fitness relatively to parental species is common, hybridization can also be beneficial, and hybrids sometimes outperform the pure species type. In this study, we examined two potential processes, Hubbs’s principle and male–male competition, which could enhance hybridization in the waterfrog complex and thus explain the proportion of heterospecific pairs collected in a natural pond. Firstly, by collecting 791 frogs in the field to study pair and chorus composition, we showed that in a mixed Rana lessonae–Rana esculenta population, the scarcity of hybrid R. esculenta males did not account for the proportion of heterospecific pairs: indeed, when examining pairing composition in six different choruses, we found that hybrid males were always under-represented and that R. esculenta females were found paired with R. lessonae males. Secondly, we investigated experimentally whether or nor male–male competition mechanism could explain pair formation in waterfrogs. Our mating speed experiment highlights mechanisms that could explain heterospecific pairs in a context of promiscuous mating where scramble competition was intense. To measure the rapidity with which a male grasps a female, we placed males in a grid cage with a female, and the dynamics of pair formation was monitored. R. esculenta males showed a lower pairing success than R. lessonae males as a smaller proportion of them amplexed females, and more time was needed for them to get amplexed. Thus, a less adaptative mechanism than female mate choice may also explain the mating pattern observed in waterfrog species.     

Studying crop sequences with CarrotAge,a HMM-based data mining software

We have developed a knowledge discovery system based on high-order hidden Markov models for analyzing spatio-temporal data bases. This system, named CarrotAge , takes as input an array of discrete data – the rows represent the spatial sites and the columns the time slots – and builds a partition together with its a posteriori probability. CarrotAge has been developed for studying the cropping patterns of a territory. It uses therefore an agricultural drench database, named Ter-Uti , which records every year the land-use category of a set of sites regularly spaced. The results of CarrotAge are interpreted by agronomists and used in research works linking agricultural land use and water management. Moreover, CarrotAge can be used to find out and study crop sequences in large territories, that is a main question for agricultural and environmental research, as discussed in this paper.     

敌草快对藻类和溞类的急性毒性及其水中含量测定

敌草快是一种非选择性、广谱的联吡啶类触杀性除草剂,主要通过干扰植物细胞膜、破坏光合作用而快速发挥效果。为探究敌草快对水生生物的毒性,测定了该化合物对羊角月芽藻和大型溞的急性毒性,并建立了高效液相色谱法测定水中敌草快含量的方法。结果表明:检测方法在1.00×10-2~3.00×10-2mg a.i.·L-1范围内的线性相关系数为0.99995,添加回收率在90.3%~109%之间,相对标准偏差(RSD)为1.10%~10.3%,保留时间在7.2 min左右。按实测浓度和理论浓度分别计算敌草快对羊角月芽藻的72 h的半数效应浓度EyC50(72 h-EyC50),分别为3.16×10-2mg a.i.·L-1和3.32×10-2mg a.i.·L-1,均为高毒;对大型溞48 h的半数效应浓度EC50(48 h-EC50)分别为1.18×10-2mg a.i.·L-1和1.33×10-2mg a.i.·L-1,均为剧毒。     

Modeling and analysis of nest-site selection by honeybee swarms: the speed and accuracy trade-off

Nest-site selection in honeybees is a process of social decision making in which the scout bees in a swarm locate several potential nest sites, evaluate them, and select the best one by means of competitive signaling. We develop a model of this process and validate that the model possesses the key features of the bees' decision-making process, as revealed by prior empirical studies. Next, we use the model to study the “design” of the nest-site selection process, with a focus on how certain behavioral parameters have been tuned by natural selection to achieve a balance between speed and accuracy. First, we study the effects of the quorum threshold and the dance decay rate. We show that evolution seems to have settled on values for these two parameters that seek a balance between speed and accuracy of decision making by minimizing the time needed to achieve a consensus and maximizing the probability that the best site is chosen. Second, we study the adaptive tuning of the tendency of bees to explore for vs be recruited to a site. We show that this tendency appears to be tuned to regulate the positive feedback process of recruitment to ensure both a reasonably rapid choice and a low probability of a poor choice. Finally we show that the probability of choosing the best site is proportional to its quality, but that this proportionality depends on its quality relative to other discovered sites.

Accumulation and phytoavailability of benzo[a]pyrene in an acid sandy soil

Effects of benzo[a]pyrene (B[a]P) on ryegrass (Lolium perenne L.) growth, plant accumulation and dissipiation of B[a]P in a red sandy soil (Hapli-Udic Argosol) were studied in a pot experiment. The plants were grown for 61 days in soil spiked with B[a]P at 0, 12.5, 25 and 50 mg kg⁻¹. Control pots without plants were also set up. Soil extractable B[a]P, plant shoot and root biomass, and concentrations of B[a]P in plant shoots and roots were determined. Ryegrass biomass was increased by addition of B[a]P and root B[a]P concentrations were significantly correlated with B[a]P application rate, but no such correlation was found for shoot B[a]P concentrations. This indicates that B[a]P enhanced the growth of the ryegrass. The extractable B[a]P concentration in the planted soil was significantly lower than that in the unplanted control soil at the rate of 50 mg B[a]P kg⁻¹. This indicates that ryegrass may help to dissipate B[a]P in soil at concentrations over 50 mg kg⁻¹ soil although the mechanism for this is not understood.     

The hypoxia avoidance behaviour of juvenile Atlantic cod (<Emphasis Type="Italic">Gadus morhua</Emphasis> L.) depends on the provision and pressure level of an O<Subscript>2</Subscript> refuge

The frequency of low O₂ (hypoxia) has increased in coastal marine areas but how fish avoid deleterious water masses is not yet clear. To assess whether the presence and oxygen pressure (PO₂) level of an O₂ refuge affects the hypoxia avoidance behaviour of fish, individual Atlantic cod (Gadus morhua L.) were exposed to a range of O₂ choices in a 2-way choice chamber at 11.4°C over two different experiments. Cod in the first experiment were allowed access to a fixed O₂ refuge (fully air-saturated seawater) whilst oxygen pressure (PO₂) on the other side was reduced in steps to a critically low level, i.e. 4.3 kPa—a point where cod can no longer regulate O₂ consumption. Under these conditions, cod did not avoid any level of hypoxia and fish swimming speed also remained unchanged. In contrast, strong avoidance reactions were exhibited in a second experiment when fish were again exposed to 4.3 kPa but the safety, i.e. PO₂, of the refuge was reduced. Fish not only spent less time at 4.3 kPa as a result of fewer sampling visits but they also swam at considerably slower speeds. The presence of an avoidance response was thus strongly related to refuge PO₂ and it is unlikely that cod, and possibly other fish species, would enter low O₂ to feed in the wild if a sufficiently safe O₂ refuge was not available. It is therefore hypothesized that the feeding range of fish may be heavily compressed if hypoxia expands and intensifies in future years.     

Feasibility and stability in randomly assembled Lotka-Volterra models

For a Lotka-Volterra model to represent a viable ecosystem it's nontrivial equilibrium must be feasible. If m is the number of species, it is shown that in a set of randomly assembled Lotka-Volterra models, the fraction of models with a feasible equilibrium is some function of m which behaves like 2^?m. Moreover a subset of Lotka-Volterra models, each of which has a feasible equilibrium, has the same stability property as a set of linear models which is assembled randomly in the same manner. This contradicts a recent claim that a Lotka-Volterra model with a feasible equilibrium tends to be stable. Thus for two reasons the probability that a Lotka-Volterra model represents a viable and stable ecosystem decreases rapidly with the number of species. This supports the theme developed by May that stability in model ecosystems decreases with diversity.     

Consistent personality differences in house-hunting behavior but not decision speed in swarms of honey bees (<Emphasis Type="BoldItalic">Apis mellifera</Emphasis>)

Speed-accuracy tradeoffs are a common feature of decision-making processes, both in individual animals and in groups of animals working together to reach a single collective decision. Individual organisms display consistent differences in their “impulsivity,” and vary in their tendency to make rapid, impulsive choices as opposed to slower, more accurate decisions. However, we do not yet know whether groups of animals consistently differ in their tendency to prioritize decision speed over accuracy. We challenged 17 swarms of honey bees (Apis mellifera) to simultaneously choose a new nest site in each of three locations, and measured their decision speeds in each trial. We found that swarms displayed consistent personality differences in the number of waggle dances and shaking signals they performed and in how actively they scouted for new nest sites. However, swarms did not consistently differ in how long they took to choose a nest site. We suggest that house-hunting A. mellifera swarms may place an especially high emphasis on decision accuracy when choosing a nest site, and that chance events—such as the time when each swarm discovers a sufficiently high-quality nest site—may consequently play a greater role in determining a swarm’s decision speed than intrinsic characteristics such as a swarm’s “impulsivity.”     

Dynamics of soil organic matter in primary and secondary forest succession on sandy soils in The Netherlands: An application of the ROMUL model

We applied the simulation model ROMUL of soil organic matter dynamics in order to analyse and predict forest soil organic matter (SOM) changes following stand growth and also to identify gaps of data and modelling problems. SOM build-up was analysed (a) from bare sand to forest soil during a primary succession in Scots pine forest and (b) on mature forest soil under Douglas fir plantations as an example of secondary succession in The Netherlands. As some of the experimental data were unreliable we compiled a set of various scenarios with different soil moisture regime, initial SOM pools and amount and quality of above and below ground litter input. This allowed us to find the scenarios that reflect the SOM dynamics more realistically. In the Scots pine forest, total litter input was estimated as 0.50 kg m⁻² year⁻¹. Two scenarios were defined for the test runs: (a) forest floor moisture regimes—‘dry, mesic and hydric’ and (b) augmenting a root litter pool with three ratios of needles and branches to roots: 1:1, 1:1.5 and 1:2.0. The scenario finally compiled had the following characteristics: (a) climate for dry site with summer drought and high winter moisture of forest floor; (b) a litter input of 0.25 kg m⁻² year⁻¹ above ground and 0.50 kg m⁻² year⁻¹ below ground; (c) a low nitrogen and ash content in all litter fall fractions. The test runs for the estimation of the initial SOM pools and the amount and proportion of above and below ground litter fall were also performed in the Douglas fir plantation. The inputs of above ground litter tested in various combinations were 0.30 and 0.60 kg m⁻² year⁻¹, and below ground litter 0.30, 0.60 and 0.90 kg m⁻² year⁻¹. The scenario that fitted the experimental data had an SOM pool of 20–25 kg m⁻², an aboveground litter input of 0.6 kg m⁻² year⁻¹and a below ground litter input of 0.9 kg m⁻² year⁻¹. The long-term simulation corresponded well with the observed patterns of soil organic matter accumulation associated with the forest soil development in primary and secondary succession. During primary succession in Scots pine forest on dry sand there is a consistent accumulation of a raw humus forest floor. The soil dynamics in the Douglas fir plantation also coincide with the observed patterns of SOM changes during the secondary succession, with SOM decreasing significantly under young forest, and SOM being restored in the older stands.     

Spatial memory, habitat auto-facilitation and the emergence of fractal home range patterns

Animals interact with their habitat in a manner which involves both negative and positive feedback mechanisms. We apply a specific modeling approach, “multi-scaled random walk”, for the scenario where a spatially explicit positive feedback process emerges from a combination of a spatial memory-dependent tendency to return to familiar patches and a consequently objective or subjective improvement of the quality of these patches (habitat auto-facilitation). In addition to the potential for local resource improvement from physically altering a patch, primarily known from the ecology of grazing ungulates, auto-facilitation from site fidelity may also embed more subtle subjective, individual-specific advantages from patch familiarity. Under the condition of resource superabundance, fitness gain from intra-home range patch fidelity creates a self-reinforcing use of the preferred patches on expense of a broader foraging in a priori equally favorable patches. Through this process, our simulations show that a spatially fractal dispersion of accumulated locations of the individual will emerge under the given model assumptions. Based on a conjecture that intra-home range patch fidelity depends on spatial memory we apply the multi-scaled random walk model to construct a spatially explicit habitat suitability parameter H_ij, which quantifies the dispersion of the generally most constraining resource from the individual's perspective. An intra-home range set of observed H-scores, H_obs, can then be estimated from a simple 2-scale calculation that is derived from the local dispersion of fixes. We show how the spatially explicit habitat utilization index H_obs not necessarily correlates positively with the local density fluctuations of fixes. The H-index solves some well-known problems from using the pattern of local densities of telemetry fixes - the classic utilization distribution - as a proxy variable for relative intra-home range habitat quality and resource selection. A pilot study on a set of telemetry fixes collected from a herd of free-ranging domestic sheep with overlapping summer home ranges illustrates how the H-index may be estimated and interpreted as a first-level approach towards a more extensive analysis of intra-home range habitat resource availability and patch preferences. Spatial memory in combination with site fidelity requires a modeling framework that explicitly describes the property of positive feedback mechanism under auto-facilitation in a spatio-temporally explicit manner.     

The theoretical basis for estimating phytoplankton production and specific growth rate from chlorophyll, light and temperature data

Phytoplankton maximum specific growth rate, μ_max, and maximum photosynthetic quantum yield, Φ_max, can be related mathematically via the photosynthetic light curve, P(I). A model is presented in which maximum quantum yield defines the initial slope of the light curve and is assumed to be a known constant, while maximum specific growth rate defines the light-saturated region of the curve and is assumed to be a known function of temperature. The effect of introducing μ_max(T) into P(I, Φ_max) is to replace the unknown, temperature-dependent light saturation parameter with a term involving the ratio μ_max/Φ_max. The advantage of writing P(I) in terms of both μ_max and Φ_max is that those parameters are particularly well documented in the literature. Consequently, estimates of nutrient-unlimited phytoplankton growth and production rates can be based solely on the constants μ_max, Φ_max and k_c (light absorption per unit of chlorophyll) and the free variables light, temperature and chlorophyll concentration. Rate estimates appear to be accurate to within a factor of two for an extremely wide range of conditions.One particularly significant result of introducing μ_max into P(I, Φ_max) is that the carbon : chlorophyll ration, θ, appears explicitly. It is possible to derive an expression for optimum θ based on the assumption that adaptive changes in carbon/chlorophyll occur so as to maximize the specific growth rate for given conditions of light and temperature. Laboratory and field data are compiled from the literature to test the formulae presented here.     

The similarity solution for turbulent mixing of two-layer stratified fluid

Experiments are reviewed in which a two-layer salt-stratified tank of water was mixed by turbulence. The density profile began as a single step and evolved to a smooth mixed profile. The turbulence was generated by many excursions of a horizontally moving vertical rod with Richardson number Ri >  0.9 and Reynolds Number Re  >  600. There was almost perfect collapse of all the profiles to one universal profile as a function of a similarity variable. We develop a theoretical model for a simple mixing law with a buoyancy flux that is a function of internal Richardson number Rii. A similarity equation is found. A flux law that increases with small Rii and decreases with large Rii is considered next. Since no analytical solution is known, the similarity concept is tested by numerically integrating the equations in space and time. With buoyancy flux monotonically increasing with internal Richardson number, the similarity approach is valid for a profile starting from a slightly smoothed step. However, a shock forms for a mixing law with higher initial Rii (so that buoyancy flux decreases with Richardson number) and the similarity approach is invalid for those initial conditions.     

Characterisation of growth and biochemical response of Onopordum acanthium L. under lead stress as affected by microbial inoculation

Microbial associations may influence the negative effects of potentially toxic elements on plants. In a greenhouse experiment, the growth; biochemical response; and Pb, Fe, and Zn uptake of Onopordum acanthium L. were investigated in response to inoculation with arbuscular mycorrhizal fungi, AMF (a mixture of Funneliformis mosseae, Rhizophagus irregularis, and Rhizophagus fasciculatus) and plant growth-promoting rhizobacteria, PGPR (a mixture of Pseudomonas species including P. putida, P. fluorescens, and P. aeruginosa) at increased Pb levels in soil. The treatments were arranged as a factorial experiment based on a randomised complete block design. Results revealed that inoculation with AMF and PGPR decreased Pb toxicity in plants. Inoculated plants with AMF and PGPR had higher shoot and root dry weight compared with the non-inoculated plants. In this study, AMF and PGPR inoculation led to a significant increase (P?≤?.05) in chlorophyll a, b, chlorophyll a+b, carotenoid, proline, and relative water content of plants. Furthermore, AMF and PGPR inoculation likely played a more important role in growth and Pb uptake in O. acanthium L. Our results suggest that AMF and Pseudomonas bacteria could be effective bio-inoculants for enhancing the plant growth and Pb uptake by inhibiting the adverse effects of Pb in O. acanthium.     

Effects of salinity on endogenous rhythm of the Manila clam, Ruditapes philippinarum (Bivalvia: Veneridae)

The Manila clam Ruditapes philippinarum, an intertidal bivalve, was exposed to different salinity regimes (from 31.0–31.7‰ down to 20‰, 15‰, 10‰, 5‰), and the endogenous rhythm in its oxygen consumption was studied using an automatic intermittent-flow respirometer. When exposed to salinities reduced from 31.5‰ to 20‰ and 15‰ under otherwise constant conditions, the clams recovered a clear endogenous circatidal rhythm in their oxygen-consumption rate after having dampened periods of 12 h and 48 h, respectively. At salinities less than 10‰, however, the oxygen-consumption rate was depressed greatly at the beginning of the experiment for about 36 h and then increased to a level higher than normal, but the rhythm of oxygen consumption was not recovered. The results of this study indicate that the Manila clam, a euryhaline organism, cannot maintain a normal metabolic activity at a salinity lower than 15‰. All clams were dead after exposure at a salinity of 5‰ for 7 days. Received: 28 February 2000 / Accepted: 26 August 2000