Predator–prey fuzzy model

In this work we have used fuzzy rule-based systems to elaborate a predator–prey type of model to study the interaction between aphids (preys) and ladybugs (predators) in citriculture, where the aphids are considered as transmitter agents of the Citrus Sudden Death (CSD). Simulations were performed and a graph was drawn to show the prey population, the potentiality of the predators, and a phase-plane. From this phase-plane, a classic model of the Holling–Tanner type is fitted and its parameters were found. Finally, we have studied the stability of the critical points of the Holling–Tanner model.     

How might we model an ecosystem?

Predicting ecosystem effects is of crucial importance in a world at threat from natural and human-mediated change. Here we propose an ecologically defensible representation of an ecosystem that facilitates predictive modelling. The representation has its roots in the early trophic and energetic theory of ecosystem dynamics and more recent functional ecology and network theory. Using the arable ecosystem of the UK as an example, we show that the representation allows simplification from the many interacting plant and invertebrate species, typically present in arable fields, to a more tractable number of trophic-functional types. Our compound hypothesis is that “trophic-functional types of plants and invertebrates can be used to explain the structure, diversity and dynamics of arable ecosystems”. The trophic-functional types act as containers for individuals, within an individual-based model, sharing similar trophic behaviour and traits of biomass transformation. Biomass, or energy, flows between the types and this allows the key ecological properties of individual abundance and body mass, at each trophic height, to be followed through simulations. Our preliminary simulation results suggest that the model shows great promise. The simulation output for simple ecosystems, populated with realistic parameter values, is consistent with current laboratory observations and provides exciting indications that it could reproduce field scale phenomena. The model also produces output that links the individual, population and community scales, and may be analysed and tested using community, network (food web) and population dynamic theory. We show that we can include management effects, as perturbations to parameter values, for modelling the effects of change and indicating management responses to change. This model will require robust analysis, testing and validation, and we discuss how we will achieve this in the future.     

Are savannas patch-dynamic systems? A landscape model

Savannas are ecosystems characterized by the coexistence of woody species (trees and bushes) and grasses. Given that savanna characteristics are mainly formed from competition, herbivory, fire, woodcutting, and patchy soil and precipitation characteristics, we propose a spatially explicit model to examine the effects of the above-mentioned parameters on savanna vegetation dynamics in space and time. Furthermore, we investigate the effects of the above-mentioned parameters on tree–bush–grass ratios, as well as the degrees of aggregation of tree–bush–grass biomass. We parameterized our model for an arid savanna with shallow soil depth as well as a mesic one with generally deeper and more variable soil depths. Our model was able to reproduce savanna vegetation characteristics for periods of time over 2000 years with daily updated time steps. According to our results, tree biomass was higher than bush biomass in the arid savanna but bush biomass exceeded tree and grass biomass in the simulated mesic savanna. Woody biomass increased in our simulations when the soil's porosity values were increased (mesic savanna), in combination with higher precipitation. Savanna vegetation varied from open savanna to woodland and back to open savanna again. Vegetation cycles varied over ∼300-year cycles in the arid and ∼220-year cycles in the mesic-simulated savanna. Autocorrelation values indicated that there are both temporal and spatial vegetation cycles. Our model indicated cycling savanna vegetation at the landscape scale, cycles in cells, and patchiness, i.e. patch dynamics.     

Field-testing the protandry-based mating system for the lizard, Anolis carolinesis: does the model organism have the right model?

Using the lizard Anolis carolinensis as its subject, an early and enduring model of psychobiology was presented in which neuroendocrines and social behavior interact to coordinate reproduction between the sexes. The adaptive context for the model was protandry, here defined as a "male-first" emergence pattern from winter dormancy to the onset of breeding. In the protandry scenario, males emerge, become reproductive, and contest for territories. Then, pre-reproductive females emerge to settle on male territories, whereby ovarian recrudescence is facilitated by the behavior of courting males. A collateral inference of the protandry sequence is that females are choosing their future mates from among local males and their territories (i.e., intersexual selection). The model and its assumptions, though never validated by field data, have served as the paradigm for many laboratory experiments on A. carolinensis. Recently, however, field studies described an intrasexually selected mating system for A. carolinensis, without evidence of direct female choice. Differences between the selective inferences from the two perspectives led us to test in the field a number of protandry-based characteristics previously ascribed to A. carolinensis. We monitored free-ranging adults across the winter-to-breeding period using data on sex ratios, social behavior, gut contents, sex steroids, and gonadal condition. We found no evidence of protandry, and little support for any of the associated assumptions. Instead, the sexes broadly overlapped in their temporal transition from winter retreats to an active status in the habitat, with average male reproductive development about 1-2 weeks in advance of females. We replace the traditional protandry-based A. carolinensis paradigm with a realistic onset sequence into the breeding season and a new model for the species' mating system. Our study underscores the need for field validation when laboratory-generated data are fitted to adaptive paradigms.     

A σ-coordinate transport model coupled with rotational boussinesq-type equations

This paper describes a σ-coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus, a reasonable representation of vertical flow structure can be captured in shallow and wavy flow fields. To solve the coupled Boussinesq and scalar transport system, a finite-volume method, based on a Godunov-type scheme with the HLL Riemann solver, is employed. Basic advection and advection–diffusion numerical tests in a non-rectangular domain were carried out and the computed results show good agreement with analytic solutions. With quantitative comparisons of dispersion experiments in an open channel, it is verified that the proposed coupled model is appropriate for both near and far field scalar transport predictions. From numerical simulations in the surf zone, physically reasonable results showing expected vertical variation are obtained.     

Does the self-similar species distribution model lead to unrealistic predictions?

J. Harte et al. demonstrated that the power law form of the species-area relationship may be derived from a bisected, self-similar landscape and a community-level probability rule. Harte's self-similarity model has been widely applied in modeling species distributions. However, R. D. Maddux showed that this self-similarity model generates biologically unrealistic predictions. We resolve the Harte-Maddux debate by demonstrating that the problems identified by Maddux result from an assumption that the probability of occurrence of a species at one scale is independent of its probability of occurrence at the next. We refer to this as a "non-heritage assumption." By altering this assumption to one in which each species in the community has an occupancy status that is partially inherited across scales (a scale-heritage assumption), the predictions of the self-similarity model are neither mathematically inconsistent nor biologically unrealistic. Harte's self-similarity model remains an important framework for modeling species distributions. Our results illustrate the importance of considering patterns of species co-occurrence, and the way in which species occupancy patterns change with scale, when modeling species distributions.     

A Poisson–Gamma model for analysis of ecological non-negative continuous data

The statistical analysis of continuous data that is non-negative is a common task in quantitative ecology. An example, and our motivation, is the weight of a given fish species in a fish trawl. The analysis task is complicated by the occurrence of exactly zero observations. It makes many statistical methods for continuous data inappropriate. In this paper we propose a model that extends a Tweedie generalised linear model. The proposed model exploits the fact that a Tweedie distribution is equivalent to the distribution obtained by summing a Poisson number of gamma random variables. In the proposed model, both the number of gamma variates, and their average size, are modelled separately. The model has a composite link and has a flexible mean-variance relationship that can vary with covariates. We illustrate the model, and compare it to other models, using data from a fish trawl survey in south-east Australia.     

Nitrogen source apportionment—a comparison between a dynamic and a statistical model

A dynamic model, HBV-N, and a statistical model, MESAW, for nitrogen source apportionment were compared regarding model performance, model uncertainty and user applicability. The HBV-N model simulates continuous series of nitrogen concentrations with meteorological data and sub-basin characteristics as input. Diffuse nitrogen emissions are defined as regional model parameters which are calibrated by comparison of observed and simulated nitrogen data. The MESAW model uses nitrogen loads for a fixed time interval at each monitoring site as response variable and sub-basin characteristics as explanatory variables to estimate diffuse nitrogen emissions through non-linear regression analysis. The two models were applied in the Matsalu Bay watershed (3640 km²) in Estonia and the same land use and point sources data were used as input. Both models gave similar levels of diffuse total nitrogen emissions and retention rates, which also fit well with previous estimates made in Estonia and Scandinavia. A sensitivity analysis of the model parameters also showed similar uncertainty levels, which indicated that the model uncertainty was more dependent on the availability of nitrogen data and land cover distribution than the choice of model. Furthermore, the sensitivity analysis showed a parameter interdependency in both models, which implied the risk of compensation between estimated diffuse emissions and retention. In conclusion, however, the study showed that both models were capable of estimating nitrogen leakage from the dominating land classes and giving reliable source apportionment from the available input data. The study indicated that the HBV-N model has its advantage in assessments where detailed outputs are needed and when run-off data are limited, while the statistical MESAW model has its advantage in extensive studies since it is easily applied to large watersheds that have dense monitoring networks.     

Use of one-dimensional modelling in estuary management: entrance depth –– model calibration

The Wairoa River, a barrier enclosed estuary situated in Hawke’s Bay, New Zealand was modelled using a one-dimensional hydrodynamic model. Water level data obtained during a flood and a bathymetric survey were available but the entrance cross-section had not been surveyed. This paper describes the calibration of the model to jointly optimise the selection of the Manning coefficient and the depth of the estuary entrance.     

Modeling Dinophysis in Western Andalucía using an autoregressive hidden Markov model

Environmental and Ecological Statistics - Dinophysis spp. can produce diarrhetic shellfish toxins (DST) including okadaic acid and dinophysistoxins, and some strains can also produce non-diarrheic...     

Fate of 17β-estradiol in terrestrial model ecosystems amended with contaminated composted biosolids

Biosolids spread onto agricultural soils are potential sources of steroidal hormones that are able to adversely affect the soil ecosystem. Here we studied the fate of the [4-¹⁴C]-17-β-estradiol hormone in laboratory experiments. First, our results show that only 2.9% of the hormone was mineralized in the soil from a French vineyard. By contrast, the mineralization increased to 7.1% when the hormone was provided in composted biosolids. Second, we found that only a minor part of the estradiol-derived ¹⁴C was mobile and partly transferred to soil leachates. Indeed, the hormone was mainly stabilized in the soil as non-extractable residues. Overall, our findings show that estradiol undergoes two main processes, complete degradation and stabilisation. We therefore conclude that the environmental risk of hormones provided to the soil through composted biosolids is negligible under the conditions of our experiments.     

The principal–agent model with multilateral externalities: An application to climate agreements

We consider contracting of a principal with an agent if multilateral externalities are present. The motivating example is that of an international climate agreement given private information about the willingness-to-pay (WTP) for emissions abatement. Due to multilateral externalities the principal uses her own emissions besides subsidies to incentivize the agent and to assure his participation. Optimal contracts equalize marginal abatement costs and, thus, can be implemented by a system of competitive permit trading. Moreover, optimal contracts can include a boundary part (i.e., the endogenous, type dependent participation constraint is binding), which is not a copy of the outside option of no contract. Compared to this outside option, a contract can increase emissions of the principal for types with a low WTP, and reduce her payoff for high types. Subsidies can be constant or even decreasing in emission reductions, and turn negative so that the agent reduces emissions and pays the principal.     

HO ‐ initiated oxidation of acridine and aminacrine in aqueous media: Kinetic model

The photodecomposition of diluted aqueous solutions of acridine and aminacrine in the presence of hydrogen peroxide was studied. Irradiation was carried out with a low pressure mercury vapour lamp. The kinetic model describes the photodegradation rate of the organic compound with respect to the technological parameters of the reactor and provides the reaction rate constants of hydroxyl radicals towards these two molecules. This model was extented to high hydrogen peroxide concentrations ([H₂O₂] > 200 μmol/l) by considering the reactivity of hydroxyl radicals towards hydrogen peroxide. This assumption allows us to define an optimal hydrogen peroxide concentration.     

Eventual saturation of the climate–carbon cycle feedback studied with a conceptual model

A saturation of climate–carbon cycle feedback was found earlier in the simulations with the IAP RAS climate model of intermediate complexity. Here, this eventual saturation is interpreted by using a conceptual linearised coupled model. It is shown that this saturation is due to weak, logarithmic, dependence of the carbon dioxide radiative forcing on its atmospheric concentration. This eventual saturation leads to the non-monotonic behaviour of climate–carbon cycle parameter f   in time. If the time scale of the atmospheric CO₂${\text{CO}}_2$ build up is _tp$t_{\text{p}}$ then, starting from an initial equilibrium, f   approaches maximum in time ?_tp$?t_{\text{p}}$. Afterwards, climate–carbon cycle parameter decreases and eventually tends to unity. The time scale of the latter decrease is _t1=(1−5)_tp$t_1=(1-5)t_{\text{p}}$. A dependence of _tm$t_{\text{m}}$ and _t1$t_1$ on governing parameters of the conceptual model is studied. It is argued that an eventual saturation of the climate–carbon cycle feedback is expected to occur also in the other integrations of sufficient length with coupled climate–carbon cycle models.     

Quasi-Poisson vs. negative binomial regression: how should we model overdispersed count data?

Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. These variance relationships affect the weights in the iteratively weighted least-squares algorithm of fitting models to data. Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. We provide an example using harbor seal counts from aerial surveys. These counts are affected by date, time of day, and time relative to low tide. We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasi-Poisson vs. negative binomial regression. This difference is described and explained in light of the different weighting used in each regression method. A general understanding of weighting can help ecologists choose between these two methods.     

Does including physiology improve species distribution model predictions of responses to recent climate change?

Thermal constraints on development are often invoked to predict insect distributions. These constraints tend to be characterized in species distribution models (SDMs) by calculating development time based on a constant lower development temperature (LDT). Here, we assessed whether species-specific estimates of LDT based on laboratory experiments can improve the ability of SDMs to predict the distribution shifts of six U.K. butterflies in response to recent climate warming. We find that species-specific and constant (5 degrees C) LDT degree-day models perform similarly at predicting distributions during the period of 1970-1982. However, when the models for the 1970-1982 period are projected to predict distributions in 1995-1999 and 2000-2004, species-specific LDT degree-day models modestly outperform constant LDT degree-day models. Our results suggest that, while including species-specific physiology in correlative models may enhance predictions of species' distribution responses to climate change, more detailed models may be needed to adequately account for interspecific physiological differences.     

Lake of flies, or lake of fish? A trophic model of Lake Malawi

Ecosystem-focused models have, for the first time, become available for the combined demersal and pelagic components of a large tropical lake ecosystem, Lake Malawi. These provide the opportunity to explore continuing controversies over the production efficiencies and ecological functioning of large tropical lakes. In Lake Malawi these models can provide important insight to the effect of fishing on fish composition, and the potential competition that the lakefly Chaoborus edulis may have with fisheries production. A mass-balanced trophic model developed for the demersal fish community of the southern and western areas of Lake Malawi was integrated with an existing trophic model developed for the open-water pelagic. Input parameters for the demersal model were obtained from a survey of fish distributions, fish food consumption studies, and from additional published quantitative and qualitative information on the various biotic components of the community. The model was constructed using the Ecopath approach and software. The graphically presented demersal food web spanned four trophic levels and was based primarily on consumption of detritus, zooplankton and sedimented diatoms. Zooplankton was imported into the system at trophic levels three and four through fish predation on carnivorous and herbivorous copepods and Chaoborus larvae. It is proposed that the primary consumption of copepods was by fish migrating into the pelagic zone. Chaoborus larvae in the demersal were probably consumed near the lakebed as they conducted a daily migration from the pelagic to seek refuge in the sediments. This evidence for strong benthic-pelagic coupling provided the opportunity for linking the demersal model to the existing model for the pelagic community so producing the first model for the complete ecosystem. Energy fluxes through the resulting combined model demonstrated that the primary import of biomass to the demersal system was detritus of pelagic origin (72.1%) and pelagic zooplankton (10.6%). Only 15.8% of the biomass consumed within the demersal system was of demersal origin. Lakefly production is efficiently utilised by the lake fish community, and any attempt to improve fishery production through introduction of a non-native plantivorous fish species would have a negative impact on the stability and productivity of the lake ecosystem.     

The influence of symbiont type on photosynthetic carbon flux in a model cnidarian–dinoflagellate symbiosis

We measured the relationship between symbiont diversity, nutritional potential, and symbiotic success in the cnidarian–dinoflagellate symbiosis, by infecting aposymbiotic (i.e. symbiont-free) specimens of the model sea anemone Aiptasia sp. with a range of Symbiodinium types. Four cultured heterologous Symbiodinium types (i.e. originally isolated from other host species) were used, plus both cultured and freshly isolated homologous zooxanthellae (i.e. from Aiptasia sp.). Rates of photosynthesis, respiration, and symbiont growth were measured during symbiosis establishment and used to estimate the contribution of the zooxanthellae to the animal’s respiratory carbon demands (CZAR). Anemones containing Symbiodinium B1 (both homologous and heterologous) tended to attain higher CZAR values and hence benefit most from their symbiotic partners. This was despite Symbiodinium B1 not achieving the highest cell densities, though it did grow more quickly during the earliest stages of the infection process. Rather, the heterologous Symbiodinium types A1.4, E2, and F5.1 attained the highest densities, with populations of E2 and F5.1 also exhibiting the highest photosynthetic rates. This apparent success was countered, however, by very high rates of symbiosis respiration that ultimately resulted in lower CZAR values. This study highlights the impact of symbiont type on the functionality and autotrophic potential of the symbiosis. Most interestingly, it suggests that certain heterologous symbionts may behave opportunistically, proliferating rapidly but in a manner that is energetically costly to the host. Such negative host–symbiont interactions may contribute to the host–symbiont specificity seen in cnidarian–dinoflagellate symbioses and potentially limit the potential for partner switching as an adaptive mechanism.     

Multi‐phase non‐steady state equilibrium model for evaluation of environmental fate of organic chemicals

A simple mathematical fate model, Multi‐Phase Non‐Steady State Equilibrium Model (MNSEM) is proposed to evaluate distribution, persistence, and concentrations of chemicals in a model environment consisting of air, water, soil and sediment phases. The model is applied to evaluation of environmental fate and concentration of trichloroethylene and 1,4‐dichlorobenzene under generic conditions representative of Japan.

Evaluated chemical concentrations in air are within a factor of 3 of average values in Japanese atmosphere, and evaluated concentrations in water, sediment, or fish are greater than an order of magnitude below detection limits in real environments, so that evaluated concentrations are in reasonable agreement with environmental measurement data in Japan.

Although MNSEM is not a model for site‐specific evaluation of environmental fate, results suggested that this model is an adequate method to aid in evaluation of fate of chemicals under generic environment conditions. Evaluated concentration‐profiles may be used to estimate average chemical exposure concentrations for humans and the environment.