A model for measuring leaf growth rate of vegetative shoot in the seagrass, Zostera marina

A new model for determining leaf growth in vegetative shoots of the seagrass Zostera marina (eelgrass) is described. This model requires the weights of individual mature and immature whole leaves and leaf plastochrone interval (P_L) as parameters, differing from the conventional leaf marking technique (CLM) that requires cutting and separation between new and old tissue of leaves. The techniques required for the model are the same as for the plastochrone method, but the parameters differ between both methods in use of the weight of individual immature leaves. In a mesocosm study, eelgrass growth was examined, and parameters for the new model and plastochrone method (the weights of individual mature and immature leaves and P_L) were measured. Leaf growth rate was measured using the CLM and determined by the new method and the plastochrone method. The results were then compared between the CLM, the new model, and the plastochrone method. The results obtained with the new model were similar to those obtained with the CLM. However, the results of the plastochrone method differed from those of the CLM, while the weight of immature leaves varied seasonally. The new model was also used to determine leaf growth in a natural eelgrass bed in Mikawa Bay, Japan, and revealed the growth rates in all shoots and those of different ages. This method would be advantageous as an accurate means of direct measurement in fieldwork, and should therefore be a useful tool for monitoring seagrass growth.     

A simple individual model for simulating weight gain dynamics in response to intake rate and daily behavior

It is often necessary to estimate the weight that an individual may be capable of gaining depending on its degree of activity. A simple individual-based model was developed for studying the dynamics of weight in terms of daily behavior and ingestion rate. It was based on the balance between the individual's energy intake and the cost of its daily activities. Costs depend on the weight of the individual and the photoperiod, as well as on the time spent on each activity. Different combinations of ingestion rate, individual's weight, photoperiod length, and time assigned to different activities were used for simulating the weight dynamics, taking the species Rhea americana as a study case. Estimations of energetic costs of the activities were obtained from specialized literature. Using different photoperiods and individual behaviors, the model yields field metabolic rate (FMR) values in agreement with those obtained from direct measurements for other omnivorous bird species.     

Ecotoxicology and population dynamics: Using DEBtox models in a Leslie modeling approach

Although the ecological risks of toxic chemicals are usually assessed on the basis of individual responses, such as survival, reproduction or growth, ecotoxicologists are now attempting to assess the impact of environmental pollution on the dynamics of naturally exposed populations. The main issue is how to infer the likely impact on the population of the toxic effects observed at the individual level. Dynamic energy budget in toxicology (DEBtox) is the most user-friendly software currently available to analyze the experimental data obtained in toxicity tests performed on individuals. Because toxic effects are diverse and because the sensitivity of individuals varies considerably depending on life-cycle stage, Leslie models offer a convenient way of predicting toxicant effects on population dynamics.In the present study, we first show how parameter inputs, estimated from individual data using DEBtox, can be coupled using a Leslie matrix population model. Then, using experimental data obtained with Chironomus riparius, we show how the effects of a pesticide (methiocarb) on the population growth rate of a laboratory population can be estimated. Lastly, we perform a complex sensitivity analysis to pinpoint critical age classes within the population for the purposes of the field management of populations.     

Application of a temperature-dependent von Bertalanffy growth model to bullhead (Cottus gobio)

The most studied and commonly applied model of fish growth is the von Bertalanffy model. However, this model does not take water temperature into account, which is one of the most important environmental factors affecting the life cycle of fish, as many physiological processes that determine growth, e.g. metabolic rate and oxygen supply, are directly influenced by temperature. In the present study we propose a version of the von Bertalanffy growth model that includes mean annual water temperatures by correlating the growth coefficient, k, explicitly and the asymptotic length, L_∞, implicitly to water temperature. All relationships include parameters with an obvious biological relevance that makes them easier to identify. The model is used to fit growth data of bullhead (Cottus gobio) at different locations in the Bez River network (Drme, France). We show that temperature explains much of the growth variability at the different sampling sites of the network.     

A model approach to evaluate the effect of temperature and food concentration on individual life-history and population dynamics of Daphnia

We present a model framework for the simulation of growth and reproduction of Daphnia at varying conditions of food concentration and temperature. The core of our framework consists of an individual level model that simulates allocation of assimilated carbon into somatic growth, maintenance costs, and reproduction on the basis of a closed carbon budget. A fixed percentage of assimilated carbon is allocated into somatic growth and maintenance costs. Special physiological adaptations in energy acquisition and usage allow realistic model performance even at very low food concentrations close to minimal food requirements. All model parameters are based on physiological measures taken from the literature. Model outputs were thoroughly validated on data from a life-table experiment with Daphnia galeata. For the first time, a successful model validation was performed at such low food concentrations. The escalator boxcar train (EBT) was used to integrate this individual level model into a stage-structured population model. In advance to previous applications of the EBT to Daphnia we included an additional clutch compartment into the model structure that accounts for the characteristic time delay between egg deposition and hatching in cladocerans. By linking two levels of biological organisation, this model approach represents a comprehensive framework for studying Daphnia both at laboratory conditions and in the field. We compared outputs of our stage-structured model with predictions by two other models having analogous parameterisation: (i) another individual level Daphnia model (Kooijman–Metz model) and (ii) a classical unstructured population model. In contrast to our Daphnia model, the Kooijman–Metz model lacks the structure to account for the optimisation of energy acquisition and maintenance requirements by individual daphnids. The unstructured population model showed different patterns of population dynamics that were not in concordance with typical patterns observed in the field. Thus, we conclude our model provides a comprehensive tool for the simulation of growth and reproduction of Daphnia and corresponding population dynamics.     

Allowing macroalgae growth forms to emerge: Use of an agent-based model to understand the growth and spread of macroalgae in Florida coral reefs,with emphasis on Halimeda tuna

The growth patterns of macroalgae in three-dimensional space can provide important information regarding the environments in which they live, and insights into changes that may occur when those environments change due to anthropogenic and/or natural causes. To decipher these patterns and their attendant mechanisms and influencing factors, a spatially explicit model has been developed. The model SPREAD (SPatially-explicit Reef Algae Dynamics), which incorporates the key morphogenetic characteristics of clonality and morphological plasticity, is used to investigate the influences of light, temperature, nutrients and disturbance on the growth and spatial occupancy of dominant macroalgae in the Florida Reef Tract. The model species, Halimeda and Dictyota spp., are modular organisms, with an “individual” being made up of repeating structures. These species can also propagate asexually through clonal fragmentation. These traits lead to potentially indefinite growth and plastic morphology that can respond to environmental conditions in various ways. The growth of an individual is modeled as the iteration of discrete macroalgal modules whose dynamics are affected by the light, temperature, and nutrient regimes. Fragmentation is included as a source of asexual reproduction and/or mortality. Model outputs are the same metrics that are obtained in the field, thus allowing for easy comparison. The performance of SPREAD was tested through sensitivity analysis and comparison with independent field data from four study sites in the Florida Reef Tract. Halimeda tuna was selected for initial model comparisons because the relatively untangled growth form permits detailed characterization in the field. Differences in the growth patterns of H. tuna were observed among these reefs. SPREAD was able to closely reproduce these variations, and indicate the potential importance of light and nutrient variations in producing these patterns.     

Individual-based modeling of flooding and salinity effects on a coastal swamp forest

Coastal swamps are among the rapidly vanishing wetland habitats in Louisiana. Increased flooding, nutrient and sediment deprivation, and salt-water intrusion have been implicated as probable causes of the decline of coastal swamps. We developed a two-species individual-based forest succession model to compare the growth and composition of a cypress-tupelo swamp under various combinations of flooding intensity and salinity levels, using historical time-series of stage and salinity data as inputs. Our model simulates forest succession over 500 years by representing the growth, mortality, and reproduction of individual Taxodium distichum (baldcypress) and Nyssa aquatica (water tupelo) trees in a 1-km² spatial grid of 10 m × 10 m cells that vary in water levels and salinity through differences in elevation. We independently adjusted the elevations of each cell to obtain different grid-wide mean elevations and standard deviations of elevation; this affected the temporal and spatial pattern of flooding. We calibrated the model by adjusting selected parameters until averaged basal area, stem density and wood production rates under two different mean elevations (partially versus highly flooded) were qualitatively similar to comparable values reported for swamps in the literature. Corroboration involved comparing model predictions to four well-monitored contrasting habitat sites within the Maurepas Basin, Louisiana, USA. Model predictions of both species combined showed the same patterns among sites as the data, but the model overestimated wood production and the dominance of T. distichum. Exploratory simulations predicted that increased flooding leads to swamps with reduced basal areas and stem densities, while increased salinity resulted in lower basal areas at low salinity concentration (∼1-3 psu) and complete tree mortality at higher salinity concentrations (∼2-6 psu). Our model can provide insight into the succession dynamics of coastal swamps and information for the effective design of restoration actions.     

Influence of low and decreasing food levels on Daphnia-algal interactions: Numerical experiments with a new dynamic energy budget model

Based on numerical experiments with a new physiologically structured population model we demonstrate that predator physiology under low food and under starving conditions can have substantial implications for population dynamics in predator-prey interactions. We focused on Daphnia-algae interactions as model system and developed a new dynamic energy budget (DEB) model for individual daphnids. This model integrates the κ-rule approach common to net assimilation models into a net-production model, but uses a fixed allocation of net-productive energy in juveniles. The new DEB-model agrees well with the results of life history experiments with Daphnia. Compared to a pure κ-rule model the new allocation scheme leads to significant earlier maturation at low food levels and thus is in better agreement with the data. Incorporation of the new DEB-model into a physiologically structured population model using a box-car elevator technique revealed that the dynamics of Daphnia-algae interactions are highly sensitive to the assumptions on the energy allocation of juveniles under low food conditions. Additionally we show that also other energy allocation rules of our DEB-model concerning decreasing food levels and starving conditions at the individual level have strong implications for Daphnia-algae interactions at the population level. With increasing carrying capacity of algae a stable equilibrium with coexistence of Daphnia occurs and algae shifts to limit cycles. The amplitudes of the limit cycles increase with increasing percentage of sustainable weight loss. If a κ-rule energy allocation is applied to juveniles, the stable equilibrium occurs for a much narrower range of algal carrying capacities, the algal concentration at equilibrium is about 2 times larger, and the range of algae carrying capacities at which daphnids become extinct extends to higher carrying capacities than in the new DEB-model. Because predator-prey dynamics are very sensitive to predator physiology under low food and starving conditions, empirical constraints of predator physiology under these conditions are essential when comparing model results with observations in laboratory experiments or in the field.     

A discrete model for estimating the development time from egg to infecting larva of Ostertagia ostertagi parametrized using a fuzzy rule-based system

Ostertagia ostertagi is a nematode, predominantly affecting cattle in the Pampean region of Argentina. A mathematical model parametrized using fuzzy rule-based systems of the Takagi-Sugeno-Kant type (FTSK) for estimating the development time from egg to infecting larval stage L3 of the gastrointestinal parasite O. ostertagi is here proposed. The estimation of development time of O. ostertagi is essential for the generation of appropriate control mechanisms, since this provides information about the time when parasites are ready to migrate to pastures. For the purpose of reflecting the natural environmental conditions, the mean daily temperature is taken as the main and only regulator of the development time. Humidity conditions are considered to be sufficient for the normal development of the larvae. Hence the individual's daily growth is a function of its length and the mean temperature recorded on the previous day. It is expressed in terms of a difference equation with fuzzy parameters, which are defined using laboratory data. Model outputs are tested against results of field experiments. Simulation results are very satisfactory, yielding a mean estimation error (MEE) of 0.64 weeks, with variance 0.34, and a determination coefficient R² = 0.74. The model clearly exhibits an inverse relationship between development time and temperature both in controlled and in field conditions. It also exhibits a very sensitive response both to the order in which the temperature sequence occurs, - reproducing the differences observed between spring and autumn - and to the amplitude of the temperature range.     

Development and validation of an individual based Daphnia magna population model: The influence of crowding on population dynamics

An individual-based model was developed to predict the population dynamics of Daphnia magna at laboratory conditions from individual life-history traits observed in experiments with different feeding conditions. Within the model, each daphnid passes its individual life cycle including feeding on algae, aging, growing, developing and – when maturity is reached – reproducing. The modelled life cycle is driven by the amount of ingested algae and the density of the Daphnia population. At low algae densities the population dynamics is mainly driven by food supply, when the densities of algae are high, the limiting factor is “crowding” (a density-dependent mechanism due to chemical substances released by the organisms or physical contact, but independent of food competition).     

Modeling net primary production of a fast-growing forest using a light use efficiency model

As interest grows in the quantification of global carbon cycles, Light Use Efficiency (LUE) model predictions of the forest net primary production (NPP) are being developed at an accelerating rate. Such models can provide useful predictions at large scales, but evaluating their performance has been difficult. In this study, a remote sensing-based LUE model was established to estimate forest NPP. Using the forest inventory data (FID) from the regional forest inventory survey in China and established allometric biomass equations, we calculated the biomass, the biomass increment, and the NPP of Eucalyptus urophylla (E. urophylla) plantation plots in the forestry jurisdiction of the Leizhou Forestry Bureau, Southern China. The FID-based NPP and the NPP from LUE model predictions were then compared to each other. Results show that the NPP from model predictions at a spatial resolution of 30 m × 30 m varied from 0 to 265 gC/(m² month) and showed regional differences. In addition, the stand age had variable effects on the average individual biomass of the E. urophylla plantation plots. The average individual biomass of the young and mid-age forests increased exponentially and logarithmically with the stand age (R² = 0.9178 and R² = 0.8683), respectively. For young and mid-age E. urophylla plantation plots, the LUE model-predicted NPP was fairly consistent with the FID-based NPP, but the model predictions of the NPP were higher than the estimates from FID. Through the analysis of the causes of uncertainty and the possible reasons for the discrepancy between the model-based NPP and FID-based NPP, the FID-derived estimates provided a foundation for model evaluation.     

Integrating farming techniques in an ecological matrix model: Implementation on the primrose (Primula vulgaris)

Several studies have proven the importance of field margins in sustaining biodiversity and other work has been done on the effect of field management on field margin flora. However few models have been built to predict the effects of field management on the flora. Our project addresses this need for a model capable of predicting the effect of cropping techniques and their timing on the flora of field margins. Primula vulgaris is a biodiversity indicator, characteristic of undisturbed flora and found in field margins and woodlands: its population has been declining for several years. We created a temporal matrix model of P. vulgaris populations on field margins, taking into account the effects of field, field margin and roadside management based on literature and expert knowledge. We then analysed its sensitivity to demographic parameters by comparing lambda (growth rate) sensitivity and elasticity. We compared the management parameter effect using the relative growth rate of the population after 6 years of simulation. Sensitivity analysis to biological parameters showed the importance of adult survival and seed production and germination. Results show that P. vulgaris is particularly sensitive to broad-spectrum herbicides and that other management techniques like early mowing, scything and scrub-killer (diluted broad-spectrum herbicide or specific herbicide) are less aggressive. Our simulations show that management of cash crops in Brittany is too aggressive for P. vulgaris populations and that 4-5 years of grassland in the adjacent field are necessary to maintain populations.     

A process-based model of nitrogen cycling in forest plantations: Part I. Structure,calibration and analysis of the decomposition model

We present a new decomposition model of C and N cycling in forest ecosystems that simulates N mineralisation from decomposing tree litter. It incorporates a mechanistic representation of the role of soil organisms in the N mineralisation-immobilisation turnover process during decomposition. We first calibrate the model using data from decomposition of ¹⁴C-labelled cellulose and lignin and ¹⁴C-labelled legume material and then calibrate and test it using mass loss and N loss data from decomposing Eucalyptus globulus residues. The model has been linked to the plant production submodel of the G’DAY ecosystem model, which previously used the CENTURY decomposition submodel for simulating C and N cycling. The key differences between this new decomposition model and the previous one, based on the CENTURY model, are: (1) growth of microbial biomass is the process that drives N mineralisation-immobilisation, and microbial succession is simulated; (2) decomposition of litter can be N-limited, depending on soil inorganic N availability relative to N requirements for microbial growth; (3) ‘quality’ of leaf and fine root litter is expressed in terms of biochemically measurable fractions; (4) the N:C ratio of microbial biomass active in decomposing litter is a function of litter quality and N availability; and (5) the N:C ratios of soil organic matter (SOM) pools are not prescribed but are instead simulated output variables defined by litter characteristics and soil inorganic N availability. With these modifications the model is able to provide reasonable estimates of both mass loss and N loss by decomposing E. globulus leaf and branch harvest residues in litterbag experiments. A sensitivity analysis of the decomposition model to selected parameters indicates that parameters regulating the stabilisation of organic C and N, as well as those describing incorporation of soil inorganic N in Young-SOM (biochemical immobilisation of N) are particularly critical for long-term applications of the model. A parameter identifiability analysis demonstrates that simulated short-term C and N loss from decomposing litter is highly sensitive to three model parameters that are identifiable from the E. globulus litterbag data.     

A parsimonious optimal foraging model explaining mortality patterns in Serengeti wildebeest

Based on data collected over 24 years in the Serengeti in Tanzania, Sinclair and Arcese (1995) indicated that the sensitivity of blue wildebeest Connochaetes taurinus to predation risk by lions Panthera leo may cause them to change habitats between open (low risk) and wooded (risky) habitats. They found that, in poor rainfall years, predators kill wildebeest that are in better condition than those that die of natural causes. In good rainfall years, predators kill wildebeest that are in worse condition than those that die of natural causes. Sinclair and Arcese (1995) proposed the “predation-sensitive food” hypothesis. This hypothesis suggests that, as food becomes limiting, animals take greater risks to obtain more food, and some of these animals are killed. I propose a more parsimonious hypothesis based on the marginal value theorem that is consistent with the observations made by Sinclair and Arcese (1995). Wildebeest follow a single decision rule in good and poor rainfall years, viz. move when foraging elsewhere increases your rate of intake of nutritious food. Similarly, predators follow a single decision rule in good and poor rainfall years, viz. take the prey item that maximizes the intake of energy per unit effort expended. This parsimonious model does not require differences in predator sensitivity as required by Sinclair and Arcese's (1995) model. I indicate ways in which my model can be falsified.     

Variational model of microorganism polyculture development without re-supply of mutually irreplaceable resources

Stationary stage of accumulating cultures of Pseudomonas aeruginosa dissociants is described by variational model of consumption and growth. The “generalized entropy” as a goal function is used. Model's parameters are the dissociants requirements for basic nutrients: carbon, nitrogen and phosphorus. Using this model we calculate the limitation ranges for arbitrary combinations of environmental resource factors and the community population sizes at a stationary stage of growth as functions of the resources that constrain the growth. The requirements values obtained from experimental data allowed us to predict the limiting resources and dissociant's abundances. Our estimations match experimental results. The possibility of composition control is discussed in paper.     

A spatiotemporal individual-based fish model to investigate emergent properties at the organismal and the population level

A spatiotemporal individual-based model (IBM) of roach (Rutilus rutilus) including bioenergetic principles was used to study emergent properties at the individual and the population level which appeared as a result of resource allocation and time scheduling of activities related to maintenance, growth, and reproduction in a seasonally changing environment. The model was used as a virtual laboratory to consider the impact of various parameters on vital rates and spatial behaviour of roach, which is particularly difficult to study in the field. The parameterisation based on field studies performed at Lake Belau (Schleswig-Holstein, Germany) and laboratory measurements. This allowed us to explore the relationship between population structure and environmental heterogeneity on an integrated base. At the individual level emergent properties such as spatial behaviour, growth, and food consumption could be identified. Emergent properties at the population level resulted as phenotypic consequences of a trophic bottleneck, the influence of lake morphology on the phenotype as well as size-dependent winter mortality rates and post-reproductive mortality rates.     

Integrating soil carbon cycling with that of nitrogen and phosphorus in the watershed model SWAT: Theory and model testing

In this paper we describe and test a sub-model that integrates the cycling of carbon (C), nitrogen (N) and phosphorus (P) in the Soil Water Assessment Tool (SWAT) watershed model. The core of the sub-model is a multi-layer, one-pool soil organic carbon (S_C) algorithm, in which the decomposition rate of S_C and input rate to S_C (through decomposition and humification of residues) depend on the current size of S_C. The organic N and P fluxes are coupled to that of C and depend on the available mineral N and P, and the C:N and N:P ratios of the decomposing pools. Tillage explicitly affects the soil organic matter turnover rate through tool-specific coefficients. Unlike most models, the turnover of soil organic matter does not follow first order kinetics. Each soil layer has a specific maximum capacity to accumulate C or C saturation (S_x) that depends on texture and controls the turnover rate. It is shown in an analytical solution that S_x is a parameter with major influence in the model C dynamics. Testing with a 65-yr data set from the dryland wheat growing region in Oregon shows that the model adequately simulates the S_C dynamics in the topsoil (top 0.3 m) for three different treatments. Three key model parameters, the optimal decomposition and humification rates and a factor controlling the effect of soil moisture and temperature on the decomposition rate, showed low uncertainty as determined by generalized likelihood uncertainty estimation. Nonetheless, the parameter set that provided accurate simulations in the topsoil tended to overestimate S_C in the subsoil, suggesting that a mechanism that expresses at depth might not be represented in the current sub-model structure. The explicit integration of C, N, and P fluxes allows for a more cohesive simulation of nutrient cycling in the SWAT model. The sub-model has to be tested in forestland and rangeland in addition to agricultural land, and in diverse soils with extreme properties such high or low pH, an organic horizon, or volcanic soils.     

Analysis of annual fluctuations of C. nodosa in the Venice lagoon: Modeling approach

A simple simulation model was developed to describe the growth trends of Cymodocea nodosa (Ucria) Ascherson based on data sets from the Venice lagoon. The model reproduces the seasonal fluctuations in the above and belowground biomass and in shoot density. The modeling results are in good agreement with data on net production, growth rates and chemical–physical parameters of water. It was assumed that light and temperature are the most important factors controlling C. nodosa development, and that the growth was not limited by nutrient availability. The aim was to simulate biomass production as a function of external forcing variables (light, water temperature) and internal control (plant density). A series of simulation experiments were performed with the basic model showing that among the most important phenomena affecting C. nodosa growth are: (1) inhibition of production and recruitment of new shoots by high temperature and (2) light attenuation due to seasonal fluctuation.     

A population model for the peach fruit moth, Carposina sasakii Matsumura (Lepidoptera: Carposinidae), in a Korean orchard system

A population model for the peach fruit moth, Carposina sasakii Matsumura, was constructed to understand the population dynamics of this pest species and to develop an effective management strategy for various orchard (apple, peach, apple + peach) systems. The model was structured by the five developmental stages of C. sasakii: egg, larva, pupa, larval-cocoon (overwintering larva), and adult. The model consisted of a series of component models: (1) a bimodal spring adult emergence model, (2) an adult oviposition model, (3) stage emergence models of eggs, larvae, and pupae, (4) a larval survival rate model in fruits, (5) a larval-cocoon formation model, and (6) an insecticide effect model. Simulations using the model described the typical patterns of C. sasakii adult abundance in various orchard systems well, and was specific to the composition of host plants: three adult abundance peaks (first peak, mid-season peak, and last peak) a year with decreased peaks after the first peak in monoculture orchards of late apple, two adult peaks a year with a much higher last peak in monoculture orchards of early peach, and three adult peaks a year with much higher later peaks in mixed orchards of late apple and early peach. The average deviation between model outputs and actual records for first and second adult peak dates was 2.8 and 3.9 d, respectively, in simulations without an insecticide effect. The deviation decreased when insecticide effects were incorporated into the model. We also performed a sensitivity analysis of our model, and suggest possible applications of the model.     

Estimating dyad association probability under imperfect and heterogeneous detection

In animal behaviour studies, association indices estimate the proportion of time two individuals (i.e. a dyad) spend in association. In terms of dyads, all association indices can be interpreted as estimators of the probability that a dyad is associated. However, traditional indices rely on the assumptions that the probability to detect a particular individual (p) is either approximately one and/or homogeneous between associated and not associated individuals. Based on marked individuals we develop a likelihood based model to estimate the probability a dyad is associated (ψ) accounting for p < 1 and possibly varying between associated and not associated individuals. The proposed likelihood based model allows for both individual and dyadic missing observations. In addition, the model can easily be extended to incorporate covariate information for modeling p and ψ. A simulation study showed that the likelihood based model approach yield reasonably unbiased estimates, even for low and heterogeneous individual detection probabilities, while, in contrast, traditional indices showed moderate to strong biases. The application of the proposed approach is illustrated using a real data set collected from a population of Commerson's dolphin (Cephalorhynchus commersonii) in Patagonia Argentina. Finally, we discuss possible extensions of the proposed model and its applicability in animal behaviour and ecological studies.