Consideration of translocation into a growth model of a plant organ

Taking account of the Bertalanffy's differential equation on animal growth, plant growth is also considered as the net result of anabolism and catabolism. When we, however, consider the growth of a plant organ, it is necessary to add a term of translocation because it plays an important role in the growth of plant organs, such as leaf and fruit. Considering translocation, therefore, a growth model of a plant organ was proposed on the basis of the compartment model for estimating the carbon balance in the organ by using the experimental data on translocation, photosynthesis and respiration of a tropical fruit of durian (Durio zibethinus Murray). The present growth model of a plant organ belongs to an extended Bertalanffy's growth equation, and was possible to be transformed into the simple Bertalanffy's growth equation on the basis of the proportionality between the growth and translocation rates. The Bertalanffy's growth equation of a plant organ was also possible to apply to that of the whole plant on the assumption of the allomeric relationship between a plant organ and the whole plant.     

Zooplankton population model coupled to a biogeochemical model of the North Western Mediterranean Sea ecosystem

A stage structured population (SSP) model based on Fennel's [Fennel, W., 2001. Modelling copepods with links to circulation models. Journal of Plankton Research, 23, 1217–1232] equations is applied to Centropages typicus (Kröyer), a dominant copepod species of the North Western Mediterranean Sea (NWMS) and a prey of small pelagic fish. The model considers five groups of stages and development rates are represented by a mechanistic formulation depending on individual specific growth in each stage. Individual growth is calculated from the individual energy budget depending on food availability and temperature.     

Introducing effects of temperature and CO2 elevation on tree growth into a statistical growth and yield model

Impacts of elevated temperature and CO₂ on tree growth were introduced into a statistical growth and yield model for Finnish conditions based on corresponding predictions obtained from a physiological growth model. This one-way link between models was made by means of species-specific transfer functions describing the increase in stem volume growth of trees as a function of elevated temperature and CO₂, stand density and the tree's competition status in a stand of Scots pine (Pinus sylvestris), silver birch (Betula pendula) and Norway spruce (Picea abies). This method allows the inner dynamics of the statistical model to be followed when the impacts of temperature and CO₂ elevation on tree growth are introduced into the calculation of volume growth and further allocated between diameter and height growth. In this way compatibility with previous predictions of tree growth by means of statistical models and related model systems under current climatic conditions could be retained.The performance of the statistical model with species-specific transfer functions was evaluated by comparing its predictions with corresponding predictions given by a physiological model under conditions of elevated temperature and CO₂. These calculations revealed that the growth response of individual trees to elevated temperature and CO₂ can be introduced into the statistical model from a physiological growth model with an outcome that results in fairly satisfactory growth responses at the stand level as well.     

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.     

A simple Lagrangian model to simulate temporal variability of algae in the Elbe River

We present a five-year (1997–2001) numerical simulation of daily mean chlorophyll a concentrations at station Geesthacht Weir on the lower Elbe River (Germany) using an extremely simple Lagrangian model driven by (a) water discharge, global radiation, water temperature, and (b) silica observations at station Schmilka in the upper reach of the Elbe River. Notwithstanding the lack of many mechanistic details, the model is able to reproduce observed chlorophyll a variability surprisingly well, including a number of sharp valleys and ascents/descents in the observed time series. The model's success is based on the assumption of three key effects: prevailing light conditions, sporadic limitation of algal growth due to lack of silica and algae loss rates that increase above an empirically specified temperature threshold of 20 °C. Trimmed-down model versions are studied to analyse the model's success in terms of these mechanisms.In each of the five years the model consistently fails, however, to properly simulate characteristic steep increases of chlorophyll a concentrations after pronounced spring minima. Curing this model deficiency by global model re-calibration was found to be impossible. However, suspension of silica consumption by algae for up to 10 days in spring is shown to serve as a successful placeholder for processes that are disregarded in the model but apparently play an important role in the distinctly marked period of model failure. For the remainder of the year the very simple model was found to be adequate.     

Models of withdrawing renewable and non-renewable resources based on Odum's energy systems theory and Daly's quasi-sustainability principle

This paper presents a theoretical model of withdrawing resources based on Odum's energy systems diagrams. According to the theory of a general pulsing principle, withdrawing resources changes in time shifting from the initial phases of growth and maturity to the phases of descent and low energy restoration. A simulation was performed in order to hypothesize potential future trends of withdrawing renewable and non-renewable resources and to show some aspects of their sustainability–unsustainability, respectively. According to Odum's theory, after the rapid growth of the last century, our civilization is living in a climax transition phase and it is now approaching a descent phase. A “way down” will be necessary due to the exhaustion of non-renewable and to the limited use of renewable resources. An integrated “renew–non-renew” model was developed by Odum to show how a “business as usual” trend will bring us to a drastic transition to a world that uses scarce renewable resources. Nevertheless, a different choice is possible, based on Daly's concept of quasi-sustainability that can inspire a new model. The latter argued that the exploitation of a non-renewable resource must be paired with a compensating investment in a renewable substitute. Our model shows that we can use non-renewable resources better to considerably improve our capacity of capturing renewable resources in the future. We present this as a necessary condition to address a sustainable environmental policy.     

Diameter growth models for mixed-species stands of Coastal British Columbia including thinning and fertilization effects

In this study, diameter growth models for three species growing in mixed-stands of Coastal British Columbia (BC), Canada, under a variety of silvicultural treatments were developed. The three species were: Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and western redcedar (Thuja plicata Donn). A Box and Lucas model (1959) was initially fitted to the diameter growth series for each tree, as this model is very flexible and was based on processes reflective of the metabolic processes governing tree growth. Next, a random coefficients modelling approach (i.e., parameter prediction approach) was used to modify the estimated parameters for each species using functions of tree size and stage of development, site productivity, and inter-tree competition variables, while accounting for temporal correlation within trees. Impacts of fertilization on diameter growth were estimated by including the time since fertilization as an additional variable. Since state variables that are changed as a result of thinning were already in the model, accurate results post-thinning were obtained with no changes to the model. For the combined effects of thinning and fertilization, a two-step additive approach was used, where the state variables were changed following thinning and the diameter increment was modified for fertilization using the time since fertilization variable. Results indicated that multiple treatments sustain a change in growth for a longer time period following treatment than thinning or fertilization alone.     

Optimal resource management control for CO2 emission and reduction of the greenhouse effect

In recent years, the world has witnessed an ever-growing concern towards global warming caused by greenhouse gases, such as carbon dioxide (CO₂). In order to reduce the emissions of CO₂ without limiting economic growth, substantial investments should target the development of clean technology and the expansion of forested areas. Considering the limited availability of resources, investments must be used in the most effective way. The present work proposes a method to efficiently manage these resources by applying the optimal control theory to a new mathematical model that describes the dynamics of the atmospheric CO₂. The contributions of this work are twofold: (1) present a model that describes the dynamic relation of CO₂ emission with investment in reforestation and clean technology and (2) present a method to efficiently manage the available resources by casting an optimal control problem. The mathematical model uses ordinary differential equations to relate the production of CO₂ with forest area and Gross Domestic Product (GDP). The model parameters are adjusted to fit the actual published data. Given an appropriate performance index, the optimal solution is found by numerically solving the Two-Point Boundary Value Problem (TPBVP) that arises from the application of Pontriagyn's Maximum Principle. The sensitivity of the obtained numerical solution is evaluated with respect to the uncertainties in the model parameters. The main objective of this work is to provide a quantitative tool for the efficient allocation of resources to reduce the greenhouse effect caused CO₂ emissions.     

Effects of self-fertilisation and other factors on the early development of the scallop Pecten maximus

Adult Pecten maximus (L.) were dredged off north-east Anglesey, Wales, UK, during 1981. A 2×5 factorial mating was carried out involving self- and cross-fertilisation and the use of stripped spermatozoa. Assessments of yield, normality, and larval size were made at the D larva stage and larval size and mortality were measured after a fortnight's growth of the veligers. Underlying genetic variation was evident at all stages, with egg and sperm generally having a significant interactive effect. Cultures sired with stripped spermatozoa had fewer larvae, with more abnormality, grew slower and suffered higher mortality than most other cultures. Larvae from selfed cultures grew significantly slower than all other larvae. Data from past larval cultures also show that selfed larvae have a reduced growth rate. it is suggested that stripped spermatozoa may interfere with egg and sperm interaction at fertilisation, thus reducing the viability of larvae. On the other hand, the poor growth rate of selfed larvae is probably due to overall reduced heterozygosity compared to outbred larvae.     

Additive partitioning of Rao's quadratic diversity: a hierarchical approach

Ecologists have long recognized three different components of species diversity: alpha or within-community diversity (α), beta or between-community diversity (β) and gamma or total species diversity in a region (γ). In this framework, β-diversity has been traditionally linked to the other diversity components through a multiplicative model so that it can be expressed as the ratio between γ-diversity and average α-diversity in a set of plots. Yet, more recently, ecologists are starting to partition diversity using the lesser known approach that α- and β-diversities sum to give the γ-diversity. This additive diversity partitioning is based on the decomposition of concave diversity measures for which the total diversity in a pooled set of communities exceeds (or equals) the average diversity within communities. In this paper, first, I shortly revise additive diversity partitioning for traditional diversity measures that are computed from species relative abundances. Next, I show that, under some specific circumstances, the same model can be extended to Rao's quadratic entropy, a measure that combines species relative abundances and pairwise interspecies differences. Finally, in the framework of taxonomic diversity, Rao's quadratic entropy has another decomposition: the sum over the Simpson indices at all the taxonomic levels. Thus, I show that, combining both partitioning models, the contribution of each level in the taxonomic hierarchy to the α- β- and γ-diversity components of Rao's quadratic entropy is made explicit. The proposed diversity decomposition is illustrated with a worked example on data from a plant community on ultramafic soils in Tuscany (central Italy).     

A two-dimensional stochastic model of downy mildew of radish

A two-dimensional stochastic model that simulates the spread of disease over space and time was recently proposed by Xu and Ridout [Xu, X.M., Ridout, M.S., 1998. Effects of initial epidemic conditions, sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. Phytopathology 88, 1000–1012]. In a theoretical study, the authors showed the ability of their model to generate a broad range of disease patterns and disease progress rates. The objective of our study was to test if this theoretical approach was able to describe disease progress and the disease pattern of a specific disease, downy mildew (Peronospora parasitica) of radish (Raphanus sativus L.). Two field experiments with artificial inoculation were carried out and disease incidence and spatial pattern were assessed twice a week until disease incidence was greater than 0.25. Four model parameters were estimated by an algorithm that uses a least square regression together with an evolutionary optimisation strategy. Moran's I indices of spatial autocorrelation calculated both for measured und simulated data were significantly correlated (α = 0.05, r = 0.61). Also observed variances in measurements and in simulations were closely and significantly correlated (α = 0.05, r = 0.95). Thus, disease pattern (as assessed in terms of variance inflation and spatial autocorrelation) was well described by the model. The model accounted for 94% of the variation in the disease incidence data. It has, therefore, the potential to be developed into a forecast model for risk analysis and for decision support in plant protection. However, in the specific case of downy mildew on radish more experimental data are required for model validation and to parameterise the effects of environment on infection, sporulation and spore dispersal.     

Estimation of coral growth-rates from laboratory 45Ca-incorporation rates

Laboratory ⁴⁵Ca-incorporation rates in hermatypic coral skeletons have previously been used successfully as an index of physiological function. This laboratory method would become more meanigful if it also provided an absolute measure of coral growth rates. In two coral species, Porites compressa and Pocillopora damicornis, ⁴⁵Ca incorporation rates were obtained from short (0.5 h) laboratory incubations using apical (determined as fast growing) portions of freshly collected coral branches. ⁴⁵Ca exchange across the coenosarc was not significant and not corrected for, whereas diurnal fluctuation in ⁴⁵Ca in Pocillopora damicornis was significant and a necessary correction. A calculated surface area is used to express calcification rate. Typical growth rates calculated from the ⁴⁵Ca-incorporation rates were 20 and 6 mm/year for Porites compressa and Pocillopora damicornis, respectively. These rates are considerably higher than those previously obtained in the laboratory, and compare favorably with field growth rates — 24 and 14 mm/year, respectively.     

Growth and form in the reef-building coral Montastrea annularis

The in-situ growth rate of the reef coral Montastrea annularis on a reef at Jamaica, W. Indies was determined for a 1-year period using Alizarin Red-S staining techniques. Growth rate is correlated with water depth and growth form. The flattened growth form of M. annularis allows for continued rapid increase in colony surface area at low light intensities. The geomorphology of Jamaican reefs may in part be controlled by the population ecology of M. annularis.     

Assessing the impact of biological control of Plutella xylostella through the application of Lotka–Volterra model

The Lotka–Volterra model was applied to the population densities of diamondback moth (DBM), Plutella xylostella (L.) and its exotic larval parasitoid Diadegma semiclausum (Hellen) data that was collected earlier by icipe's DBM biological control team. The collections were done for 15 months before the release and 36 months after release of the parasitoid in two areas; in Werugha, Coast Province of Kenya and Tharuni, Central Province of Kenya, respectively. For each area in pre- and post-release periods, we estimated Lotka–Volterra model parameters from the minimization of the loss function between the theoretical and experimental time-series datasets following the Nelder-Mead multidimensional method. The model estimated a reduction in the value of the steady state of DBM population from 4.86 to 2.17 in Werugha and from 6.11 to 3.76 and 3.45 (with and without exclusion of the time before D. semiclausum recovery) in Tharuni when transiting from the pre- and post-release periods, respectively. This change was a consequence of the newly introduced parasitoid, in the areas. The study presented a successful and detailed technique for non-linear model parameters restoration which was demonstrated by the correct mimicking of empirical datasets from the classical biological control with D. semiclausum, in different areas of Kenya. The applied model has measured the parasitoids impact on the DBM biological control through a quantitative estimate of the effectiveness of the newly introduced species D. semiclausum. These equations may therefore be used as tool for decision making in the implementation for such pests’ management system strategy.     

Importance of food quantity to structural growth rate and neutral lipid reserves accumulated in Calanus finmarchicus

 Growth and developmental rates were determined for copepodids of Calanus finmarchicus (Gunnerus) from experimental seawater mesocosms in a western Norwegian fjord. The instantaneous growth rates (g) from copepodid stage I (CI) to adult ranged from 0.08 to 0.10 d⁻¹. Daily per capita mortality rate of the cohorts was as low as 0.012 d⁻¹ (1.2% d⁻¹). At local increasing temperatures (5.1 to 8.3 °C), development was equiproportional, and the cumulative median development time from egg to CV was approximately 65 d. CV moulted to males and females, and egg production was initiated. Enhancement of food resources by nutrient addition caused a 23.4% increase in growth rates from CI to adult. Additionally, copepodid stages showed a generally larger body size, carbon and nitrogen content and total storage lipid content (wax esters + triacylglycerols) in response to enhanced resources. Our data support an elsewhere proposed exponential-growth hypothesis; growth of the structural compartments and store lipids (mostly wax esters) was exponential during the copepodid stages. However, a sigmoidal pattern of growth best described growth of adult stages if reared at high resources, and depot lipid accumulation in late CVs and adults at high resources. Body nitrogen growth increased exponentially, however, no significant changes in nitrogen specific growth rates were found between individuals from low and high resources. CV and adults seem to have reached near-maximal weights at high resources, whereas structural weight continued to increase at low resources. Despite the differences in structural growth dynamics, cohort development was similar until the end of CV. During the onset of sexual differentiation, the male:female ratio and the adult:CV ratio were highest at high food resources, suggesting that the time used for the final moult depends on the feeding history of the copepods in relation to food quality and quantity. It appears that relatively small changes in food availability strongly influence the biochemical composition of C. finmarchicus copepodids. Received: 28 May 1999 / Accepted: 10 February 2000     

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.     

Calculation and use of selectivity coefficients of feeding: Zooplankton grazing

A straightforward method for calculating selectivity coefficients (W_ij) of predation from raw data, mortality rates of prey, filtering rates, feeding rates and electivity indices is derived. Results from a comparison of selectivity coefficients for the copepod Diaptomus oregonensis grazing under a number of experimental conditions suggest that W_ij's for size-selective feeding are invariant, a conclusion also supported by the leaky-sieve model. Recommendations are made on how to use W_ij's in linear and nonlinear feeding constructs for zooplankton and other animals.     

Modelling the impact of defoliation and leaf damage on forest plantation function and production

After presenting a short review of process-based model requirements to capture the plant dynamic response to defoliation, this paper describes the development and testing of a model of crown damage and defoliation for Eucalyptus. A model that calculates light interception and photosynthetic production for canopies that vary spatially and temporally in leaf area and photosynthetic properties is linked to the forest growth model CABALA. The process of photosynthetic up-regulation following defoliation is modelled with a simple conditional switch that triggers up-regulation when foliar damage or removal causes the ratio of functional leaf area to living tissue in the tree to change.We show that the model predicts satisfactorily when validated with trees of Eucalyptus nitens and Eucalyptus globulus from a range of sites of different ages, subject to different types of stress and different types of defoliation events (R² = 0.96 across a range of sites). However, the complexity of particular situations can cause the model to fail (e.g. very heavy defoliation events where branch death occurs).It is concluded that while the model will not cope with all situations, an appropriate level of generality has been captured to represent many of the physiological processes and feedbacks that occur following defoliation or leaf damage. This makes the model useful for guiding management interventions following pest attack and allows the development of scenarios including climate change impact analyses and decision-making on the merits of post-defoliation fertilisation to expedite recovery.     

Temperature-dependent ranges of coexistence in a model of a two-prey-one-predator microbial food web

The objective of our study was to analyze the effects of temperature on the population dynamics of a three-species food web consisting of two prey bacteria (Pedobacter sp. and Acinetobacter johnsonii) and a protozoan predator (Tetrahymena pyriformis) as model organisms. We assessed the effects of temperature on the growth rates of all three species with the objective of developing a model with four differential equations based on the experimental data. The following hypotheses were tested at a theoretical level: Firstly, temperature changes can affect the dynamic behavior of a system by temperature-dependent parameters and interactions and secondly, food web response to temperature cannot be derived from the single species temperature response. The main outcome of the study is that temperature changes affect the parameter range where coexistence is possible within all three species. This has significant consequences on our ideas regarding the evaluation of effects of global warming.