Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.     

DUM neurons in locust flight: a model system for amine-mediated peripheral adjustments to the requirements of a central motor program

In both vertebrates and invertebrates, multiple effects of biogenic amines on neuromuscular transmission, muscle contraction kinetics and metabolism have been described. Nevertheless, it is not yet known whether and how these different effects work in concert during the performance of a specific behavior. In the locust flight system, the biogenic amine octopamine is released as a neurohormone into the haemolymph, and also delivered directly onto specific target muscles by individually identified dorsal unpaired median neurons. Determining the connectivity of these neurons and their activation during behavior, we show for the first time that different types of dorsal unpaired median neurons are differentially connected to certain components of the flight circuitry. During flight, all types of pterothoracic dorsal unpaired median neurons innervating flight muscles receive inhibitory inputs from tegula proprioceptive afferents and from the central flight circuitry, whereas all other types of dorsal unpaired median neurons are excited by wind-sensitive pathways and by the central pattern generator. Considering the results of other studies which investigated metabolic effects of octopamine, we propose a model in which the differential activation of dorsal unpaired median neurons during flight may lead to an adequately controlled release or removal of octopamine to adjust metabolic processes to the requirements of a specific motor program. Accepted: 24 February 1999     

Extrapolating leaf CO2 exchange to the canopy: a generalized model of forest photosynthesis compared with measurements by eddy correlation

Over the last 4 years, two data sets have emerged which allow increased accuracy and resolution in the definition and validation of a photosynthesis model for whole forest canopies. The first is a greatly expanded set of data on the nitrogen-photosynthesis relationship for temperate and tropical woody species. The second is a unique set of long-term (4 year) daily carbon balance measurements at the Harvard Forest, Petersham, Massachusetts, collected by the eddy-correlation technique. A model (PhET-Day) is presented which is derived directly from, and validated against, these data sets. The PnET-Day model uses foliar nitrogen concentration to calculate maximum instantaneous rates of gross and net photosynthesis which are then reduced for suboptimal temperature, photosynthetically active radiation (PAR), and vapor pressure deficit (VPD). Predicted daily gross photosynthesis is closely related to gross carbon exchange at the Harvard Forest as determined by eddy-correlation measurements. Predictions made by the full canopy model were significantly better than those produced by a multiple linear regression model. Sensitivity analyses for this model for a deciduous broad-leaved forest showed results to be much more sensitive to parameters related to maximum leaf-level photosynthetic rate (A _max) than to those related to light, temperature, VPD or total foliar mass. Aggregation analyses suggest that using monthly mean climatic data to drive the canopy model will give results similar to those achieved by averaging daily eddy correlation measurements of gross carbon exchange (GCE).     

Predicting the population dynamics of the house dust mite Dermatophagoides pteronyssinus (Acari: Pyroglyphidae) in response to a constant hygrothermal environment using a model of the mite life cycle

A generalised model of the life cycle of a house dust mite, which can be tailored to any particular species of domestic mite, is presented. The model takes into account the effects of hygrothermal conditions on each life cycle phase. It is used in a computer simulation program, called POPMITE, which, by incorporating a population age structure, is able to predict population dynamics. The POPMITE simulation is adapted to the Dermatophagoides pteronyssinus (Acari: Pyroglyphidae) (DP) mite using published data on the egg development period, total development period, adult longevity, mortality during egg development, mortality during juvenile development, and fecundity of individual DP mites held at a range of constant hygrothermal conditions. An example is given which illustrates how the model functions under constant hygrothermal conditions. A preliminary validation of POPMITE is made by a comparison of the POPMITE predictions with published measurements of population growth of DP mites held at a range constant hygrothermal conditions for 21 days. The POPMITE simulation is used to provide predictions of population growth or decline for a wide range of constant relative humidity and temperature combinations for 30 and 60 days. The adaptation of the model to correctly take account of fluctuating hygrothermal conditions is discussed.     

The net carbon flux due to deforestation and forest re-growth in the Brazilian Amazon: analysis using a process-based model

We developed a process‐based model of forest growth, carbon cycling and land‐cover dynamics named CARLUC (for CARbon and Land‐Use Change) to estimate the size of terrestrial carbon pools in terra firme (nonflooded) forests across the Brazilian Legal Amazon and the net flux of carbon resulting from forest disturbance and forest recovery from disturbance. Our goal in building the model was to construct a relatively simple ecosystem model that would respond to soil and climatic heterogeneity that allows us to study the impact of Amazonian deforestation, selective logging and accidental fire on the global carbon cycle. This paper focuses on the net flux caused by deforestation and forest re‐growth over the period from 1970 to 1998. We calculate that the net flux to the atmosphere during this period reached a maximum of ～0.35 PgC yr^?1 (1 PgC= 1 × 10¹⁵ gC) in 1990, with a cumulative release of ～7 PgC from 1970 to 1998. The net flux is higher than predicted by an earlier study ( Houghton et al., 2000 ) by a total of 1 PgC over the period 1989–1998 mainly because CARLUC predicts relatively high mature forest carbon storage compared with the datasets used in the earlier study. Incorporating the dynamics of litter and soil carbon pools into the model increases the cumulative net flux by～1 PgC from 1970 to 1998, while different assumptions about land‐cover dynamics only caused small changes. The uncertainty of the net flux, calculated with a Monte‐Carlo approach, is roughly 35% of the mean value (1 SD).     

A model describing the effect of sex-reversed YY fish in an established wild population: The use of a Trojan Y chromosome to cause extinction of an introduced exotic species

A novel means of inducing extinction of an exotic fish population is proposed using a genetic approach to shift the ratio of male to females within a population. In the proposed strategy, sex-reversed fish containing two Y chromosomes are introduced into a normal fish population. These YY fish result in the production of a disproportionate number of male fish in subsequent generations. Mathematical modeling of the system following introduction of YY fish at a constant rate reveals that female fish decline in numbers over time, leading to eventual extinction of the population.     

Changes in the light sensitivity of buried Polygonum aviculare seeds in relation to cold-induced dormancy loss: development of a predictive model

The effect of cold (stratification) temperature on changes in the sensitivity of Polygonum aviculare seeds to light was investigated. Seeds buried in pots were stored under stratification temperatures (1.6, 7 and 12 degrees C) for 137 d. Seeds exhumed at regular intervals during storage were exposed to different light treatments. Germination responses obtained for seeds exposed to different light treatments and stratification temperatures were used to develop a model to predict the sensitivity of buried seeds to light. Seed sensitivity to light increased as dormancy loss progressed, showing the successive acquisition of low-fluence responses (LFR), very low-fluence responses (VLFR), and the loss of the light requirement for germination for a fraction of the seed population. These changes were inversely correlated to stratification temperature, allowing the use of a thermal time index to relate observed changes in seed light sensitivity to stratification temperature. The rate of increase in sensitivity of P. aviculare seeds to light during stratification is inversely correlated to soil temperature, and these changes in light sensitivity could be predicted in relation to temperature using thermal-time models.     

Germination responses to temperature and water potential in Jatropha curcas seeds: a hydrotime model explains the difference between dormancy expression and dormancy induction at different incubation temperatures

Background and Aims

Jatropha curcas is a drought-resistant tree whose seeds are a good source of oil that can be used for producing biodiesel. A successful crop establishment depends on a rapid and uniform germination of the seed. In this work we aimed to characterize the responses of J. curcas seeds to temperature and water availability, using thermal time and hydrotime analysis,

Methods

Thermal and hydrotime analysis was performed on germination data obtained from the incubation of seeds at different temperatures and at different water potentials.

Key Results

Base and optimum temperatures were 14·4 and 30 °C, respectively. Approximately 20 % of the seed population displayed absolute dormancy and part of it displayed relative dormancy which was progressively expressed in further fractions when incubation temperatures departed from 25 °C. The thermal time model, but not the hydrotime model, failed to describe adequately final germination percentages at temperatures other than 25 °C. The hydrotime constant, θ_H, was reduced when the incubation temperature was increased up to 30 °C, the base water potential for 50 % germination,Ψ_b(50), was less negative at 20 and 30 °C than at 25 °C, indicating either expression or induction of dormancy. At 20 °C this less negative Ψ_b(50) explained satisfactorily the germination curves obtained at all water potentials, while at 30 °C it had to be corrected towards even less negative values to match observed curves at water potentials below 0. Hence, Ψ_b(50) appeared to have been further displaced to less negative values as exposure to 30 °C was prolonged by osmoticum. These results suggest expression of dormancy at 20 °C and induction of secondary dormancy above 25 °C. This was confirmed by an experiment showing that inhibition of germination imposed by temperatures higher than 30 °C, but not that imposed at 20 °C, is a permanent effect.

Conclusions

This study revealed (a) the extremely narrow thermal range within which dormancy problems (either through expression or induction of dormancy) may not be encountered; and (b) the high sensitivity displayed by these seeds to water shortage. In addition, this work is the first one in which temperature effects on dormancy expression could be discriminated from those on dormancy induction using a hydrotime analysis.