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Background and Objectives: Levodopa concentration in patients with Parkinson’s disease is frequently modelled with ordinary differential equations (ODEs). Here, we investigate a pharmacokinetic model of plasma levodopa concentration in patients with Parkinson’s disease by introducing stochasticity to separate the intra-individual variability into measurement and system noise, and to account for auto-correlated errors. We also investigate whether the induced stochasticity provides a better fit than the ODE approach. Methods: In this study, a system noise variable is added to the pharmacokinetic model for duodenal levodopa/carbidopa gel (LCIG) infusion described by three ODEs through a standard Wiener process, leading to a stochastic differential equations (SDE) model. The R package population stochastic modelling (PSM) was used for model fitting with data from previous studies for modelling plasma levodopa concentration and parameter estimation. First, the diffusion scale parameter (σw), measurement noise variance, and bioavailability are estimated with the SDE model. Second, σwis fixed to certain values from 0 to 1 and bioavailability is estimated. Cross-validation was performed to compare the average root mean square errors (RMSE) of predicted plasma levodopa concentration. Results: Both the ODE and the SDE models estimated bioavailability to be approximately 75%. The SDE model converged at different values of σwthat were significantly different from zero. The average RMSE for the ODE model was 0.313, and the lowest average RMSE for the SDE model was 0.297 when σwwas fixed to 0.9, and these two values are significantly different. Conclusions: The SDE model provided a better fit for LCIG plasma levodopa concentration by approximately 5.5% in terms of mean percentage change of RMSE.

When individuals interact, their phenotypes may be affected not only by their own genes but also by genes in their social partners. This phenomenon is known as Indirect Genetic Effects (IGEs). In aquaculture species and some plants, however, competition not only affects trait levels of individuals, but also inflates variability of trait values among individuals. In the field of quantitative genetics, the variability of trait values has been studied as a quantitative trait in itself, and is often referred to as inherited variability. Such studies, however, consider only the genetic effect of the focal individual on trait variability and do not make a connection to competition. Although the observed phenotypic relationship between competition and variability suggests an underlying genetic relationship, the current quantitative genetic models of IGE and inherited variability do not allow for such a relationship. The lack of quantitative genetic models that connect IGEs to inherited variability limits our understanding of the potential of variability to respond to selection, both in nature and agriculture. Models of trait levels, for example, show that IGEs may considerably change heritable variation in trait values. Currently, we lack the tools to investigate whether this result extends to variability of trait values. Here we present a model that integrates IGEs and inherited variability. In this model, the target phenotype, say growth rate, is a function of the genetic and environmental effects of the focal individual and of the difference in trait value between the social partner and the focal individual, multiplied by a regression coefficient. The regression coefficient is a genetic trait, which is a measure of cooperation; a negative value indicates competition, a positive value cooperation, and an increasing value due to selection indicates the evolution of cooperation. In contrast to the existing quantitative genetic models, our model allows for co-evolution of IGEs and variability, as the regression coefficient can respond to selection. Our simulations show that the model results in increased variability of body weight with increasing competition. When competition decreases, i.e., cooperation evolves, variability becomes significantly smaller. Hence, our model facilitates quantitative genetic studies on the relationship between IGEs and inherited variability. Moreover, our findings suggest that we may have been overlooking an entire level of genetic variation in variability, the one due to IGEs.

National road databases often lack important information for long-term maintenance planning of paved roads. In the Swedish case, latent variables of which there are no recordings in the pavement management systems database are, for example, underlying road construction, subsoil conditions, and amount of heavy traffic measured by the equivalent single-axle load. The mixed proportional hazards model with random effects was used to capture the effect of these latent variables on a road’s risk of needing maintenance. Estimation of random effects makes it possible to identify sections that have shorter or longer lifetimes than could be expected from the observed explanatory variables (traffic load, pavement type, road type, climate zone, road width, speed limit, and bearing capacity restrictions). The results indicate that the mixed proportional hazards model is useful for maintenance planning because the weakest and strongest sections in a road network can be identified. The effect of the latent variables was visualized by plotting the random effect of each section in a map of the road network. In addition, the spatial correlation between road sections was evaluated by fitting the random effects in an intrinsic conditional autoregressive model. The spatial correlation was estimated to explain 17% of the variation in lifetimes of roads that occur because of the latent variables. The Swedish example shows that the mixed proportional hazards and intrinsic conditional autoregressive models are suitable for analyzing the effect of latent variables in national road databases.

National road databases often lack important information for long-term maintenance planning of paved roads. In the Swedish case, latent variables of which there are no recordings in the pavement management systems database are, for example, underlying road construction, subsoil conditions, and amount of heavy traffic measured by the equivalent single-axle load. The mixed proportional hazards model with random effects was used to capture the effect of these latent variables on a road’s risk of needing maintenance. Estimation of random effects makes it possible to identify sections that have shorter or longer lifetimes than could be expected from the observed explanatory variables (traffic load, pavement type, road type, climate zone, road width, speed limit, and bearing capacity restrictions). The results indicate that the mixed proportional hazards model is useful for maintenance planning because the weakest and strongest sections in a road network can be identified. The effect of the latent variables was visualized by plotting the random effect of each section in a map of the road network. In addition, the spatial correlation between road sections was evaluated by fitting the random effects in an intrinsic conditional autoregressive model. The spatial correlation was estimated to explain 17% of the variation in lifetimes of roads that occur because of the latent variables. The Swedish example shows that the mixed proportional hazards and intrinsic conditional autoregressive models are suitable for analyzing the effect of latent variables in national road databases.

Various survey methods are used to monitor and manage ungulate populations. The choice of optimal method depends on estimation accuracy, management objective and financial constraints. Here we compare estimates produced by four different methods for estimating population size, i.e. aerial counts, hunter observations, pellet group counts and cohort analysis. A Swedish moose Alces alces population was studied during 1973–2005 in the Grimsö Wildlife Research Area (135?km2). The highest correlation was found between cohort analysis and aerial counts (r=0.69, P<0.05), and the hunter observations and the aerial counts (r=0.76, P<0.10). The different methods produced relatively consistent trends in population estimates over years. Pellet group counts prior to 1997 were not significantly correlated with the other methods, probably due to unrepresentative spatial sampling. A comparison of the aerial and pellet group counts in 2002 and 2006, showed that the average defecation rate was estimated at approximately 14 pellet groups per day per moose. Our results show the importance of having representative spatial sampling in pellet group surveys and indicate that hunter observations can be a useful tool for estimating long-term population trends even in moderately sized areas.

Summary:This study analyzed the missing data in a commercial real-time location system (RTLS) within 2 dairy barns. Higher proportions of missing data were found along one of the walls on both farms. There was significant variation between individual tags.