Stochastic growth models for analyzing crustacean data

The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed for crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as "jumps" (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e. g. red curve in Figure 1). [GRAPHICS]

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.

Stochastic growth of the Eastern King Prawn (melicertus plebejus (hess, 1865)) harvested off Eastern Australia

Stochastic growth models were fitted to length-increment data of eastern king prawns, Melicertus plebejus (Hess, 1865), tagged across eastern Australia. The estimated growth parameters and growth transition matrix are for each sex representative of the species' geographical distribution. Our study explicitly displays the stochastic nature of prawn growth. Capturing length-increment growth heterogeneity for short-lived exploited species such as prawns that cannot be readily aged is essential for length-based modelling and improved management.

Stochastic growth and monetary policy: the impacts on the term structure of interest rates

This paper builds a simple, empirically-verifiable rational expectations model for term structure of nominal interest rates analysis. It solves an stochastic growth model with investment costs and sticky inflation, susceptible to the intervention of the monetary authority following a policy rule. The model predicts several patterns of the term structure which are in accordance to observed empirical facts: (i) pro-cyclical pattern of the level of nominal interest rates; (ii) countercyclical pattern of the term spread; (iii) pro-cyclical pattern of the curvature of the yield curve; (iv) lower predictability of the slope of the middle of the term structure; and (v) negative correlation of changes in real rates and expected inflation at short horizons.

Stochastic demography and population dynamics in the red kangaroo Macropus rufus

1. Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity. 2. We analyse a stochastic environment model of the red kangaroo (Macropus rufus), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates. 3. Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate. 4. Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates. 5. Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c. 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c. 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Uncertainty, learning and growth

The paper extends Blackburn and Galindev's (Economics Letters, Vol. 79 (2003), pp. 417-421) stochastic growth model in which productivity growth entails both external and internal learning behaviour with a constant relative risk aversion utility function and productivity shocks. Consequently, the relationship between long-term growth and short-term volatility depends not only on the relative importance of each learning mechanism but also on a parameter measuring individuals' attitude towards risk.

Conformational Spread as a Mechanism for Cooperativity in the Bacterial Flagellar Switch

The bacterial flagellar switch that controls the direction of flagellar rotation during Chemotaxis has a highly cooperative response. This has previously been understood in terms of the classic two-state, concerted model of allosteric regulation. Here, we used high-resolution optical microscopy to observe switching of single motors and uncover the stochastic multistate nature of the switch. Our observations are in detailed quantitative agreement with a recent general model of allosteric cooperativity that exhibits conformational spread-the stochastic growth and shrinkage of domains of adjacent subunits sharing a particular conformational state. We expect that conformational spread will be important in explaining cooperativity in other large signaling complexes.

Asset Pricing in a Production Economy with Chew–Dekel Preferences

In this paper we provide a thorough characterization of the asset returns implied by a simple general equilibrium production economy with Chew–Dekel risk preferences and convex capital adjustment costs. When households display levels of disappointment aversion consistent with the experimental evidence, a version of the model parameterized to match the volatility of output and consumption growth generates unconditional expected asset returns and price of risk in line with the historical data. For the model with Epstein–Zin preferences to generate similar statistics, the relative risk aversion coefficient needs to be about 55, two orders of magnitude higher than the available estimates. We argue that this is not surprising, given the limited risk imposed on agents by a reasonably calibrated stochastic growth model.

Asymmetries in Business Cycles

Esta disertación busca estudiar los mecanismos de transmisión que vinculan el comportamiento de agentes y firmas con las asimetrías presentes en los ciclos económicos. Para lograr esto, se construyeron tres modelos DSGE. El en primer capítulo, el supuesto de función cuadrática simétrica de ajuste de la inversión fue removido, y el modelo canónico RBC fue reformulado suponiendo que des-invertir es más costoso que invertir una unidad de capital físico. En el segundo capítulo, la contribución más importante de esta disertación es presentada: la construcción de una función de utilidad general que anida aversión a la pérdida, aversión al riesgo y formación de hábitos, por medio de una función de transición suave. La razón para hacerlo así es el hecho de que los individuos son aversos a la pérdidad en recesiones, y son aversos al riesgo en auges. En el tercer capítulo, las asimetrías en los ciclos económicos son analizadas junto con ajuste asimétrico en precios y salarios en un contexto neokeynesiano, con el fin de encontrar una explicación teórica de la bien documentada asimetría presente en la Curva de Phillips.