A stochastic gompertz model with hereditary effect

Summary In this paper we have studied a stochastic version of the Gompertz model for population growth of a single species after incorporating the aspect of heredity. Various statistical characteristics-the mean-value function, covariance-kernel, etc.-are evaluated for a delta-correlated process and their asymptotic values obtained. The effect of the hereditary kernel on the various statistics is discussed and it is found that it is to shift the distribution towards the origin.     

Cascading effects of mass mortality events in Arctic marine communities

Mass mortality events caused by pulse anthropogenic or environmental perturbations (e.g., extreme weather, toxic spills or epizootics) severely reduce the abundance of a population in a short time. The frequency and impact of these events are likely to increase across the globe. Studies on how such events may affect ecological communities of interacting species are scarce. By combining a multispecies Gompertz model with a Bayesian state‐space framework, we quantify community‐level effects of a mass mortality event in a single species. We present a case study on a community of fish and zooplankton in the Barents Sea to illustrate how a mass mortality event of different intensities affecting the lower trophic level (krill) may propagate to higher trophic levels (capelin and cod). This approach is especially valuable for assessing community‐level effects of potential anthropogenic‐driven mass mortality events, owing to the ability to account for uncertainty in the assessed impact due to uncertainty about the ecological dynamics. We hence quantify how the assessed impact of a mass mortality event depends on the degree of precaution considered. We suggest that this approach can be useful for assessing the possible detrimental outcomes of toxic spills, for example oil spills, in relatively simple communities such as often found in the Arctic, a region under increasing influence of human activities due to increased land and sea use.     

Characterization of the Mixtures of Gompertz Distributions by Conditional Expectation of Order Statistics

The mixtures of Gompertz random variables (Gompertz , 1825) X₁ and X₂ are identified in terms of relations between the conditional expectation of [exp (αX_2:2) — exp (αX_1:2)]^k given X_1:2 and the hazard rate function of the distribution, k is a positive integer and α < 0. Here X_1:2 and X_2:2 denote the corresponding order statistics. In addition, we also mention some related theorems to characterize the mixtures of Gompertz distributions. Finally, when the sample size is n, the above results are also valid and we also give an application to Multi-Hit models of carcinogenesis (Parallel Systems).     

New Better than Used and Other Concepts for a Class of Life Distributions

It is well-known that the inequalities used in the definition of the New Better than Used (N. B. U.) and the New Better than Used in Expectation (N.B.U.E.) concepts, see BARLOW and PROSCHAN (1965, 1975) become equalities if, and only if, the life length of an organism follows an exponential distribution. It is proved in the present paper that these inequalities also reduce to equalities for the class of life distributions that have the “setting the clock back to zero” property. Simple examples of these distributions include the exponential, the linear hazard exponential and the Gompertz distributions. The General Krane distributions (Krane 1963) belong to this class, as well as a recent model introduced by CHIANG and CONFORTI (1989) of a survival distribution in which the hazard rate is a function of the accumulated effect of an individual's continuous exposure to the toxic material in the environment and his biological reaction to the toxin absorbed. As a simple application of the result proved in the paper, the life expectancy of an organism at age γ₀ involved in the N.B.U.E. concept is evaluated for the Gompertzian growth process and for the Chiang and Conforti model.     

Effect of microaerobic conditions on the degradation kinetics of cellulose

Limited oxygen supply to sludge digesters has shown to be an effective method to eliminate hydrogen sulfide from the biogas produced during anaerobic digestion but uneven results have been found in terms of the effect on the degradation of complex organic matter. In this study, the effect that the limited oxygen supply provoked on the “anaerobic” degradation of cellulose was evaluated in batch-tests. The microaerobic assays showed to reach a similar maximum production of methane than the anaerobic ones after 19 d and a similar hydrolytic activity (considering a first order rate constant); however, the microaerobic assays presented a shorter lag-phase time than the anaerobic test resulting in faster production of methane during the first steps of the degradation; specifically, the maximum methane production found in the anaerobic test in 19 d was found in the microaerobic test before the day 15.     

Using quantile regression methodology to evaluate changes in the shape of growth curves in pigs selected for increased feed efficiency based on residual feed intake

Growth rate is a major component of feed efficiency when estimating residual feed intake (RFI). Quantile regression (QR) methodology can be used to identify animals with different growth trajectories. The objective of this study was to evaluate the use of QR to identify phenotypic and genetic differences in pigs selected for low RFI. Using performance data on 750 Yorkshire pigs selected for low RFI, individual average daily gain (ADG), average daily feed intake (ADFI), RFI and Gompertz growth curve parameters (asymptotic weight (a), inflection point (b) and decay parameter (c)) were estimated for each pig. Using QR methodology, three Gompertz growth curves were estimated for the whole population for three quantiles (0.1, 0.5 and 0.9) of the BW data. Each animal was classified into one of the quantile regression groups (QRG) based on their overall Euclidian distance between each observed and estimated BW from the quantile growth curves. These three curves were also estimated using only part of the data (generations −1 to 3, and −1 to 4) in order to evaluate the agreement classification rate of animals from later generations into QRGs. We evaluated the effect of QRG on growth parameters and performance traits. Genetic parameters were estimated for these traits, as well as for QRG. In addition, genetic trends for each QRG were estimated. Three distinct growth curves were observed for animals classified into either quantiles 0.1 (QRG_0.1), 0.5 (QRG_0.5) or 0.9 (QRG_0.9). When only part of the data was used to estimate quantile growth curves, all animals from QRG_0.1 were correctly classified in their group. Animals in QRG_0.1 had significantly lower ADFI, ADG and RFI, and greater a, b and c than animals in the other groups. Quantile regression groups analysed as a trait was highly heritable (0.41) and had high (0.8) and moderate (0.46) genetic correlations with ADG and RFI, respectively. Selection for reduced RFI increased the number of animals classified as QRG_0.1 in the population. Overall, downward genetic trends were observed for all traits as a function of selection for reduced RFI. However, QRG_0.1 was the only group that had a positive genetic trend for ADG. Altogether, these results indicate that selection for reduced RFI changes the shape of growth curves in Yorkshire in pigs, and that QR methodology was able to identify animals having different genetic potential for feed efficiency, bringing a new opportunity to improve selection for reduced RFI.     

不同性别河北柴鸡早期生长规律及其生长曲线拟合

本研究运用Logistic、Gompertz和Bertalanffy三种非线性模型对不同性别河北柴鸡早期生长规律和生长曲线进行分析及拟合比较.结果表明,3种曲线模型拟合度均达到0.99以上,但Gompertz曲线模型在拟合度和预测极限生长量、拐点周龄和最大周增重等方面相对较好.进一步分析表明,河北柴鸡公鸡的极限体重和拐点体重均高于母鸡,拐点周龄性别间差异不大,公鸡最大周增重与实际观测值接近.本文有助于了解不同性别河北柴鸡各自的生长模式及其对营养、环境的需求,为开展规模化饲养提供参考.     

A mathematical model of pollen-tube penetration in apple styles

Cross-compatible pollen tubes were cultured in detached flowers of apple (Malus domestica Borkh. cv. Cox's Orange Pippin). Although the culture method was simple, the detached flowers proved to be adequate for our requirements, and after pollination they were incubated at 12 constant temperatures from 3·5° C to 33·5° C and sampled at intervals for microscopy. S-shaped growth curves (Gompertz function) were fitted to measurements of pollen-tube penetration within the styles, and each of the Gompertz parameters was expressed as a function of temperature. The model was defective at temperatures below 6° C, but a modification is described which improves this deficiency and yields a ten-parameter empirical model with temperature and incubation time as inputs, and pollen penetration as its output. An application of the model is described in which it provides a numerically integrated output of pollentube penetration from a series of temperature records. Potential uses for the model include predictions of pollen penetration for experimental use and testing for small differences in pollen-tube response to temperature, between cultivars, or between experimental treatments.     

A generalized Luria-Delbrück model

We develop extensions of the Luria-Delbrück model that explicitly consider non-exponential growth of normal cells and a birth-death process with mean exponential or Gompertz growth of mutants. Death of mutant cells can be important in clones arising during cancer progression. The use of a birth-death process for growth of mutant cells, as opposed to a pure birth process as in previous work on the Luria-Delbrück model, leads to a large increase in the extra Poisson variation in the size of the mutant cell populations, which needs to be addressed in statistical analyses. We also discuss connections with previous work on carcinogenesis models.