AGE STRUCTURE AND GROWTH OF THE BOTTLENOSE DOLPHIN (TURSIOPS TRUNCATUS) FROM STRANDINGS IN THE MISSISSIPPI SOUND REGION OF THE NORTH-CENTRAL GULF OF MEXICO FROM 1986 TO 2003

Despite their high abundance and wide distribution, little is known about the historical or current growth and age structure of coastal bottlenose dolphins ( Tursiops truncatus ) in the north-central Gulf of Mexico. Between 1986 and 2003, teeth were collected from bottlenose dolphins stranded on the mainland coast of Mississippi and the adjacent barrier islands. Bottlenose dolphin strandings occurred year round, peaking in March and April. Neonate strandings also peaked during these 2 mo. Age estimates were obtained from 111 animals by reading the growth layer groups in the dentine layer of the teeth. The ages ranged from <1 yr to 30 yr of age. The two-stage Laird–Gompertz growth model was fitted to the total length and age data. On the basis of this model, the asymptotic lengths were estimated at 250 cm for females and 255 cm for males. The length at birth estimates were 98–103 cm for females and 100–107 cm for males. These lengths are similar to those of bottlenose dolphin populations from other Gulf of Mexico areas and from the North Atlantic Ocean along the southeastern United States.     

Models for estimating empirical Gompertz mortality: With an application to evolution of the Gompertzian slope

Using data from the human mortality database (HMD), and five different modeling approaches, we estimate Gompertz mortality parameters for 7,704 life tables. To gauge model fit, we predict life expectancy at age 40 from these parameters, and compare predicted to empirical values. Across a diversity of human populations, and both sexes, the overall best way to estimate Gompertz parameters is weighted least squares, although Poisson regression performs better in 996 cases for males and 1,027 cases for females, out of 3,852 populations per sex. We recommend against using unweighted least squares unless death counts (to use as weights or to allow Poisson estimation) are unavailable. We also recommend fitting to logged death rates. Over time in human populations, the Gompertz slope parameter has increased, indicating a more severe increase in mortality rates as age goes up. However, it is well-known that the two parameters of the Gompertz model are very tightly (and negatively) correlated. When the slope goes up, the level goes down, and, overall, mortality rates are decreasing over time. An analysis of Gompertz parameters for all of the HMD countries shows a distinct pattern for males in the formerly socialist economies of Europe.     

Shapes and functions of species–area curves: a review of possible models

Aim This paper reviews possible candidate models that may be used in theoretical modelling and empirical studies of species–area relationships (SARs). The SAR is an important and well‐proven tool in ecology. The power and the exponential functions are by far the models that are best known and most frequently applied to species–area data, but they might not be the most appropriate. Recent work indicates that the shape of species–area curves in arithmetic space is often not convex but sigmoid and also has an upper asymptote. Methods Characteristics of six convex and eight sigmoid models are discussed and interpretations of different parameters summarized. The convex models include the power, exponential, Monod, negative exponential, asymptotic regression and rational functions, and the sigmoid models include the logistic, Gompertz, extreme value, Morgan–Mercer–Flodin, Hill, Michaelis–Menten, Lomolino and Chapman–Richards functions plus the cumulative Weibull and beta‐P distributions. Conclusions There are two main types of species–area curves: sample curves that are inherently convex and isolate curves, which are sigmoid. Both types may have an upper asymptote. A few have attempted to fit convex asymptotic and/or sigmoid models to species–area data instead of the power or exponential models. Some of these or other models reviewed in this paper should be useful, especially if species–area models are to be based more on biological processes and patterns in nature than mere curve fitting. The negative exponential function is an example of a convex model and the cumulative Weibull distribution an example of a sigmoid model that should prove useful. A location parameter may be added to these two and some of the other models to simulate absolute minimum area requirements.     

三参数增长模型拟合:以季风常绿阔叶林中两个优势乔木种群为例

Logistic、Mitscherlich、Gompertz方程是一类三参数饱和增长曲线模型,广泛地应用于许多学科领域．本文基于logistic方程饱和值K估计的三点法、四点法,推导出Mitscherlich、Gompertz方程K值的三点法、四点法估计公式,并以南亚热带季风常绿阔叶林中两种优势乔木厚壳桂、黄果厚壳桂种群为例,先用三点法或四点法估计出K值,再通过线性回归与非线性回归相结合的方法,可获得三个增长模型中三个参数的最优无偏估计．实例研究表明,两个优势种群增长数据均符合三个增长模型,但更符合增长曲线呈S形的logistic、Gompertz方程,且以logistic方程最适合于观察;黄果厚壳桂种群增长快于厚壳桂种群．     

Defective regression models for cure rate modeling with interval‐censored data

Regression models in survival analysis are most commonly applied for right‐censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval‐censored mechanism is ignored. We present a cure rate defective model for interval‐censored event‐time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.     

Prenatal data impacts common bottlenose dolphin (Tursiops truncatus) growth parameters estimated by length‐at‐age curves

Compilation of marine mammal demographic data is central to management efforts. However, marine mammal length‐at‐age growth curves demonstrate limitations. Physiological growth parameters of terrestrial mammals are typically estimated using curvilinear models fit to size‐at‐age data along a time series from conception to senescence. The difficulty of collecting and aging prenatal cetaceans is addressed here, and growth parameters of common bottlenose dolphins (Tursiops truncatus) along coastal Texas were estimated using length‐at‐age information from a broader scope of age classes, including late‐term fetuses. A Gompertz growth curve fit to pre‐ and postnatal data underestimated size parameters, but demonstrated similar growth rate constants (k) to an exclusively postnatal model. However, when growth parameters were broken out, the absolute growth rate (G) and rate of growth decay (g) decreased (0.44 from 0.27 and 0.55 from 0.39, respectively), which underscores the importance of reporting k in its expanded form (G/g). Although the Gompertz fits most age classes well, it cannot explain growth in all age classes. We argue that a novel sigmoidal model would be more useful for inference.     

The Use of the Gompertz Function in the Treatment of – Quantal Response Data

In this paper it is shown that the Gompertz function can be used in the treatment of quantal response data. It is argued that the fitting of this function is particularly indicated when the ordinate of the inflection point is smaller than 0.5. An example where the Gompertz function leads to the best fitting is provided.