The growth pattern of chimpanzees: Somatic growth and reproductive maturation inPan troglodytes

Growth of chimpanzees reared at the Kumamoto Primates Park of Sanwa Kagaku Kenkyusho Co. Ltd. was studied cross-sectionally from the viewpoints of somatic growth and reproductive maturation. Distance and velocity curves were expressed using spline function method. Males showed adolescent growth acceleration in body weight, with a peak at 7.86 yrs of age, but not in trunk length. Females showed continuous rapid growth from mid-juvenile to adolescent phase in both body weight and trunk length, but no isolated adolescent spurt. The Sanwa chimpanzees matured at about 12.5 yrs of age for females and 15.0 yrs for males. The mean adult weights and trunk lengths were 53.2 kg and 507.8 mm for males and 42.7 kg and 481.6 mm for females. The Sanwa chimpanzees had similar growth patterns to those of the Yerkes chimpanzees, although they showed a slight delay in infancy, and a higher growth rate from the early juvenile phase onwards. Growth patterns in these two laboratories may be regarded as “normative” for laboratory-reared chimpanzees. They matured earlier than wild chimpanzees by more than two years. The major reason for the retarded maturation in wild chimpanzees is the delay of growth from infant to the early juvenile phases (0–4 yrs of age), probably owing to a limited nutritional supply from the mother. Development of the testes comprised three phases: slow growth from infant to juvenile (until 6.4 yrs); rapid growth around adolescence (until 9.2 yrs); and adult (mean testicular volume, 187 cm³). Setting the nutritional standard at 2,000–2,600 Cal/day (= Kcal/day) per adult, calories were considered for captive chimpanzees in each age class.     

Semiparametric estimation of tag loss and reporting rates for tag-recovery experiments using exact time-at-liberty data

We present a semiparametric likelihood approach to estimating reporting rates and tag-loss rates from the tags returned from capture-recapture studies. Such studies are commonly used to estimate critical population parameters. Tag loss rates are estimated using double-tagged animals, while reporting rates are estimated using information from high-reward tags. A likelihood function is constructed based on the conditional distribution of the type of tag returned (low or high reward, single or double tag), given that a tag has been returned. This involves many sparse 5 x 1 tag-return contingency tables, and choosing a good functional form for the tag loss rate is difficult with such data. We model tag-loss rates using monotone-smoothing splines, and use these nonparametric estimates to diagnose the parametric form of the tag-loss rate. The nonparametric methods can also be used directly to model tag-loss rates.     

A morphometric approach to the geographic variation of the terrestrial isopod species Armadillo tuberculatus (Isopoda: Oniscidea)

The terrestrial isopod species Armadillo tuberculatus Vogl, 1876 (Crustacea, Isopoda, Oniscidea) is a widely polymorphic species distributed in the south-central Aegean region (Greece) with a different morph on each island. Variation consists in coloration, size of cuticular tubercules, shape of telson and the shape of the male first pleopod exopodite (secondary sexual character of taxonomic importance). We studied the allometric growth of a cuticular tubercule in 17 populations (for both male and female individuals) and the shape variation of the first male pleopod exopodite in 10 populations using Elliptic Fourier Analysis, in order to test for patterns of intraspecific variation and possible relationships between morphs. In addition, Thin Plate Spline analysis was used for the calculation of the minimum bending energy between different exopodite shapes, which was then used for estimating the minimum spanning network (MSN) connecting them. The different allometric growth rates of the tubercule among island groups were significantly related to island latitude and climatic factors. On the other hand, the clustering of islands and the MSN based on male exopodite shape differences were not related to the palaeogeography of the Aegean region or to the present geographic distances of islands. These results are interpreted as evidence for non-adaptive radiation of the morphs.     

Inference for the Break Point in Segmented Regression with Application to Longitudinal Data

This paper considers inference for the break point in the segmented regression or piece‐wise regression model. Standard likelihood theory does not apply because the break point is absent under the null hypothesis. We use results by Davies for this type of non‐standard set‐up [Biometrika 64 (1977), 247–254 and 74 (1987), 33–43] to obtain a test for the null hypothesis of no break point. A confidence interval can be constructed provided replicate data are available. The methods are exemplified using two longitudinal datasets, the one from ecology, the other from pharmacology.     

Spatial variance of nutrient limitation of periphyton in montane, headwater streams (McLeod River, Alberta, Canada)

There have been few studies that have examined the spatial variance of nutrient limitation over the scale of an entire set of headwater streams. We used nutrient diffusing substrata experiments (control, nitrogen addition, phosphorus addition, and nitrogen+phosphorus addition) to examine how nutrient limitation varied throughout the five creeks that comprise the McLeod River headwaters (Alberta, Canada). We assessed the variance of chlorophyll a accrual at spatial scales within reach, within creek, among creeks and across linear distance within the entire watershed to assess the consistency and scale of nutrient limitation. We analyzed the importance of the spatial scale using several methods. We assessed the coefficient of variation at different scales, the spatial covariance of nitrogen and phosphorus deficiency indices using a spline correlogram, and the variance through traditional analyses of variance methods. Chlorophyll a accrual responded significantly to nutrients in all creeks, though the response varied in magnitude and in the limiting nutrient among reaches and among creeks. Variance in chlorophyll a accrual was due primarily to the factor of creek (R ²=0.40) and secondarily to reach (R ²=0.07). The CV was 31.4% among creeks, 18.4% among reaches, and 17.9% within reaches. The N deficiency index showed a positive correlation at sites located <4 km apart and a negative correlation at sites greater than 6.5 km apart. The P deficiency index showed no discernible spatial correlation. Our results suggest that nutrient limitation varies on small scales and is often driven by local processes.     

Low-rank scale-invariant tensor product smooths for generalized additive mixed models

A general method for constructing low-rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented. A penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately, these "marginal" smooths being represented using a low-rank basis with an associated quadratic wiggliness penalty. The smooths offer several advantages: (i) they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates, making them useful when there is no "natural" way to scale covariates relative to each other; (ii) they have a useful tuneable range of smoothness, unlike single-penalty tensor product smooths that are scale invariant; (iii) the relatively low rank of the smooths means that they are computationally efficient; (iv) the penalties on the smooths are easily interpretable in terms of function shape; (v) the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties, giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task; and (vi) the smooths can easily be written as components of a standard linear or generalized linear mixed model, allowing them to be used as components of the rich family of such models implemented in standard software, and to take advantage of the efficient and stable computational methods that have been developed for such models. A small simulation study shows that the methods can compare favorably with recently developed smoothing spline ANOVA methods.     

A general theory of life table construction and a precise abridged life table method

"In this paper we lay the foundation of life table construction by unifying the existing life table methods. We also present a new method of constructing current (period) abridged life tables.... The development includes (1) a careful formulation and computation of age-specific death rates, (2) derivation of a new set of formulas for computing the survivorship function from the observed age-specific death rates and populations, (3) estimation of the main life table functions by spline interpolation, integration and differentiation, and (4) use of a quadratic and a Gompertz function to close the life table.... The method is illustrated with construction of abridged life tables using Canadian data."     

Merging Spline Approximations with Analysis of Nonlinear Regression Models

The paper outlines a method of analysis of intricically non-linear regression functions. The nonlinear model is first approximated by a cubic spline function. Thereafter, the standard methods of analysis in linear models are applied to obtain estimates and test statistics.     

Nonparametric mixed effects models for unequally sampled noisy curves

We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low-rank, low-frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as best linear unbiased predictor (BLUP) estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniques--Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross-validation--to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis.