Internal model control for structured rank deficient system based on full rank decomposition

In this paper, an internal model control method is first proposed for structured rank deficient systems based on full rank decomposition. The system is first converted into a column full rank system by designing a pre-compensator. Then a feedback-compensator is designed to improve the dynamic characteristics of the full rank system and decrease the controller design difficulties. Rather than performing complex designing calculations, the pre- and feedback- compensators are designed by the full rank decomposition method. Furthermore, the non-square relative gain subsystem selection criterion is used to choose the square subsystem and to realize loop pairing. Consequently, the selected square subsystem is used as an internal model to design the internal model controller. Finally, a simple process is taken as the simulation object to demonstrate the validity and feasibility of the new method. Simulations results illustrate that the proposed strategy is not only simple and easy to implement but also has a good performance even the system model is mismatched.     

Synergistic effects of kinship, sex and rank in the behavioural interactions of captive stump-tailed macaques

In almost all non-human primate species kinship, sex and rank bias the patterning of interactions among subjects, seemingly in a way that favours the individual's fitness. A number of studies have been done in order to study separately the effects of these variables, concluding that an adequate model of interactions cannot be developed assuming preponderance of a single variable. The 'willingness' of one animal to interact with another can be explained as the result of assessing the possible outcomes (proximate and/or ultimate) of the interaction. The interrelationship of variables such as kinship, sex and rank, among others, provides the actors with a basis for deciding their rates of social interactions. The following study was done to assess whether kinship, rank and sex exerted independent, additive effects in the within-group distributions of eight social behaviour categories of captive groups of stump-tailed macaques. We found that the three variables synergistically affected the patterning of all behavioural categories. This suggests that the pay-offs of social interactions do not vary linearly, being intrinsically correlated with the actors' attributes so that uncertainty in the choice of a potential partner is minimized.     

Male dominance rank and reproductive success in primate groups

The relationship between male dominance rank and reproductive success has been a topic of interest since the beginning of primatology. From a theoretical point of view the existence or absence of this relationship has great implications with respect to the meaning of dominance rank and more general of the social relationships between individuals within social groups. Until fairly recently mating behaviour has been used as an indicator of reproductive success, but these two variables need not be correlated. The relations between mating success, reproductive success, and dominance rank indicate whether selective mating is involved (different mating partners at different phases of fertility, for example through male contest or female choice). With the development of genetic techniques to determine reproductive success directly, it has now become possible to investigate these relations. In our study on wild long-tailed macaques (Macaca fascicularis) we find a relatively strong correlation between rank and reproductive success which is attributable to selective mating by the alpha male during fertile periods of the females. In most previous studies no such clear results have been obtained, and we discuss the differences in outcome in relation to the study conditions, group sizes, and possible differences between species in terms of reproductive strategies.     

Measuring Evolutionary Constraints Through the Dimensionality of the Phenotype: Adjusted Bootstrap Method to Estimate Rank of Phenotypic Covariance Matrices

The potential and direction of phenotypic evolution is constrained by the distribution of genetic variation for the traits as described by the phenotypic (P) and genetic covariance matrices (G). The rank of the covariance matrix reflects the number of independent variational dimensions of the phenotype. Covariance matrices with less than full rank indicate lack of variation in some directions of the phenotype space and thus are an indication of absolute evolutionary constraints. Because selection acts upon phenotypic variation, the rank of P represents the upper limit of the dimensionality in G, relevant for selection response. The limitations of current methods to estimate matrix rank motivated us to analyze and adjust a bootstrap method and evaluate its performance by simulation. The results show that the modified bootstrap method (ABRE) gives reliable and rather conservative rank estimates when the sample size is sufficient for the number of variables studied (the sample size is at least five-fold the number of variables). Applying the method to various datasets suggests high phenotypic dimensionality in all cases. The analysis thus provides no evidence for absolute evolutionary constraints. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Stochastically Independent Components in the Analysis of Variance

In this paper an analysis of a sum of squares for linear hypothesis in a fixed linear model is presented. The analysis is based on a partition of sum of squares into independent components. These components are treated as sums of squares for hypotheses implied by an overall one. In the special case components of a sum of squares are distributed with one degree of freedom each and hypotheses concern single parametric functions. In the model not of full rank the form of a sum of squares is transformed before partitioning. The case of the model for cross classification is considered in details. Next the cases of the model of full rank and the one with restrictions on parameters are discussed. The model for balanced design with unweighted restrictions on parameters is considered in details. In this case sume of squares for orthogonal contrasts are obtained from analysis of the sum of squares for hypothesis concerning main or interaction effects.     

Matrilineal rank Inheritance varies with absolute rank in Japanese macaques

In many cercopithecine primates, females form linear dominance hierarchies based on kinship. It is known that female rank follows the rules of matrilineal rank inheritance (MIR): (1) maternal rank inheritance, (2) maternal dominance, and (3) youngest ascendancy among sisters. Although, several determining such variation remain largely unknown. In this paper, I investigate the dominance relation-ships of 69 adult (>6 yr old) female Japanese macaques (Macaca fuscata fuscata) in a free-ranging provisioned troop living in Shiga-Heights (Nagano Prefecture, Japan) and report new evidence of intra-group variation. Dominance relationships among high-ranking females followed MRI within kin units, those among low-ranking females did not. Maternal rank inheritance and youngest ascendancy operated between mother/daughter dyads and sister dyads of high-rank, but not in the dyads of low-rank. The dominance ranks of females from low-ranking kin units were dispersed and less predictable. These findings suggest that MRI varies with absolute dominance rank, and are discussed in relation to other asymmetries between high-and low-rank     

The Polynomial Model in the Multivariate Analysis of Variance

Assuming that the independent variables (factors) are quantitative, there exist besides the coding schemes generally used for the multivariate analysis of variance (dummy-coded or effect-coded design matrices) the so-called polynomial models. The advantage of these polynomial models are the full rank design matrices, which allow a more comprehensible analysis, i.e. the unambiguous interpretation of tested hypotheses and simultaneous confidence intervals.     

Reduced rank proportional hazards model for competing risks

Competing events concerning individual subjects are of interest in many medical studies. For example, leukemia-free patients surviving a bone marrow transplant are at risk of developing acute or chronic graft-versus-host disease, or they might develop infections. In this situation, competing risks models provide a natural framework to describe the disease. When incorporating covariates influencing the transition intensities, an obvious approach is to use Cox's proportional hazards model for each of the transitions separately. A practical problem then is how to deal with the abundance of regression parameters. Our objective is to describe the competing risks model in fewer parameters, both in order to avoid imprecise estimation in transitions with rare events and in order to facilitate interpretation of these estimates. Suppose that the regression parameters are gathered into a p x K matrix B, with p and K as the number of covariates and transitions, respectively. We propose the use of reduced rank models, where B is required to be of lower rank R, smaller than both p and K. One way to achieve this is to write B = AGamma(intercal) with A and Gamma matrices of dimensions p x R and K x R, respectively. We shall outline an algorithm to obtain estimates and their standard errors in a reduced rank proportional hazards model for competing risks and illustrate the approach on a competing risks model applied to 8966 leukemia patients from the European Group for Blood and Marrow Transplantation.     

Variation in social rank acquisition influences lifetime reproductive success in black-capped chickadees

Dominance relationships structure many animal societies, yet the process of rank attainment is poorly understood. We investigated acquisition of social dominance in winter flocks and its fitness consequences in male black-capped chickadees (Poecile atricapillus) over a 10-year period. Age was the best predictor of rank, and paired comparisons showed high-ranked males to be older than their low-ranked flock-mates. When controlling for age, morphological variables did not predict male social rank, but high-ranked males were heavier, had lower fat scores and were in leaner condition than low-ranked males. Males that survived between years tended to increase in rank over time; however, the rate of rank advancement varied individually. Rank reversals between familiar contestants were rare, and changes in male social rank were associated with changes in flock membership. Average lifetime reproductive success (LRS) of males and females was variable and best predicted by lifespan. Male rank history also influenced realized reproductive success. Birds with higher average rank over their lifespan were more likely to reproduce successfully. However, among successful birds, average rank did not significantly predict LRS. Thus, birds that lived longer and attained high social rank earlier had higher fitness, but this effect was not manifested as fine-scale differences among successful individuals. Taken together, these findings demonstrate the importance of social factors influencing individual fitness.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 90 , 85–95.     

On dominance rank and kinship of a wild Japanese monkey troop in Arashiyama

Observations on dominance rank and kinship of a wild Japanese monkey troop living in Arashiyama, Kyoto, were made as follows: (1) Ranking exists among consanguineous-relatives, and their dominance relation has a great effect on the ranking of individual infants, the influence of which remains after they have grown; (2) With the development of individual infants, a dominance rank is formed by the age of 1 among males and females of the same age according to the ranking of their mothers in the troop, that is, the ranking of consanguineous-relatives, and it remains unchanged through the age of 2; (3) Comparison between individual males and females in ranking becomes difficult to assess after about 3 years of age, though the dominance rank based on mothers' rank still exists among both males and females of the same age. And this dominance' rank becomes very stable; (4) The principle of “youngest ascendency” becomes effective among sisters more than 4 years old. The youngest sister ranks just below her mother and holds the second rank among lineal consanguineous-relatives; (5) Brothers of very close ages temporarily tend toward youngest ascendency when they are 2 or 3 years old, but this relation is soon reversed into the dominance of the elder brother over the younger; (6) Whether male or female, a younger infant of a higher-ranking mother challenges an elder one of a lower-ranking mother and outranks it. In the case of males especially, disparity of age, joint effects of a group, dependent effects on the central part that attend on peripheralization play an important role in outranking.     

An organism-specific method to rank predicted coding regions in Trypanosoma brucei

Genome annotation in differently evolved organisms presents challenges because the lack of sequence-based homology limits the ability to determine the function of putative coding regions. To provide an alternative to annotation by sequence homology, we developed a method that takes advantage of unusual trypanosomatid biology and skews in nucleotide composition between coding regions and upstream regions to rank putative open reading frames based on the likelihood of coding. The method is 93% accurate when tested on known genes. We have applied our method to the full complement of open reading frames on Chromosome I of Trypanosoma brucei, and we can predict with high confidence that 226 putative coding regions are likely to be functional. Methods such as the one described here for discriminating true coding regions are critical for genome annotation when other sources of evidence for function are limited.     

Dominance rank reversals and rank instability among male Lemur catta: the effects of female behavior and ejaculation

In this study, dominance rank instability among male Lemur catta during mating was investigated. Also, data on agonism and sexual behavior across five consecutive mating seasons in a population of L. catta on St. Catherines Island, USA, were collected. Instances of male rank instability were categorized into three types. Type 1 consisted of a temporary switch in the dominance ranks of two males, which lasted for a period of minutes or hours. Type 2 dyadic male agonistic interactions showed highly variable outcomes for a period of time during which wins and losses were neither predictable nor consistent. Type 3 interactions consisted of a single agonistic win by a lower-ranked male over a more dominant male. More Type 2 interactions (indicating greater dominance instability) occurred when males had not spent the previous mating season in the same group, but this trend was not statistically significant. The majority of periods of male rank instability were preceded by female proceptivity or receptivity directed to a lower-ranked male. As such, exhibition of female mate choice for a lower-ranking male appeared to incite male-male competition. Following receipt of female proceptivity or receptivity, males who were lower-ranking took significantly longer to achieve their first agonistic win over a more dominant male than did males who were higher-ranked. Ejaculation frequently preceded loss of dominance. In conclusion, temporary rank reversals and overall dominance rank instability commonly occur among male L. catta in mating contexts, and these temporary increases in dominance status appear to positively affect male mating success.     

Incorporation of clustering effects for the Wilcoxon rank sum test: a large-sample approach

The Wilcoxon rank sum test is frequently used in statistical practice for the comparison of measures of location when the underlying distributions are far from normal or not known in advance. An assumption of the ordinary rank sum test is that individual sampling units are independent. In many ophthalmologic clinical trials, the Early Treatment for Diabetic Retinopathy Scale (ETDRS) is a principal endpoint used for measuring the level of diabetic retinopathy. This is an ordinal scale, and it is natural to consider the Wilcoxon rank sum test for the comparison of the level of diabetic retinopathy between treatment groups. However, under this design, unlike the usual Wilcoxon rank sum test, the subject is the unit of randomization, but the eye is the unit of analysis. Furthermore, a person will tend to have different, but correlated, ETDRS scores for fellow eyes. Thus, we propose a correction to the variance of the Wilcoxon rank sum statistic that accounts for clustering effects and that can be used for both balanced (same number of subunits per cluster) or unbalanced (different number of subunits per cluster) data, both in the presence or absence of ties, with p-value adjusted accordingly. In this article, we present large-sample theory and simulation results for this test procedure and apply it to diabetic retinopathy data from type I diabetics in the Sorbinil Retinopathy Trial.     

The Wilcoxon signed rank test for paired comparisons of clustered data

The Wilcoxon signed rank test is a frequently used nonparametric test for paired data (e.g., consisting of pre- and posttreatment measurements) based on independent units of analysis. This test cannot be used for paired comparisons arising from clustered data (e.g., if paired comparisons are available for each of two eyes of an individual). To incorporate clustering, a generalization of the randomization test formulation for the signed rank test is proposed, where the unit of randomization is at the cluster level (e.g., person), while the individual paired units of analysis are at the subunit within cluster level (e.g., eye within person). An adjusted variance estimate of the signed rank test statistic is then derived, which can be used for either balanced (same number of subunits per cluster) or unbalanced (different number of subunits per cluster) data, with an exchangeable correlation structure, with or without tied values. The resulting test statistic is shown to be asymptotically normal as the number of clusters becomes large, if the cluster size is bounded. Simulation studies are performed based on simulating correlated ranked data from a signed log-normal distribution. These studies indicate appropriate type I error for data sets with > or =20 clusters and a superior power profile compared with either the ordinary signed rank test based on the average cluster difference score or the multivariate signed rank test of Puri and Sen. Finally, the methods are illustrated with two data sets, (i) an ophthalmologic data set involving a comparison of electroretinogram (ERG) data in retinitis pigmentosa (RP) patients before and after undergoing an experimental surgical procedure, and (ii) a nutritional data set based on a randomized prospective study of nutritional supplements in RP patients where vitamin E intake outside of study capsules is compared before and after randomization to monitor compliance with nutritional protocols.     

Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication)

Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme.     

Analysis of the apoC-II gene in apoC-II deficient patients

Apolipoprotein C-II (apoC-II), a 79 amino acid protein, is a cofactor for lipoprotein lipase, the enzyme which catalyzes the lipolysis of triglycerides on plasma chylomicrons and VLDL. Patients with apoC-II deficiency have marked elevations in plasma triglycerides, chylomicrons, VLDL, and a type I hyperlipoproteinemia. In order to evaluate the molecular defect in apoC-II deficiency, genomic DNA was analyzed using Southern Blot from 2 independent apoC-II deficient patients and compared to normal controls. Restriction digests of genomic DNA were performed with five different enzymes and the restriction fragments analyzed utilizing a 354 base pair nick-translated apoC-II probe for hybridization following Southern blotting. The restriction fragments varied from 0.8 to 21 Kb, and the pattern with normal DNA was identical to that of the two apoC-II deficient patients. The present study reveals that the apoC-II gene is present in patients with apoC-II deficiency. In addition, no insertional or deletional polymorphism was detected in the apoC-II gene of apoC-II deficient patients.     

Social rank affects reproductive development in male lambs

Under field conditions, dominant rams may prevent mating by other rams, thereby depressing flock fertility. However, little is known about the effects of social rank on prepuberal reproductive development in male lambs. The objective of this experiment was to determine if social rank of lambs is related to body weight, scrotal circumference, testosterone concentrations, semen production and courtship behavior until 38 weeks of age. An additional aim was to characterize male-male sexual behavior and to determine if this behavior was related to social rank. Body weight, scrotal circumference and testosterone serum concentrations were measured weekly in 13 male lambs. In addition, semen was obtained by electroejaculation, and sexual behavior towards non-estrous ewes was registered every 2 weeks. Male-male mounts were also recorded weekly. Individual social rank success indexes were determined using the food competition test when lambs were 3 and 6 months old. The five rams with greater (GR) and the five with lesser (LR) success indexes were used in the experiment. Body weight and scrotal circumference increases were greater in GR than in LR lambs. Testosterone concentrations increased with age, but were not related to social rank. Semen characteristics matured earlier in GR than in LR lambs. Most courtship and mating behaviors (lateral approaches, flehmen, ejaculations and ejaculations/total mounts) increased with age, but no effect of social rank was observed. The number of ano-genital sniffing and mount attempts increased with age and was greater in GR than LR. The total number of male-male mounts in which each lamb took part was positively related with the success index (r=0.48; P=0.05), and tended to be related with the number of times each lamb was mounted (r=0.42; P=0.06). No relation was observed between the number of times each lamb mounted and the social rank success index. We observed that GR lambs mature earlier than LR lambs, which is reflected by a greater increase of their body weight and scrotal circumference. Semen production and male-female sexual behavior also occurred earlier in high-ranked than in low-ranked lambs. It remains to be determined if low-ranked lambs can achieve similar development than high-ranked lambs over longer time intervals, or if their maximum developmental capacity is lower than the maximum obtained by high-ranked lambs.     

Longitudinal changes of dominance rank among the females of the Koshima group of Japanese monkeys

The changes of dominance rank among female Japanese monkeys of the Koshima group over a period of 29 years from 1957 were studied. The dominance rank order was relatively stable in the early population growing phase, while large scale-changes of dominance rank order occurred successively in the phase of population decrease brought about by the severe control of artificial feeding after 1972. Nevertheless, the rank order of several females of the highest status was stable. Furthermore, the reproductive success of these highest status females was high (Mori, 1979a;Watanabe et al., in prep.). Divergence of the dominance rank order fromKawamura's rules (Kawamura, 1958) was observed in the following respects: (1) Some females significantly elevated their rank depending on the leader males. (2) If mothers died when their daughters were still juveniles or nulliparous, the dominance rank of some of these offspring females was significantly lower than the mother's one. However 55% of daughters which lost their mothers at a young age inherited the mother's rank. (3) Dominance among sisters whose mother had died when at least one of the daughters was under 6 years old followed the rule of youngest ascendancy in 60% (Kawamura, 1958), and in 80% when both of the daughters were nulliparous at the mother's death. The mean rate of aggressive interactions for each female with subordinates to her was calculated by dividing the total aggressive interactions between the female in question and her subordinates by the number of subordinate females to the female in question. A female which showed a high rate of aggressive interactions with her subordinates was categorized as an “Attacker”, and a female showing a lower rate was categorized as a “Non-attacker”. Similarly, categories of “Attacked”, and “Non-attacked” were distinguished by using the rate of aggressive interactions with dominant females. Several females which were once categorized in one category in a year were repeatedly categorized in the same category over different years. The “Attacked” tended to be females of higher rank, and “Non-attackers” tended to be females of lower rank. “The second-higher-status females”, were “Attacked”, and their rank was unstable. In particular, females of lower rank within the lineage of the highest rank suffered this kind of severe status. Most of the daughters of these females showed a sharp drop of rank, and died when they were still at a young age, i.e. “the second-higher-status females” displayed low fitness. “Non-attackers” were significantly “Non-attacked”; i.e. they were females which showed a non-social attitude. Females which underwent a drop of rank tended to be “Non-attackers”. The most important factor which determined the females' rank was the memory of their dominance relations under the influence of their mother [dependent rank (Kawai, 1958)] in their early life during development. This finding corresponds well with the results in baboons obtained byWalter (1980); the target females of aggressive interactions by adolescent females were determined by the rank of the mothers when these adolescent females were born.     

The rank ordering of genotypic fitness values predicts genetic constraint on natural selection on landscapes lacking sign epistasis

Sewall Wright's genotypic fitness landscape makes explicit one mechanism by which epistasis for fitness can constrain evolution by natural selection. Wright distinguished between landscapes possessing multiple fitness peaks and those with only a single peak and emphasized that the former class imposes substantially greater constraint on natural selection. Here I present novel formalism that more finely partitions the universe of possible fitness landscapes on the basis of the rank ordering of their genotypic fitness values. In this report I focus on fitness landscapes lacking sign epistasis (i.e., landscapes that lack mutations the sign of whose fitness effect varies epistatically), which constitute a subset of Wright's single peaked landscapes. More than one fitness rank ordering lacking sign epistasis exists for L > 2 (where L is the number of interacting loci), and I find that a highly statistically significant effect exists between landscape membership in fitness rank-ordering partition and two different proxies for genetic constraint, even within this subset of landscapes. This statistical association is robust to population size, permitting general inferences about some of the characteristics of fitness rank orderings responsible for genetic constraint on natural selection.     

Age,dominance rank,natal status,and tenure among male macaques

Age and rank are often related among males in multi-male groups of macaques. However, recent studies have not consistently reported that age and rank are correlated. This paper reviews studies providing data on at least age and rank for each individual in the sample to investigate how the demographic composition of data samples can affect whether statistical analysis finds significant correlations between age and rank. I reanalyzed data on the age composition, natal status, and length of tenure of the males comprising the samples. Significant nonlinear age-rank relations existed in four of seven studies reviewed. Samples lost statistical significance after removing younger individuals, but at different lower age limits. Samples showing no significant age-rank correlation consisted mostly of adults or natal males. The length of tenure in a troop and natal status showed strong correlations with residuals of the nonlinear age-rank regressions, implying that these factors tend to weaken age-rank correlations, but tenure may have little effect independent of age among males staying in troops longer than about 1 year. The data suggest that the demographic composition of study samples, especially age, may still explain some differences in conclusions among studies on rank and reproductive success focused on “adult” samples. Relatively younger or older males may have contributed to significant correlations between rank and measures of mating success, as they do for age and rank. Primatologists may need to apply nonlinear statistical techniques to samples composed of wide age ranges without subdivision to investigate the causes of both the cross-age and within-age variation in dominance rank or reproductive success. Am J Phys Anthropol 105:511–521, 1998. © 1998 Wiley-Liss, Inc.