Application of maximum likelihood paired comparison ranking to estimation of a linear dominance hierarchy in animal societies

Dominance hierarchies have been widely used for describing the outcome of competitive interactions in an animal group. We present a procedure for estimating the linear dominance hierarchy. The procedure uses the statistical method of paired comparisons, assuming weak stochastic transitivity to model interactions within a linear dominance hierarchy. The linear dominance hierarchy is estimated using a maximum likelihood ranking procedure. This method allows unequal numbers of encounters between pairs and does not require all pairs to have observed encounters. The method is illustrated by application to behavioural data from a group of 10 baboons (Papio cynocephalus anubis).     

Dominance and queen succession in captive colonies of the eusocial naked mole-rat,Heterocephalus glaber.

Naked mole-rat colonies exhibit a high reproductive skew, breeding being typically restricted to one female (the ''queen'') and one to three males. Other colony members are reproductively suppressed, although this suppression can be reversed following the removal or death of the queen. We examined dominance and queen succession within captive colonies to investigate the relationship between urinary testosterone and cortisol, dominance rank and reproductive status; and to determine if behavioural and/or physiological parameters can be used as predictors of queen succession. Social structure was characterized by a linear dominance hierarchy before and after queen removal. Prior to queen removal, dominance rank was negatively correlated with body weight and urinary testosterone and cortisol titres in males and females. Queen removal results in social instability and aggression between high ranking individuals. Dominance rank appears to be a good predictor of reproductive status: queens are the highest ranking colony females and are succeeded by the next highest ranking females. The intense dominance-related aggression that accompanies reproductive succession in naked mole-rats provides empirical support for optimal skew theory.     

Gamete-competition models

The gamete-competition model is an application of the Bradley-Terry model for ranking of sports teams. If allele i of a marker locus is assigned parameter taui>0, then the probability that a parent with heterozygous genotype i/j transmits allele i is Pr(i/j-->)=tau(i)/(tau(i) + tau(j). Mendelian segregation corresponds to the choice tau(i)=1 for all i. To test whether Mendelian segregation is true, one can estimate the tau(i) from pedigree data and perform a likelihood-ratio test under the constraint that one tau(i) equals 1. Although this procedure generates an interesting method for performance of segregation analysis with a marker locus, its real promise lies in generalization of the transmission/disequilibrium test. Quantitative as well as qualitative outcomes can be considered. The gamete-competition model uses full pedigree data and gives an estimate of the strength of transmission distortion to affected children for each allele. Covariates are incorporated by rewriting of tau(i)=exp(beta(t)x(k)), where beta is a parameter vector and xk is a covariate vector for the kth transmitted gamete. Examples of covariates include disease-severity indicators for the child, sex of the child, or repeat number for tandem-repeat alleles.     

A Cognitive Model for Aggregating People's Rankings

We develop a cognitive modeling approach, motivated by classic theories of knowledge representation and judgment from psychology, for combining people''s rankings of items. The model makes simple assumptions about how individual differences in knowledge lead to observed ranking data in behavioral tasks. We implement the cognitive model as a Bayesian graphical model, and use computational sampling to infer an aggregate ranking and measures of the individual expertise. Applications of the model to 23 data sets, dealing with general knowledge and prediction tasks, show that the model performs well in producing an aggregate ranking that is often close to the ground truth and, as in the “wisdom of the crowd” effect, usually performs better than most of individuals. We also present some evidence that the model outperforms the traditional statistical Borda count method, and that the model is able to infer people''s relative expertise surprisingly well without knowing the ground truth. We discuss the advantages of the cognitive modeling approach to combining ranking data, and in wisdom of the crowd research generally, as well as highlighting a number of potential directions for future model development.     

Aggression or ovarian development as determinants of reproductive dominance in Bombus terrestris: interpretation using a simulation model

Insect societies generally manifest reproductive division of labor with one or a few fecund females (queens) and sterile helpers (workers). This is generally mediated by behavioural hierarchy that reduces the cost of within-group aggression. Aggressive behaviour and ovarian development are thus two co-occurring correlates of reproductive skew, but their mutual influence remains unclear. Here we examined the interplay between these factors by constructing a simulation model, based on the biology of Bombus terrestris, to test whether aggression levels are determined by the level of ovarian development or vice versa. We approached this question using virtual groups composed of either equally or unequally matched workers, as well as supplementing the simulation data by experimental data using actual bee groups. The simulation revealed that previous encounter experience (win/lose) rather than mutual assessment of reproductive status determines and maintains hierarchy in B. terrestris. Furthermore, although bumblebee workers largely vary in their aggression tendencies, pre-existing differences between nest-mates were not obligatory for establishment of the hierarchy. The initially formed linear hierarchy became polynomial after 10 days, clearly separating between egg-laying workers and helpers. This was consistent with the results obtained for actual bee groups. We propose that aggressive behaviour and the outcome of previous encounters are major determinants of ovarian development and not vice versa. Workers may gain a head start in the competition due to variation in their innate aggressive tendencies, or by fortuitously winning their first encounters. Small differences in aggressiveness between workers are amplified to initially form a short-term linear hierarchy that subsequently turns to polynomial hierarchy, creating the most basic phenomenon of social groups, reproductive division of labor.     

Ranking Competitors Using Degree-Neutralized Random Walks

Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each edge that guides the random walker towards the weaker (or the stronger) node, which enables us to interpret the steady-state occupancy as the measure of the node''s weakness (or strength) that is free of unwarranted degree-induced bias. We apply our method to two real-world competition networks and explore the issues of ranking stabilization and prediction accuracy, finding that our method outperforms other methods including the baseline win–loss differential method in sparse networks.     

Your Relevance Feedback Is Essential: Enhancing the Learning to Rank Using the Virtual Feature Based Logistic Regression

Information retrieval applications have to publish their output in the form of ranked lists. Such a requirement motivates researchers to develop methods that can automatically learn effective ranking models. Many existing methods usually perform analysis on multidimensional features of query-document pairs directly and don''t take users'' interactive feedback information into account. They thus incur the high computation overhead and low retrieval performance due to an indefinite query expression. In this paper, we propose a Virtual Feature based Logistic Regression (VFLR) ranking method that conducts the logistic regression on a set of essential but independent variables, called virtual features (VF). They are extracted via the principal component analysis (PCA) method with the user''s relevance feedback. We then predict the ranking score of each queried document to produce a ranked list. We systematically evaluate our method using the LETOR 4.0 benchmark datasets. The experimental results demonstrate that the proposal outperforms the state-of-the-art methods in terms of the Mean Average Precision (MAP), the Precision at position k (k@P), and the Normalized Discounted Cumulative Gain at position k (k@GCDN).     

Branches in the lines of descent: Charles Darwin and the evolution of the species concept

Charles Darwin introduced a novel idea into the concept of species, namely that species are branches in the lines of descent (segments of population lineages). In addition to this novel evolutionary component, Darwin's species concept also retained an older taxonomic component, namely the view that the species category is a taxonomic rank; moreover, he adopted amount of difference as a criterion for ranking lineages as species. Subsequent biologists retained both components of Darwin's species concept, although they replaced Darwin's ranking criterion with ranking criteria that either are more objectively defined or relate more directly to the biological bases of lineage separation and divergence. Numerous alternative ranking criteria were proposed, resulting in a proliferation of species definitions and a controversy concerning the concept of species. That controversy can be resolved by distinguishing more explicitly between the theoretical concept of species and the operational criteria that are used to apply the concept in practice. By viewing the various alternative ranking criteria as operational indicators of lineage separation rather than necessary properties of species, the conflicts among competing species concepts are eliminated, resulting in a unified concept of species. A brief examination of the history of biology reveals that an important shift related to the unified species concept has been emerging ever since Darwin reformulated the concept of species with an evolutionary basis. The species category is effectively being decoupled from the hierarchy of taxonomic ranks and transferred to the hierarchy of biological organization. Published 2011. This article is a US Government work and is in the public domain in the USA. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 103 , 19–35.     

Queen Succession in the Social Wasp,Polistes annularis

Outcomes of conflicts among social animals can strongly affect individual fitness and therefore partly determine how sociality evolves. In the social wasp, Polistes annularis, conflicts over egg laying result in a linear dominance hierarchy discernible from which wasps attack which others. We investigated the structure and maintenance of dominance hierarchies in colonies containing both nest foundresses and workers. We also investigated the outcome of a potential conflict between foundresses and workers over the identity of the female which becomes queen after the original queen disappears. To investigate queen replacement we recorded individuals' behavior before and after removal of the queen from 13 nests. This experiment simulated natural queen disappearance which occurs frequently. All foundresses were ranked over workers; high ranking females were most aggressive and directed most of their attacks to the female directly beneath them in the hierarchy. This hierarchy determined succession to queenship; the beta female became queen within 3 h. Therefore a foundress became the new queen whenever one was present. There was no evidence of conflict between workers and foundresses when a foundress became queen. This chance of becoming queen contributes to the expected fitness of a female that accepts a subordinate role in spring.     

How feeding competition determines female chimpanzee gregariousness and ranging in the Taï National Park, Côte d'Ivoire

Socioecological theory suggests that feeding competition shapes female social relationships. Chimpanzees (Pan troglodytes) live in fission–fusion societies that allow them to react flexibly to increased feeding competition by forming smaller foraging parties when food is scarce. In chimpanzees at Gombe and Kibale, female dominance rank can crucially influence feeding competition and reproductive success as high‐ranking females monopolize core areas of relatively high quality, are more gregarious, and have higher body mass and reproductive success than low‐ranking females. Chimpanzee females in Taï National Park do not monopolize core areas; they use the entire territory as do the males of their community and are highly gregarious. Although female chimpanzees in Taï generally exhibit a linear dominance hierarchy benefits of high rank are currently not well understood. We used a multivariate analysis of long‐term data from two Taï chimpanzee communities to test whether high‐ranking females (1) increase gregariousness and (2) minimize their travel costs. We found that high‐ranking females were more gregarious than low‐rankers only when food was scarce. During periods of food scarcity, high rank allowed females to enjoy benefits of gregariousness, while low‐ranking females strongly decreased their gregariousness. High‐ranking females traveled more than low‐ranking females, suggesting that low‐rankers might follow a strategy to minimize energy expenditure. Our results suggest that, in contrast to other chimpanzee populations and depending on the prevailing ecological conditions, female chimpanzees at Taï respond differently to varying levels of feeding competition. Care needs to be taken before generalizing results found in any one chimpanzee population to the species level. Am. J. Primatol. 73:305–313, 2011. © 2010 Wiley‐Liss, Inc.     

The Maintenance of Stable Dominance Hierarchies and the Pattern of Aggression: Support for the Suppression Hypothesis

Three hypotheses have been proposed to explain the development and maintenance of dominance hierarchies. According to the first hypothesis the dominance hierarchy is a result of the animals fighting once at their first encounter and then using the outcome of that fight to determine the rank order. The second hypothesis proposes that a dominance hierarchy reflects the fighting ability of the individuals in the group at each moment and is therefore relatively fluid with individuals continuously fighting for position. A third hypothesis, the suppression hypothesis, states that the dominance hierarchy is based to a large extent on the outcome of the first fight between the individuals but the dominant animal in each pair continuously attacks the subdominant individuals to condition them to lose in future encounters. We studied six well‐established flocks containing six adult hens each (Gallus gallus domesticus). Five of the flocks had linear hierarchies. The aggression was significantly more often directed towards the next low‐ranking individual. There was a good correlation between rank and comb size (height × width), but no significant correlation between rank and weight, or rank and level of fluctuating asymmetry. There was no significant correlation between levels of aggression and similarity of comb size for individuals of neighboring ranks. Our results tentatively support the suppression hypothesis for the maintenance of dominance hierarchies in the domestic hen.     

From hierarchy to network: a richer view of evidence for evidence-based medicine

Evidence-based medicine (EBM) advocates the improvement of patient care through the use of current best research evidence in medical decision making. In practice, "best evidence" generally refers to where a study fits on a hierarchy of evidence, which places randomized controlled trials (RCTs) and other population-level research above laboratory research. Because population research is concerned primarily with average results obtained from large groups of people, ranking evidence on the basis of its place in the hierarchy is shortsighted and ultimately limits the ability of research results to inform the care of individual patients. The history and methodology of epidemiology reveals a close relationship between population-level and laboratory research; both types of research are necessary if we are to understand the causes of a disease. What EBM does not take into account in its hierarchy of evidence is that the same thing is true for research on the safety and efficacy of medical interventions. To maximize the information that clinical research can provide for clinical care, RCTs should be designed to elucidate within-group variability. This can only be done if the hierarchy of evidence is replaced by a network that takes into account the relationship between epidemiological and laboratory research.     

Can transitive inference evolve in animals playing the hawk-dove game?

What should an individual do if there are no reliable cues to the strength of a competitor when fighting with it for resources? We herein examine the evolutionarily stable strategy (ESS) in the hawk-dove game, if the opponent's resource-holding potential (RHP) can only indirectly be inferred from the outcome of past interactions in the population. The strategies we examined include the classical mixed strategy in which no information on past games is utilized, the 'imprinting' strategy in which a player increases/decreases its aggressiveness if it wins/loses a game, the 'immediate inference' strategy in which a player can infer the strength of those opponents it fought before, and the 'transitive inference' strategy in which a player can infer the strength of a new opponent through a third party with which both players have fought before. Invasibility analysis for each pair of strategies revealed that (i) the transitive-inference strategy can always invade the mixed strategy and the imprinting strategy, and itself refuses invasion by these strategies; (ii) the largest advantage for transitive inference is achieved when the number of games played per individual in one generation is small and when the cost of losing an escalated game is large; (iii) the immediate inference, rather than the transitive inference, can be an ESS if the cost of fighting is small; (iv) a strong linear ranking is established in the population of transitive-inference strategists, though it does not perfectly correlate to the ranking by actual RHPs. We found that the advantage of the transitive inference is not in its ability to correct a misassessment (it is actually the worst in doing so), but in the ability of quickly lining up either incorrect or correct assessments to form a linear dominance hierarchy.     

Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse‐engineering and a colonization–competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co‐occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio‐temporal samples of assemblages in homogenous environments or environmental gradients.     

How to Infer Relative Fitness from a Sample of Genomic Sequences

Mounting evidence suggests that natural populations can harbor extensive fitness diversity with numerous genomic loci under selection. It is also known that genealogical trees for populations under selection are quantifiably different from those expected under neutral evolution and described statistically by Kingman’s coalescent. While differences in the statistical structure of genealogies have long been used as a test for the presence of selection, the full extent of the information that they contain has not been exploited. Here we demonstrate that the shape of the reconstructed genealogical tree for a moderately large number of random genomic samples taken from a fitness diverse, but otherwise unstructured, asexual population can be used to predict the relative fitness of individuals within the sample. To achieve this we define a heuristic algorithm, which we test in silico, using simulations of a Wright–Fisher model for a realistic range of mutation rates and selection strength. Our inferred fitness ranking is based on a linear discriminator that identifies rapidly coalescing lineages in the reconstructed tree. Inferred fitness ranking correlates strongly with actual fitness, with a genome in the top 10% ranked being in the top 20% fittest with false discovery rate of 0.1–0.3, depending on the mutation/selection parameters. The ranking also enables us to predict the genotypes that future populations inherit from the present one. While the inference accuracy increases monotonically with sample size, samples of 200 nearly saturate the performance. We propose that our approach can be used for inferring relative fitness of genomes obtained in single-cell sequencing of tumors and in monitoring viral outbreaks.     

Energy-based graph convolutional networks for scoring protein docking models

Structural information about protein-protein interactions, often missing at the interactome scale, is important for mechanistic understanding of cells and rational discovery of therapeutics. Protein docking provides a computational alternative for such information. However, ranking near-native docked models high among a large number of candidates, often known as the scoring problem, remains a critical challenge. Moreover, estimating model quality, also known as the quality assessment problem, is rarely addressed in protein docking. In this study, the two challenging problems in protein docking are regarded as relative and absolute scoring, respectively, and addressed in one physics-inspired deep learning framework. We represent protein and complex structures as intra- and inter-molecular residue contact graphs with atom-resolution node and edge features. And we propose a novel graph convolutional kernel that aggregates interacting nodes’ features through edges so that generalized interaction energies can be learned directly from 3D data. The resulting energy-based graph convolutional networks (EGCN) with multihead attention are trained to predict intra- and inter-molecular energies, binding affinities, and quality measures (interface RMSD) for encounter complexes. Compared to a state-of-the-art scoring function for model ranking, EGCN significantly improves ranking for a critical assessment of predicted interactions (CAPRI) test set involving homology docking; and is comparable or slightly better for Score_set, a CAPRI benchmark set generated by diverse community-wide docking protocols not known to training data. For Score_set quality assessment, EGCN shows about 27% improvement to our previous efforts. Directly learning from 3D structure data in graph representation, EGCN represents the first successful development of graph convolutional networks for protein docking.     

Benefits and Costs of Dominance in the Angelfish Centropyge bicolor

Social groups are often structured by dominance hierarchies in which subordinates consistently defer to dominants. High‐ranking individuals benefit by gaining inequitable access to resources, and often achieve higher reproductive success; but may also suffer costs associated with maintaining dominance. We used a large‐scale field study to investigate the benefits and costs of dominance in the angelfish Centropyge bicolor, a sequential hermaphrodite. Each haremic group contains a single linear body size‐based hierarchy with the male being most dominant, followed by several females in descending size order. Compared to their subordinate females, dominant males clearly benefited from disproportionately high spawning frequencies, but bore costs in lower foraging rates and greater aggressive defence of their large territories. Within the female hierarchy, more dominant individuals benefited from higher spawning frequencies and larger home ranges, but displayed neither higher foraging rates nor spawn order priority. However, dominance in females was also linked to aggressiveness, particularly towards immediate subordinates, suggesting that females were using energetically costly aggression to maintain their high rank. We further showed by experimentally removing dominant females that the linear hierarchy was also a social queue, with subordinates growing to inherit higher rank with its attendant benefits and costs when dominants disappeared. We suggest that in C. bicolor, the primary benefit of high rank is increased reproductive success in terms of current spawning frequency and the prospect of inheriting the male position in the near future, which may be traded off against the cost of aggressively defending rank and territory.     

The Absence of Grooming for Rank-Related Benefits in Female Assamese Macaques (Macaca assamensis)

Seyfarth’s model of social grooming proposes that by grooming females higher ranking than themselves, females can gain access to important rank-related benefits, such as agonistic support. This, in turn, produces a distinctive pattern of grooming in which females direct their grooming up the female dominance hierarchy and compete for access to the highest ranking individuals. We aimed to test to what extent the grooming behavior of female Assamese macaques (Macaca assamensis) fits the assumptions and predictions of Seyfarth’s model. During two 1-yr sampling periods (October 2007–September 2008, May 2010–April 2011) we collected >2100 focal hours of data from a single wild group in their natural habitat at Phu Khieo Wildlife Sanctuary, Thailand. Subjects included all adult female group members (N?=?12 in 2007/8; N?=?15 in 2010/11). We collected detailed data on grooming interactions, approaches, and departures as well as all aggressive and submissive behaviors between all subjects. We found no evidence that grooming was exchanged for rank-related benefits. In line with this we found no evidence that the grooming of female Assamese macaques fits the pattern predicted by Seyfarth’s model. These results are surprising given that such deviations from Seyfarth’s model are relatively rare among macaques. We propose that our findings are best explained as a lack of a need for rank-related benefits by females in this group.     

Recognizing Sequences of Sequences

The brain''s decoding of fast sensory streams is currently impossible to emulate, even approximately, with artificial agents. For example, robust speech recognition is relatively easy for humans but exceptionally difficult for artificial speech recognition systems. In this paper, we propose that recognition can be simplified with an internal model of how sensory input is generated, when formulated in a Bayesian framework. We show that a plausible candidate for an internal or generative model is a hierarchy of ‘stable heteroclinic channels’. This model describes continuous dynamics in the environment as a hierarchy of sequences, where slower sequences cause faster sequences. Under this model, online recognition corresponds to the dynamic decoding of causal sequences, giving a representation of the environment with predictive power on several timescales. We illustrate the ensuing decoding or recognition scheme using synthetic sequences of syllables, where syllables are sequences of phonemes and phonemes are sequences of sound-wave modulations. By presenting anomalous stimuli, we find that the resulting recognition dynamics disclose inference at multiple time scales and are reminiscent of neuronal dynamics seen in the real brain.