Optimization over a class of tree shape statistics

Tree shape statistics quantify some aspect of the shape of a phylogenetic tree. They are commonly used to compare reconstructed trees to evolutionary models and to find evidence of tree reconstruction bias. Historically, to find a useful tree shape statistic, formulas have been invented by hand and then evaluated for utility. This paper presents the first method which is capable of optimizing over a class of tree shape statistics, called binary recursive tree shape statistics (BRTSS). After defining the BRTSS class, a set of algebraic expressions is defined which can be used in the recursions. The set of tree shape statistics definable using these expressions in the BRTSS is very general and includes many of the statistics with which phylogenetic researchers are already familiar. We then present a practical genetic algorithm which is capable of performing optimization over BRTSS given any objective function. The chapter concludes with a successful application of the methods to find a new statistic which indicates a significant difference between two distributions on trees which were previously postulated to have similar properties.     

Evaluating phylogenetic tree shape: two modifications to Fusco & Cronk's method.

Measurement of the degree of asymmetry in phylogenetic trees is important because a tree's shape reflects the process by which it has grown. For example, highly asymmetric trees are evidence that species have had different potential for diversification. Of the tree shape measures in the literature, that proposed by Fusco & Cronk (J. theor. Biol.175, 235-243) appears to be particularly useful, because it does not require fully-resolved trees whose terminals are of equal taxonomic rank. The value of the asymmetry or imbalance at a node is intended to be independent of the number of species ultimately descended from the node. In this paper, however, we point out that the value does depend upon species number. We propose two modifications that remove the dependency and so increase the measure's usefulness. We illustrate the use of the modified measures, which are implemented in a freely-available program, MESA.     

Intron evolution: a statistical comparison of two models.

The two most frequently occurring explanations for the existence and distribution of introns in the genes of different species are: (1) introns are remnants of the original genetic material. (2) Introns were introduced during evolution. We construct mathematical models corresponding to these two explanations, and calculate the probabilities that the intron distribution in genes from different species coding for actin, alpha-tubulin, triosephosphate isomerase and superoxide dismutase are described by these models. In both models, the branch lengths as well as the structure of the corresponding evolutionary tree is taken into account. Every branch in the evolutionary tree is assumed to have its own individual rate of loss of introns for the first model and rate of gain of introns for the second model. These rate constants are estimated from the actual number of introns. Using the rate constants we stimulate the intron evolution and calculate the probabilities that the actual intron arrangements are produced. The results for actin and alpha-tubulin, which are the two genes we have the most data for, favor the model corresponding conjecture (1), i.e. the idea that introns are old. This contradicts the results from an earlier attempt to model intron evolution where almost the same data was used (Dibb & Newman, 1989, EMBO J. 8, 2015-2021).     

The accuracy of species tree estimation under simulation: a comparison of methods

Numerous simulation studies have investigated the accuracy of phylogenetic inference of gene trees under maximum parsimony, maximum likelihood, and Bayesian techniques. The relative accuracy of species tree inference methods under simulation has received less study. The number of analytical techniques available for inferring species trees is increasing rapidly, and in this paper, we compare the performance of several species tree inference techniques at estimating recent species divergences using computer simulation. Simulating gene trees within species trees of different shapes and with varying tree lengths (T) and population sizes (), and evolving sequences on those gene trees, allows us to determine how phylogenetic accuracy changes in relation to different levels of deep coalescence and phylogenetic signal. When the probability of discordance between the gene trees and the species tree is high (i.e., T is small and/or is large), Bayesian species tree inference using the multispecies coalescent (BEST) outperforms other methods. The performance of all methods improves as the total length of the species tree is increased, which reflects the combined benefits of decreasing the probability of discordance between species trees and gene trees and gaining more accurate estimates for gene trees. Decreasing the probability of deep coalescences by reducing also leads to accuracy gains for most methods. Increasing the number of loci from 10 to 100 improves accuracy under difficult demographic scenarios (i.e., coalescent units ≤ 4N(e)), but 10 loci are adequate for estimating the correct species tree in cases where deep coalescence is limited or absent. In general, the correlation between the phylogenetic accuracy and the posterior probability values obtained from BEST is high, although posterior probabilities are overestimated when the prior distribution for is misspecified.     

Ecological opportunity and diversification in a continental radiation of birds: climbing adaptations and cladogenesis in the Furnariidae

Ecological theories of adaptive radiation predict that ecological opportunity stimulates cladogenesis through its effects on competitive release and niche expansion. Given that key innovations may confer ecological opportunity, we investigated the effect of the acquisition of climbing adaptations on rates of cladogenesis in a major avian radiation, the Neotropical bird family Furnariidae, using a species-level phylogeny. Morphological specializations for vertical climbing originated in the woodcreepers ～23 million years ago, well before that adaptation occurred in woodpeckers (Picidae) or in other potential competitors in South America. This suggests that the acquisition of climbing adaptations conferred ample ecological opportunity to early woodcreepers. Nonetheless, we found that increases in speciation rates in Furnariidae did not coincide with the acquisition of climbing adaptations and that the relationship between the accumulation of climbing adaptations and rates of speciation was negative. In addition, we did not detect a diversity-dependent decline in woodcreeper diversification rates consistent with saturation of the trunk-climbing niche. These findings do not support the hypothesis that ecological opportunity related to trunk foraging stimulated cladogenesis in this radiation. The negative effect of climbing on diversification may be mediated by an indirect positive effect of climbing on dispersal ability, which may reduce speciation rates over evolutionary timescales.     

Responses of crown development to canopy openings by saplings of eight tropical submontane forest tree species in Indonesia: a comparison with cool-temperate trees

BACKGROUND AND AIMS: Growth in trunk height in canopy openings is important for saplings. How saplings increase height growth in canopy openings may relate to crown architectural constraints. Responses of crown development to canopy openings in relation to trunk height growth were studied for saplings (0.2-2.5 m tall) of eight tropical submontane forest tree species in Indonesia. The results of this study were also compared with those of temperate trees in northern Japan. METHODS: The crown architecture differed among the eight tropical species, i.e. they had sparsely to highly developed branching structures. Crown allometry was compared among the eight species in each canopy condition (closed canopy or canopy openings), and between closed canopy and canopy openings within a species. A general linear regression model was used to analyse how each species increases height growth rate in canopy openings. Crown allometry and its plasticity were compared between tropical and temperate trees by a nested analysis of covariance. KEY RESULTS: Tropical submontane trees had responses similar to cool-temperate trees, showing an increase in height in canopy openings, i.e. taller saplings of sparsely branched species increase height growth rates by increasing the sapling leaf area. Cool-temperate trees have a wider crown projection area and a smaller leaf area per crown projection area to avoid self-shading within a crown compared with tropical submontane trees. Plasticity of the crown projection area is greater in cool-temperate trees than in tropical submontane trees, probably because of the difference in leaf longevity. CONCLUSIONS: This study concluded that interspecific variation in the responses of crown development to canopy openings in regard to increasing height related to the species' branching structure, and that different life-forms, such as evergreen and deciduous trees, had different crown allometry and plasticity.     

Recognizing the forest for the trees: testing temporal patterns of cladogenesis using a null model of stochastic diversification

Computer simulations are developed and employed to examine the expected temporal distributions of nodes under a null model of stochastic lineage bifurcation and extinction. These Markovian models of phylogenetic process were constructed so as to permit direct comparisons against empirical phylogenetic trees generated from molecular or other information available solely from extant species. For replicate simulated phylads with n extant species, cumulative distribution functions (cdf's) of branching times were calculated, and compared (using the Kolmogorov-Smirnov test statistic D) to those from three published empirical trees. Molecular phylogenies for columbine plants and avian cranes showed statistically significant departures from the null expectations, in directions indicating recent and ancient species' radiations, respectively, whereas a molecular phylogeny for the Drosophila virilis species group showed no apparent historical clustering of branching events. Effects of outgroup choice and phylogenetic frame of reference were investigated for the columbines and found to have a predictable influence on the types of conclusions to be drawn from such analyses. To enable other investigators to statistically test for nonrandomness in temporal cladogenetic pattern in empirical trees generated from data on extant species, we present tables of mean cdf's and associated probabilities under the null model for expected branching times in phylads of varying size. The approaches developed in this report complement and extend those of other recent methods for employing null models to assess the statistical significance of pattern in evolutionary trees.      

The quantitative genetics of fluctuating asymmetry: a comparison of two models

The genetic basis of fluctuating asymmetry (FA), a measure of random deviations from perfect bilateral symmetry, has been the subject of much recent work. In this paper we compare two perspectives on the quantitative genetic analysis of FA and directional asymmetry (DA). We call these two approaches the character-state model and the environmental responsiveness model. In the former approach, the right and left sides are viewed as separate traits whose genetic coupling is manifested by the genetic correlation. This model leads to the relationship, h2(DA) = h2[(1-rA)/(1-rp)), where h2 is the heritability of each component trait (assumed to be the same), rA and rp are the genetic and phenotypic correlations between traits, respectively. Simulation shows that, under this model, the heritability of FA is considerably less than that of DA, except when heritabilities are very close to zero. The environmental responsiveness model permits genetic variance in FA even when the genetic correlation between traits is + 1. Simulation shows that under this model the heritability of FA can be uncoupled from that of DA. The additive and nonadditive components of the component (right and left) traits, their DA and FA values are estimated using a diallel cross of seven inbred lines of the sand cricket, Gryllus firmus. Four leg measurements were made and both the individual DA and FA values and the compound measures DASUM and CFA estimated. The heritabilities of the compound measures are slightly larger than the individual estimates. Dominance variance is observed in the individual traits but predicted to be an even smaller component of the phenotypic variance than the additive genetic variance. The estimated values confirm this, although a previous study has demonstrated that dominance variance is present. Because the heritabilities of FA are generally larger than those of DA, which never exceed 0.02, the environmental responsiveness model is more consistent with the data than the character-state model. A review of other data suggests that both sources of variation might be found in some species.     

The shape of supertrees to come: tree shape related properties of fourteen supertree methods

Using a simple example and simulations, we explore the impact of input tree shape upon a broad range of supertree methods. We find that input tree shape can affect how conflict is resolved by several supertree methods and that input tree shape effects may be substantial. Standard and irreversible matrix representation with parsimony (MRP), MinFlip, duplication-only Gene Tree Parsimony (GTP), and an implementation of the average consensus method have a tendency to resolve conflict in favor of relationships in unbalanced trees. Purvis MRP and the average dendrogram method appear to have an opposite tendency. Biases with respect to tree shape are correlated with objective functions that are based upon unusual asymmetric tree-to-tree distance or fit measures. Split, quartet, and triplet fit, most similar supertree, and MinCut methods (provided the latter are interpreted as Adams consensus-like supertrees) are not revealed to have any bias with respect to tree shape by our example, but whether this holds more generally is an open problem. Future development and evaluation of supertree methods should consider explicitly the undesirable biases and other properties that we highlight. In the meantime, use of a single, arbitrarily chosen supertree method is discouraged. Use of multiple methods and/or weighting schemes may allow practical assessment of the extent to which inferences from real data depend upon methodological biases with respect to input tree shape or size.     

Stick-and-diffuse and caged diffusion: a comparison of two models of synaptic vesicle dynamics

Two models were recently proposed to enable us to understand the dynamics of synaptic vesicles in hippocampal neurons. In the caged diffusion model, the vesicles diffuse in small circular cages located randomly in the bouton, while in the stick-and-diffuse model the vesicles bind and release from a cellular cytomatrix. In this article, we obtain analytic expressions for the fluorescence correlation spectroscopy (FCS) autocorrelation function for the two models and test their predictions against our earlier FCS measurements of the vesicle dynamics. We find that the stick-and-diffuse model agrees much better with the experiment. We find also that, due to the slow dynamics of the vesicles, the finite experimental integration time has an important effect on the FCS autocorrelation function and demonstrate its effect for the different models. The two models of the dynamics are also relevant to other cellular environments where mobile species undergo slow diffusionlike motion in restricted spaces or bind and release from a stationary substrate.     

Measuring social structure: a comparison of eight dominance indices

Measurement of social status is an important component of many behavioural studies. A variety of techniques have been developed and adopted, but while there have been some analyses of index properties using simulated data, the rationale for selecting a method remains poorly documented. As a first step in exploring the implications of index choice, we compared the characteristics of eight popular indices by applying each to the same data set from interactions between male fowl Gallus gallus, the system in which social hierarchies were first described. Data from eight social groups, observed over four successive breeding seasons, were analysed to determine whether different indices produced consistent dominance scores. These scores were then used in tests of the relation between social status and crowing to explore whether index choice affected the results obtained. We also examined the pattern of dominance index use over the last decade to infer whether this has likely been influenced by tradition, or by taxa of study animal. Overall agreement among methods was good when groups of birds had perfectly linear hierarchies, but results diverged when social structure was more complex, with either intransitive triads or reversals. While all regression analyses revealed a positive relationship between dominance and vocal behaviour, there were substantial differences in the amount of variance accounted for, even though the original data were identical in every case. Index selection can hence perturb estimates of the importance of dominance, relative to other factors. We also found that several methods have been adopted only by particular research teams, while the use of others has been taxonomically constrained, patterns implying that indices have not always been chosen solely upon their merits. Taken together, our results read as a cautionary tale. We suggest that selection of a dominance index requires careful consideration both of algorithm properties and of the factors affecting social status in the system of interest.     

Nonlinearities make a difference: comparison of two common Hill-type models with real muscle

Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component (model [CC+SEC]), or is connected in parallel only with the contractile component (model [CC]). As soon as at least one of the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off, the two models are mechanically different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus better. Ramp experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using supramaximal nerve stimulation. Hill-type models containing force–length and force–velocity relationship, excitation–contraction coupling and series and parallel elastic force–elongation relations were fitted to the data. To test which model might represent the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations with negligible passive force, the force–velocity relation and the series elastic component relation are independent of the chosen model. In contrast to model [CC+SEC], these relations predicted by model [CC] were in accordance with experimental relations. In conclusion model [CC] seemed to better represent the cat soleus contraction dynamics and should be preferred in the nonlinear regression of muscle parameters and in musculoskeletal modeling.     

Small sperm,uniparental inheritance and selfish cytoplasmic elements: a comparison of two models

It has previously been suggested that small sperm size may be an adaptation to achieve uniparental inheritance of organelles, and hence to prevent the spread of selfish cytoplasmic elements. Such an explanation for anisogamy implies a mechanism whereby the male gamete eliminates its own cytoplasm prior to fusion with the egg. A model has been presented demonstrating the invasion and persistence of a modifier that acts gametically to kill its own organelles. Here we show, however, that this model is far from robust; indeed, if any cost is associated with the modifier it cannot persist. We also show that despite an empirically demonstrated association between anisogamy and multicellularity, this result also applies if the analysis is applied in the multicellular case. This class of model contrasts with the majority of analyses in which the modifier kills off the incoming gamete’s organelles. We show that these models are highly robust, even if uniparental inheritance is imperfect.     

Computation of diagnostic data from coronary sinus pressure: a comparison between two possible models

We have evaluated two mathematical models to describe the increase in coronary sinus pressure (CSP) following pressure controlled intermittent coronary sinus occlusion (PICSO). The models are evaluated and compared on the basis of human and canine data. Both models were fitted by non-linear least squares algorithms. Next, derived quantities, such as plateau, rise-time and mean integral of the coronary sinus pressure were calculated from the model parameters. Corresponding quantities for the two models were compared with regard to mean values, rate of successful calculation and specific features characterizing the human or canine case. One model was found to be superior for investigational purposes. The other model was found to be more stable in critical situations and is therefore suggested for usage in closed loop regulation of PICSO. Physiologically, the differences in mean values of the derived quantities between the two models were found to be negligible. The formal statistical significance of the differences is but a consequence of the large number of PICSO cycles analysed.     

The power and statistical behaviour of allele-sharing statistics when applied to models with two disease loci

We have evaluated the power for detecting a common trait determined by two loci, using seven statistics, of which five are implemented in the computer program SimWalk2, and two are implemented in GENEHUNTER. Unlike most previous reports which involve evaluations of the power of allelesharing statistics for a single disease locus, we have used a simulated data set of general pedigrees in which a twolocus disease is segregating and evaluated several nonparametric linkage statistics implemented in the two programs. We found that the power for detecting linkage using the S_all statistic in GENEHUNTER (GH, version 2.1), implemented as statisticE in SimWalk2 (version 2.82), is different in the two. TheP values associated with statisticE output by SimWalk2 are consistently more conservative than those from GENEHUNTER except when the underlying model includes heterogeneity at a level of 50% where theP values output are very comparable. On the other hand, when the thresholds are determined empirically under the null hypothesis, S_all in GENEHUNTER and statisticE have similar power.