A priori and a posteriori methods in comparative evolutionary studies of host–parasite associations

Brooks parsimony analysis (BPA) and reconciliation methods in studies of host–parasite associations differ fundamentally, despite using the same null hypothesis. Reconciliation methods may eliminate or modify input data to maximize fit of single parasite clades to a null hypothesis of cospeciation, by invoking different a priori assumptions, including a known host phylogeny. By examining the degree of phylogenetic congruence among multiple parasite clades, using hosts as analogs of taxa but not presuming a host phylogeny or any degree of cospeciation a priori, BPA modifies the null hypothesis of cospeciation if necessary to maintain the integrity of the input data. Two exemplars illustrate critical empirical differences between reconciliation methods and BPA: (1) reconciliation methods rather than BPA may select the incorrect general host cladogram for a set of data from different clades of parasites, (2) BPA rather than reconciliation methods provides the most parsimonious interpretation of all available data, and (3) secondary BPA, proposed in 1990, when applied to data sets in which host‐switching produces hosts with reticulate histories, provides the most parsimonious and biologically realistic interpretations of general host cladograms. The extent to which these general host cladograms, based on cospeciation among different parasite clades inhabiting the same hosts, correspond to host phylogeny can be tested, a posteriori, by comparison with a host phylogeny generated from nonparasite data. These observations lead to the conclusion that BPA and reconciliation methods are designed to implement different research programs based on different epistemologies. BPA is an a posteriori method that is designed to assess the host context of parasite speciation events, whereas reconciliation methods are a priori methods that are designed to fit parasite phylogenies to a host phylogeny. Host‐switching events are essential for explaining complex histories of host–parasite associations. BPA assumes coevolutionary complexity (historical contingency), relying on parsimony as an a posteriori explanatory tool to summarize complex results, whereas reconciliation methods, which embody formalized assumptions of maximum cospeciation, are based on a priori conceptual parsimony. Modifications of basic reconciliation methods, embodied in TreeMap 1.0 and TreeMap 2.02, represent the addition of weighting schemes in which the researcher specifies allowed departures from cospeciation a priori, with the result that TreeMap results more closely agree with BPA results than do reconciled tree analysis results.     

When simplicity is not parsimonious: a priori and a posteriori methods in historical biogeography

Despite using the same null hypothesis, a priori and a posteriori approaches in historical biogeography differ fundamentally. Methods such as Component Analysis (CA) and Reconciled Tree Analysis (RTA) may eliminate or modify input data in order to maximize fit to the null hypothesis, by invoking assumptions 1 and 2. Methods such as Brooks Parsimony Analysis (BPA) modify the null hypothesis, if necessary, to maintain the integrity of the input data, as required by assumption 0. Two exemplars illustrate critical empirical differences between CA/RTA and BPA: (1) CA rather than BPA may select the incorrect general area cladogram for a set of data (2) BPA, not RTA, provides the most parsimonious interpretation of all available data and (3) secondary BPA, proposed in 1990, applied to data sets for which dispersal producing areas with reticulate histories is most parsimonious, provides biologically realistic interpretations of area cladograms. These observations lead to the conclusion that BPA and CA/RTA are designed to implement different research programmes based on different conceptual frameworks. BPA is designed to assess the biogeographic context of speciation events, whereas CA/RTA are designed to find the best fitting pattern of relationships among areas based on the taxa that inhabit them. Unique distributional elements and reticulate (hybrid) histories of areas are essential for explaining complex histories of speciation. The conceptual framework for BPA, thus, assumes biogeographical complexity, relying on parsimony as an explanatory tool to summarize complex results, whereas CA/RTA assumes biogeographical simplicity, assuming conceptual parsimony a priori .     

Sex differentiation in mammals and tempo of growth: probabilities vs. switches

In the conventional model of sex differentiation in placental mammals, a switch is envisaged to steer the indifferent gonad into the path of either testicular or ovarian development. The immediate cause of the switch is thought to be the presence or absence of Sertoli cells, which in turn is controlled by the presence or absence of the testis-determining factor on the Y chromosome (TDF in humans, Tdy in mice). Quantitative investigations indicate, however, that the rate of growth of XY gonads is faster than that of XX gonads before the formation of Sertoli cells, and furthermore, that XY embryos develop faster than XX embryos long before the formation of gonadal ridges. Since the genetic constitution of the sex chromosomes appears to manifest itself from the earliest embryonic stages onwards, the concept of indifferent gonads being switched into alternate pathways becomes inappropriate. A model is proposed in which gonadal differentiation depends on developmental thresholds: the formation of Sertoli cells needs to occur by a particular stage in time in a sufficiently developed gonad, failing which the gonad will enter the ovarian pathway. While TDF is the principal factor enhancing the rate of gonadal growth, other factors which influence development rates can modulate the probability of a gonad becoming either a testis or an ovary.     

A segmental maximum a posteriori approach to genome-wide copy number profiling

MOTIVATION: Copy number profiling methods aim at assigning DNA copy numbers to chromosomal regions using measurements from microarray-based comparative genomic hybridizations. Among the proposed methods to this end, Hidden Markov Model (HMM)-based approaches seem promising since DNA copy number transitions are naturally captured in the model. Current discrete-index HMM-based approaches do not, however, take into account heterogeneous information regarding the genomic overlap between clones. Moreover, the majority of existing methods are restricted to chromosome-wise analysis. RESULTS: We introduce a novel Segmental Maximum A Posteriori approach, SMAP, for DNA copy number profiling. Our method is based on discrete-index Hidden Markov Modeling and incorporates genomic distance and overlap between clones. We exploit a priori information through user-controllable parameterization that enables the identification of copy number deviations of various lengths and amplitudes. The model parameters may be inferred at a genome-wide scale to avoid overfitting of model parameters often resulting from chromosome-wise model inference. We report superior performances of SMAP on synthetic data when compared with two recent methods. When applied on our new experimental data, SMAP readily recognizes already known genetic aberrations including both large-scale regions with aberrant DNA copy number and changes affecting only single features on the array. We highlight the differences between the prediction of SMAP and the compared methods and show that SMAP accurately determines copy number changes and benefits from overlap consideration.     

A priori prediction of disease invasion dynamics in a novel environment

Directly transmitted infectious diseases spread through wildlife populations as travelling waves away from the sites of original introduction. These waves often become distorted through their interaction with environmental and population heterogeneities and by long-distance translocation of infected individuals. Accurate a priori predictions of travelling waves of infection depend upon understanding and quantifying these distorting factors. We assess the effects of anisotropies arising from the orientation of rivers in relation to the direction of disease-front propagation and the damming effect of mountains on disease movement in natural populations. The model successfully predicts the local and large-scale prevaccination spread of raccoon rabies through New York State, based on a previous spatially heterogeneous model of raccoon-rabies invasion across the state of Connecticut. Use of this model provides a rare example of a priori prediction of an epidemic invasion over a naturally heterogeneous landscape. Model predictions matched to data can also be used to evaluate the most likely points of disease introduction. These results have general implications for predicting future pathogen invasions and evaluating potential containment strategies.     

A priori contact preferences in molecular recognition

A molecular interaction library modeling favorable non-bonded interactions between atoms and molecular fragments is considered. In this paper, we represent the structure of the interaction library by a network diagram, which demonstrates that the underlying prediction model obtained for a molecular fragment is multi-layered. We clustered the molecular fragments into four groups by analyzing the pairwise distances between the molecular fragments. The distances are represented as an unrooted tree, in which the molecular fragments fall into four groups according to their function. For each fragment group, we modeled a group-specific a priori distribution with a Dirichlet distribution. The group-specific Dirichlet distributions enable us to derive a large population of similar molecular fragments that vary only in their contact preferences. Bayes' theorem then leads to a population distribution of the posterior probability vectors referred to as a "Dickey-Savage"-density. Two known methods for approximating multivariate integrals are applied to obtain marginal distributions of the Dickey-Savage density. The results of the numerical integration methods are compared with the simulated marginal distributions. By studying interactions between the protein structure of cyclohydrolase and its ligand guanosine-5'-triphosphate, we show that the marginal distributions of the posterior probabilities are more informative than the corresponding point estimates.     

A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs

The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.     

Risks and probabilities of breast cancer: short-term versus lifetime probabilities.

OBJECTIVE: To calculate age-specific short-term and lifetime probabilities of breast cancer among a cohort of Canadian women. DESIGN: Double decrement life table. SETTING: Alberta. SUBJECTS: Women with first invasive breast cancers registered with the Alberta Cancer Registry between 1985 and 1987. MAIN OUTCOME MEASURES: Lifetime probability of breast cancer from birth and for women at various ages; short-term (up to 10 years) probability of breast cancer for women at various ages. RESULTS: The lifetime probability of breast cancer is 10.17% at birth and peaks at 10.34% at age 25 years, after which it decreases owing to a decline in the number of years over which breast cancer risk will be experienced. However, the probability of manifesting breast cancer in the next year increases steadily from the age of 30 onward, reaching 0.36% at 85 years. The probability of manifesting the disease within the next 10 years peaks at 2.97% at age 70 and decreases thereafter, again owing to declining probabilities of surviving the interval. CONCLUSIONS: Given that the incidence of breast cancer among Albertan women during the study period was similar to the national average, we conclude that currently more than 1 in 10 women in Canada can expect to have breast cancer at some point during their life. However, risk varies considerably over a woman''s lifetime, with most risk concentrated after age 49. On the basis of the shorter-term age-specific risks that we present, the clinician can put breast cancer risk into perspective for younger women and heighten awareness among women aged 50 years or more.     

Autophagy vs. Group A Streptococcus

We have identified several mammalian protein components of the autophagy pathway. By using them as powerful tools to examine the functional significance of this degradation pathway, we recently showed that autophagy efficiently kills a pathogenic bacterium, Group A Streptococcus, after it invades host cells. However, the autophagosomes induced by these bacteria have features distinct from those of the canonical pathway.     

A priori and a posteriori approaches for finding genes of evolutionary interest in non-model species: Osmoregulatory genes in the kidney transcriptome of the desert rodent Dipodomys spectabilis (banner-tailed kangaroo rat)

One common goal in evolutionary biology is the identification of genes underlying adaptive traits of evolutionary interest. Recently next-generation sequencing techniques have greatly facilitated such evolutionary studies in species otherwise depauperate of genomic resources. Kangaroo rats (Dipodomys sp.) serve as exemplars of adaptation in that they inhabit extremely arid environments, yet require no drinking water because of ultra-efficient kidney function and osmoregulation. As a basis for identifying water conservation genes in kangaroo rats, we conducted a priori bioinformatics searches in model rodents (Mus musculus and Rattus norvegicus) to identify candidate genes with known or suspected osmoregulatory function. We then obtained 446,758 reads via 454 pyrosequencing to characterize genes expressed in the kidney of banner-tailed kangaroo rats (Dipodomys spectabilis). We also determined candidates a posteriori by identifying genes that were overexpressed in the kidney. The kangaroo rat sequences revealed nine different a priori candidate genes predicted from our Mus and Rattus searches, as well as 32 a posteriori candidate genes that were overexpressed in kidney. Mutations in two of these genes, Slc12a1 and Slc12a3, cause human renal diseases that result in the inability to concentrate urine. These genes are likely key determinants of physiological water conservation in desert rodents.     

Autophagy vs. Group A Streptococcus

We have identified several mammalian protein components of the autophagy pathway. By using them as powerful tools to examine the functional significance of this degradation pathway, we recently showed that autophagy efficiently kills a pathogenic bacterium, Group A Streptococcus, after it invades host cells. However, the autophagosomes induced by these bacteria have features distinct from those of the canonical pathway.     

A posteriori time-varying filtering of averaged evoked potentials

The problem of estimating an unknown transient signal, given an ensemble of waveforms, in which this signal appears as a nonrandom component in the presence of additive noise is considered. This problem is solved by generalizing the method of a posteriori Wiener filtering. In the new method, the ensemble average is filtered by a time-varying system which is based on estimated time-varying power spectra of signal and noise. The nature of this system, and the computational procedures involved, are discussed in detail. A software package for time-varying filtering is briefly described. Application of the method is illustrated by a simulation example, which also provides a comparison to time-invariant a posteriori Wiener filtering.     

A priori choice of hybrid parents in plants

Plant breeding deals with high-yielding genotypes. However, how best to choose parents of these genotypes remains an unsolved question. Here, we focus on a priori choice based on parental distances by means of agronomic and molecular data. Despite numerous theoretical and empirical studies, a priori choice continues to be a controversial procedure. Both success and failure are commonly reported. We looked at these ambiguous results in order to investigate their possible causes. A total of 139 articles on genetic divergence were sampled to examine aspects such as type and number of markers utilized. We suggest that the mean number of 160, 281 and 25 for RAPD and RFLP markers, and SSR loci, respectively, which we found in these papers, should be increased for accurate analysis. A second sample composed of 54 articles was used to evaluate the divergence-heterosis association. Most of them (28) detected positive divergence-heterosis association, whereas 26 revealed negative or inconclusive results. We examined several causes that influence a priori choice positively and negatively.     

A priori crystal structure prediction of native celluloses

The packing of beta-1,4-glucopyranose chains has been modeled to further elaborate the molecular structures of native cellulose microfibrils. A chain pairing procedure was implemented that evaluates the optimal interchain distance and energy for all possible settings of the two chains. Starting with a rigid model of an isolated chain, its interaction with a second chain was studied at various helix-axis translations and mutual rotational orientations while keeping the chains at van der Waals separation. For each setting, the sum of the van der Waals and hydrogen-bonding energy was calculated. No energy minimization was performed during the initial screening, but the energy and interchain distances were mapped to a three-dimensional grid, with evaluation of parallel settings of the cellulose chains. The emergence of several energy minima suggests that parallel chains of cellulose can be paired in a variety of stable orientations. A further analysis considered all possible parallel arrangements occurring between a cellulose chain pair and a further cellulose chain. Among all the low-energy three-chain models, only a few of them yield closely packed three-dimensional arrangements. From these, unit-cell dimensions as well as lattice symmetry were derived; interestingly two of them correspond closely to the observed allomorphs of crystalline native cellulose. The most favorable structural models were then optimized using a minicrystal procedure in conjunction with the MM3 force field. The two best crystal lattice predictions were for a triclinic (P(1)) and a monoclinic (P2(1)) arrangement with unit cell dimensions a = 0.63, b = 0.69, c = 1.036 nm, alpha = 113.0, beta = 121.1, gamma = 76.0 degrees, and a = 0.87, b = 0.75, c = 1.036 nm, gamma = 94.1 degrees, respectively. They correspond closely to the respective lattice symmetry and unit-cell dimensions that have been reported for cellulose Ialpha and cellulose Ibeta allomorphs. The suitability of the modeling protocol is endorsed by the agreement between the predicted and experimental unit-cell dimensions. The results provide pertinent information toward the construction of macromolecular models of microfibrils.     

A computational and experimental approach toward a priori identification of alternatively spliced exons

Alternative splicing is a powerful means of regulating gene expression and enhancing protein diversity. In fact, the majority of metazoan genes encode pre-mRNAs that are alternatively spliced to produce anywhere from two to tens of thousands of mRNA isoforms. Thus, an important part of determining the complete proteome of an organism is developing a catalog of all mRNA isoforms. Alternatively spliced exons are typically identified by aligning EST clusters to reference mRNAs or genomic DNA. However, this approach is not useful for genomes that lack robust EST coverage, and tools that enable accurate prediction of alternatively spliced exons would be extraordinarily useful. Here, we use comparative genomics to identify, and experimentally verify, potential alternative exons based solely on their high degree of conservation between Drosophila melanogaster and D. pseudoobscura. At least 40% of the exons that fit our prediction criteria are in fact alternatively spliced. Thus, comparative genomics can be used to accurately predict certain classes of alternative exons without relying on EST data.