Quick divergence but slow convergence during ecotype formation in lake and stream stickleback pairs of variable age

When genetic constraints restrict phenotypic evolution, diversification can be predicted to evolve along so-called lines of least resistance. To address the importance of such constraints and their resolution, studies of parallel phenotypic divergence that differ in their age are valuable. Here, we investigate the parapatric evolution of six lake and stream threespine stickleback systems from Iceland and Switzerland, ranging in age from a few decades to several millennia. Using phenotypic data, we test for parallelism in ecotypic divergence between parapatric lake and stream populations and compare the observed patterns to an ancestral-like marine population. We find strong and consistent phenotypic divergence, both among lake and stream populations and between our freshwater populations and the marine population. Interestingly, ecotypic divergence in low-dimensional phenotype space (i.e. single traits) is rapid and seems to be often completed within 100 years. Yet, the dimensionality of ecotypic divergence was highest in our oldest systems and only there parallel evolution of unrelated ecotypes was strong enough to overwrite phylogenetic contingency. Moreover, the dimensionality of divergence in different systems varies between trait complexes, suggesting different constraints and evolutionary pathways to their resolution among freshwater systems.

A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^

Late Quateranry dinoflagellate cysts of ODP Site 202-1233

The late Quaternary organic-walled dinoflagellate cyst record of Site 1233 (41°S, offshore Chile) was studied with a ?200 year resolution spanning the last 25,000 years. The study provides the first continuous record of sub-recent and recent dinoflagellate cysts in the Southeast (SE) Pacific. Major changes in the composition of the cyst association, cyst concentration and morphology of Operculodinium centrocarpum reflect changes in sea surface temperature (SST), sea surface salinity (SSS), palaeoproductivity and upwelling intensity. These changes can be associated with latitudinal shifts of the circumpolar frontal systems. The high cyst concentration, high Brigantedinium spp. abundances, low species diversity and the occurrence of certain cold water species are supportive for a 7-10° equatorward shift of the Antarctic Circumpolar Current (ACC) during the coldest phase of the Last Glacial Maximum (LGM) between 25 and 21.1 cal ka BP. Deglacial warming initiated at ~18.6 cal ka BP. Termination I (18.6-11.1 cal ka BP) is interrupted by an unstable period of extreme seasonality, rather than a cooling event, between 14.4 and 13.2 cal ka BP, synchronous with the Antarctic Cold Reversal (ACR). The Holocene Maximum is observed between 11.6 and 9.8 cal ka BP and is typified by the most southward position of the northern margin of the ACC. A cooling phase occurred during the early Holocene (until ~7 cal ka BP) and during the last ~0.8 ka. Our data indicates that the SE Pacific (41°S) climate has been influenced over the whole record by changes in the Southern Hemisphere (SH) high-latitudes, while during the mid to late Holocene, also a tropical forcing mechanism was involved, including the El Niño Southern Oscillation and the variable Hadley cell intensity. Furthermore, this study showed a relationship between the variable morphology of the spines/processes of O. centrocarpum and the combined variation of sea surface salinity and temperature (SSS/SST-ratio).

Depths and ages of seismic sequence boundaries in ODP Leg 166 holes

High-resolution, multichannel seismic data collected across the Great Bahama Bank margin and the adjacent Straits of Florida indicate that the deposition of Neogene-Quaternary strata in this transect are controlled by two sedimentation mechanisms: (1) west-dipping layers of the platform margin, which are a product of sea-level-controlled, platform-derived downslope sedimentation; and (2) east- or north-dipping drift deposits in the basinal areas, which are deposited by ocean currents. These two sediment systems are active simultaneously and interfinger at the toe-of-slope. The prograding system consists of sigmoidal clinoforms that advanced the margin some 25 km into the Straits of Florida. The foresets of the clinoforms are approximately 600 m high with variable slope angles that steepen significantly in the Pleistocene section. The seismic facies of the prograding clinoforms on the slope is characterized by dominant, partly chaotic, cut-and-fill geometries caused by submarine canyons that are oriented downslope. In the basin axis, seismic geometries and facies document deposition from and by currents. Most impressive is an 800-m-thick drift deposit at the confluence of the Santaren Channel and the Straits of Florida. This "Santaren Drift" is slightly asymmetric, thinning to the north. The drift displays a highly coherent seismic facies characterized by a continuous succession of reflections, indicating very regular sedimentation. Leg 166 of the Ocean Drilling Program (ODP) drilled a transect of five deep holes between 2 and 30 km from the modern platform margin and retrieved the sediments from both the slope and basin systems. The Neogene slope sediments consist of peri-platform oozes intercalated with turbidites, whereas the basinal drift deposits consist of more homogeneous, fine-grained carbonates that were deposited without major hiatuses by the Florida Current starting at approximately 12.4 Ma. Sea-level fluctuations, which controlled the carbonate production on Great Bahama Bank by repeated exposure of the platform top, controlled lithologic alternations and hiatuses in sedimentation across the transect. Both sedimentary systems are contained in 17 seismic sequences that were identified in the Neogene-Quaternary section. Seismic sequence boundaries were identified based on geometric unconformities beneath the Great Bahama Bank. All the sequence boundaries could be traced across the entire transect into the Straits of Florida. Biostratigraphic age determinations of seismic reflections indicate that the seismic reflections of sequence boundaries have chronostratigraphic significance across both depositional environments.