Browsing by Author "Shaw, Ruth G."
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Item Aster Models and Lande-Arnold Beta(2010-01-09) Geyer, Charles J.; Shaw, Ruth G.Lande and Arnold (1983) proposed an estimate of beta, the directional selection gradient, by ordinary least squares (OLS). Aster models (Geyer, Wagenius and Shaw, 2007; Shaw, Geyer, Wagenius, Hangelbroek, and Etterson, 2008) estimate exactly the same beta, so providing no improvement over the Lande-Arnold method in point estimation of this quantity. Aster models do provide correct confidence intervals, confidence regions, and hypothesis tests for beta; in contrast, such procedures derived from OLS are often invalid because the assumptions for OLS are grossly incorrect.Item Aster Models and Lande-Arnold Beta (revised)(2010-01-13) Geyer, Charles J.; Shaw, Ruth G.Lande and Arnold (1983) proposed an estimate of beta, the directional selection gradient, by ordinary least squares (OLS). Aster models (Geyer, Wagenius and Shaw, 2007; Shaw, Geyer, Wagenius, Hangelbroek, and Etterson, 2008) estimate exactly the same beta, so providing no improvement over the Lande-Arnold method in point estimation of this quantity. Aster models do provide correct confidence intervals, confidence regions, and hypothesis tests for beta; in contrast, such procedures derived from OLS are often invalid because the assumptions for OLS are grossly incorrect. This revision fixes a bug which made the figure incorrect in the original.Item Aster Models for Life History Analysis(University of Minnesota, 2005-09) Geyer, Charles J.; Wagenius, Stuart; Shaw, Ruth G.Item Aster Models with Random Effects and Additive Genetic Variance for Fitness(University of Minnesota, 2013-07) Geyer, Charles J.; Shaw, Ruth G.Item Aster Models with Random Effects and Additive Genetic Variance for Fitness(2013-07-10) Geyer, Charles J.; Shaw, Ruth G.This technical report is a minor supplement to the paper Geyer et al. (in press) and its accompanying technical report Geyer et al. (2012). It shows how to move variance components from the canonical parameter scale to the mean value parameter scale. This is useful in estimating additive genetic variance for fitness, and that appears in Fisher's fundamental theorem of natural selection, which predicts the rate of increase in fitness via natural selection.Item Aster Models with Random Effects via Penalized Likelihood(2012-10-09) Geyer, Charles J.; Ridley, Caroline E.; Latta, Robert G.; Etterson, Julie R.; Shaw, Ruth G.This technical report works out details of approximate maximum likelihood estimation for aster models with random effects. Fixed and random effects are estimated by penalized log likelihood. Variance components are estimated by integrating out the random effects in the Laplace approximation of the complete data likelihood following Breslow and Clayton (1993), which can be done analytically, and maximizing the resulting approximate missing data likelihood. A further approximation treats the second derivative matrix of the cumulant function of the exponential family where it appears in the approximate missing data log likelihood as a constant (not a function of parameters). Then first and second derivatives of the approximate missing data log likelihood can be done analytically. Minus the second derivative matrix of the approximate missing data log likelihood is treated as approximate Fisher information and used to estimate standard errors.Item Aster Models with Random Effects via Penalized Likelihood(University of Minnesota, 2010-07) Geyer, Charles J.; Ridley, Caroline E.; Latta, Robert G.; Etterson, Julie R.; Shaw, Ruth G.Item Commentary on Lande-Arnold Analysis(University of Minnesota, 2008-05) Geyer, Charles J.; Shaw, Ruth G.Item Commentary on Lande-Arnold Analysis(School of Statistics, University of Minnesota, 2008-05-14) Geyer, Charles J.; Shaw, Ruth G.A solution to the problem of estimating fitness landscapes was proposed by Lande and Arnold (1983). Another solution, which avoids problematic aspects of the Lande-Arnold methodology, was proposed by Shaw, Geyer, Wagenius, Hangelbroek, and Etterson (2008). This technical report goes through Lande-Arnold theory in detail paying careful attention to problematic aspects. The only completely new material is a theoretical analysis of when the best quadratic approximation to a fitness landscape, which is what the Lande-Arnold method estimates, is a good approximation to the actual fitness landscape.Item Density-dependence in Salvia lyrata L.(1983) Shaw, Ruth G.One of the central puzzles in ecology is what determines the size of populations in nature. Strident debate between those claiming precedence of density-independent factors over density-dependent ones, and vice versa, has subsided with the realization that both may play a role in limiting population size of any species. Nevertheless, very few attempts have been made to directly assess the effect of density on population growth in nature. This is particularly disturbing, because theoretical ecology 1s largely based on the density-dependent population growth routinely documented in laboratory experiments. Similarly, explanations of the existence of variation in life history among and within species, in particular the weedy vs. non-weedy habit, have invoked density-dependent selection. Yet such selection has never been demonstrated in nature, and thus its efficacy in maintaining genetic variation is unknown. The experiments reported here were devised to determine the extent to which density limits growth of a population of Salvia lyrata L., an herbaceous perennial plant common in North Carolina grasslands, and whether density-dependent selection structures its genetic variation. The local density of Salvia was altered by sowing in seed at different densities, and by transplanting or removing established individuals. In most cases, these manipulations elicited weak or conflicting responses; however density-dependent mortality and stunting of seedlings was evident at unnaturally high densities of sowing. Thus density is rarely sufficient to limit an individual's contribution to this population, but density effects can limit population size at extreme seedling densities. In additional experiments, evidence of genetic variation in density response was sought by planting individuals of known genetic origin into arrangements of varying density. An experiment in protected conditions showed variation among families in the response of flowering probability to density, but not in survival nor in the number of seeds produced. A field experiment showed variation among families in the reponse of a size trait, number of leaves, to density. Given that survival and fecundity are size-dependent, as documented in observations of the natural population, this result suggests the potential for density-dependent selection in nature.Item Evolutionary responses to changing climate(2005) Davis, Margaret B.; Shaw, Ruth G.; Etterson, Julie R.Until now, Quaternary paleoecologists have regarded evolution as a slow process relative to climate change, predicting that the primary biotic response to changing climate is not adaptation, but instead (1) persistence in situ if changing climate remains within the species' tolerance limits, (2) range shifts (migration) to regions where climate is currently within the species' tolerance limits, or (3) extinction. We argue here that all three of these outcomes involve evolutionary processes. Genetic differentiation within species is ubiquitous, commonly via adaptation of populations to differing environmental conditions. Detectable adaptive divergence evolves on a time scale comparable to change in climate, within decades for herbaceous plant species, and within centuries or millennia for longer-lived trees, implying that biologically significant evolutionary response can accompany temporal change in climate. Models and empirical studies suggest that the speed with which a population adapts to a changing environment affects invasion rate of new habitat and thus migration rate, population growth rate and thus probability of extinction, and growth and mortality of individual plants and thus productivity of regional vegetation. Recent models and experiments investigate the stability of species tolerance limits, the influence of environmental gradients on marginal populations, and the interplay of demography, gene flow, mutation rate, and other genetic processes on the rate of adaptation to changed environments. New techniques enable ecologists to document adaptation to changing conditions directly by resurrecting ancient populations from propagules buried in decades-old sediment. Improved taxonomic resolution from morphological studies of macrofossils and DNA recovered from pollen grains and macroremains provides additional information on range shifts, changes in population sizes, and extinctions. Collaboration between paleoecologists and evolutionary biologists can refine interpretations of paleorecords, and improve predictions of biotic response to anticipated climate change.Item Hypothesis Tests and Confidence Intervals Involving Fitness Landscapes fit by Aster Models(2010-01-09) Geyer, Charles J.; Shaw, Ruth G.This technical report explores some issues left open in Technical Reports 669 and 670 (Geyer and Shaw, 2008a,b): for fitness landscapes fit using an aster models, we propose hypothesis tests of whether the landscape has a maximum and confidence regions for the location of the maximum. All analyses are done in R (R Development Core Team, 2008) using the aster contributed package described by Geyer, Wagenius and Shaw (2007) and Shaw, Geyer, Wagenius, Hangelbroek, and Etterson (2008). Furthermore, all analyses are done using the Sweave function in R, so this entire technical report and all of the analyses reported in it are completely reproducible by anyone who has R with the aster package installed and the R noweb file specifying the document. The revision fixes one error in the confidence ellipsoids in Section 4 (a square root was forgotten so the regions in the original were too big).Item Model Selection in Estimation of Fitness Landscapes(University of Minnesota, 2008-07) Geyer, Charles J.; Shaw, Ruth G.Item Model Selection in Estimation of Fitness Landscapes(School of Statistics, University of Minnesota, 2009-07-06) Geyer, Charles J.; Shaw, Ruth G.A solution to the problem of estimating fitness landscapes was proposed by Lande and Arnold (1983). Another solution, which avoids problematic aspects of the Lande-Arnold methodology, was proposed by Shaw, Geyer, Wagenius, Hangelbroek, and Etterson (2008), who also provided an illustrative example involving real data. An earlier technical report (Geyer and Shaw, 2008) gave an example that was simpler in some ways (the data are simulated from the aster model so there are no issues making the data fit the model one has with real data) and much more complicated in others (each individual has five measured components of fitness over four time periods, 20 variables in all) and illustrates the full richness possible in aster analysis of fitness landscapes. The one issue that technical report did not deal with is model selection. When many phenotypic variables are measured, one often does not know which to put in the model. Lande and Arnold (1983) proposed using principal components regression as a method of dimension reduction, but this method is known to have no theoretical basis. Much of late 20th century and 21st century statistics is about model selection and model averaging, and we apply some of this methodology (which does have strong theoretical basis) to estimation of fitness landscapes using another simulated data set. All analyses are done in R (R Development Core Team, 2008) using the aster contributed package described by Geyer, Wagenius and Shaw (2007) except for analyses in the style of Lande and Arnold (1983), which use ordinary least squares regression. Furthermore, all analyses are done using the Sweave function in R, so this entire technical report and all of the analyses reported in it are completely reproducible by anyone who has R with the aster package installed and the R noweb file specifying the document. This revision corrects major errors in the frequentist model averaging calculations (Section 8) in the first version of the technical report.Item More Supporting Data Analysis for "Unifying Life History Analysis for Inference of Fitness and Population Growth"(University of Minnesota, 2007-11) Geyer, Charles J.; Wagenius, Stuart; Shaw, Ruth G.; Hangelbroek, Helen H.; Etterson, Julie R.Item (Revised) Aster Models and Lande-Arnold Beta(University of Minnesota, 2010-01) Geyer, Charles J.; Shaw, Ruth G.Item (Revised) Hypothesis Tests and Confidence Intervals Involving Fitness Landscapes fit by Aster Models(University of Minnesota, 2010-01) Geyer, Charles J.; Shaw, Ruth G.Item Supporting Data Analysis for "Unifying Life History Analysis for Inference of Fitness and Population Growth"(University of Minnesota, 2007-07) Geyer, Charles J.; Wagenius, Stuart; Shaw, Ruth G.; Hangelbroek, Helen H.; Etterson, Julie R.Item Supporting Data Analysis for a talk to be given at Evolution 2008 University of Minnesota, June 20-24(University of Minnesota, 2008-05) Geyer, Charles J.; Shaw, Ruth G.Item Supporting Data Analysis for a talk to be given at Evolution 2008 University of Minnesota, June 20-24(School of Statistics, University of Minnesota, 2008-05-14) Geyer, Charles J.; Shaw, Ruth G.A solution to the problem of estimating fitness landscapes was proposed by Lande and Arnold (1983). Another solution, which avoids problematic aspects of the Lande-Arnold methodology, was proposed by Shaw, Geyer, Wagenius, Hangelbroek, and Etterson (2008), who also provided an illustrative example. Here we provide another example using simulated data that are more suitable to aster analysis. All analyses are done in R (R Development Core Team, 2008) using the aster contributed package described by Geyer et al. (2007) except for analyses in the style of Lande and Arnold (1983), which use ordinary least squares regression. Furthermore, all analyses are done using the Sweave function in R, so this entire technical report and all of the analyses reported in it are completely reproducible by anyone who has R with the aster package installed and the R noweb file specifying the document.