Using Bayesian inference to understand the allocation of resources between sexual and asexual reproduction

We address the problem of Markov chain Monte Carlo analysis of a complex ecological system by using a Bayesian inferential approach. We describe a complete likelihood framework for the life history of the wavyleaf thistle, including missing information and density dependence. We indicate how, to make inference on life history transitions involving both missing information and density dependence, the stochastic models underlying each component can be combined with each other and with priors to obtain expressions that can be directly sampled. This innovation and the principles described could be extended to other species featuring such missing stage information, with potential for improving inference relating to a range of ecological or evolutionary questions. Copyright (c) 2009 Royal Statistical Society.

[1]  A. Gelman A Bayesian Formulation of Exploratory Data Analysis and Goodness‐of‐fit Testing * , 2003 .

[2]  W. Link,et al.  Individual Covariation in Life‐History Traits: Seeing the Trees Despite the Forest , 2002, The American Naturalist.

[3]  S. Ellner,et al.  Integral Projection Models for Species with Complex Demography , 2006, The American Naturalist.

[4]  S. Louda,et al.  Effect of Inflorescence‐Feeding Insects on the Demography and Lifetime of a Native Plant , 1995 .

[5]  Philip Heidelberger,et al.  Simulation Run Length Control in the Presence of an Initial Transient , 1983, Oper. Res..

[6]  Marc Kéry,et al.  Demographic estimation methods for plants with unobservable life‐states , 2005 .

[7]  Byron J. T. Morgan,et al.  Bayesian methods for analysing ringing data , 2002 .

[8]  James S. Clark,et al.  UNCERTAINTY AND VARIABILITY IN DEMOGRAPHY AND POPULATION GROWTH: A HIERARCHICAL APPROACH , 2003 .

[9]  Marc Mangel,et al.  MODELING INVESTMENTS IN SEEDS, CLONAL OFFSPRING, AND TRANSLOCATION IN A CLONAL PLANT , 1999 .

[10]  N. Hjort,et al.  Post-Processing Posterior Predictive p Values , 2006 .

[11]  Adrian E. Raftery,et al.  [Practical Markov Chain Monte Carlo]: Comment: One Long Run with Diagnostics: Implementation Strategies for Markov Chain Monte Carlo , 1992 .

[12]  C. Robert,et al.  Deviance information criteria for missing data models , 2006 .

[13]  M. Rees,et al.  DEMOGRAPHIC AND EVOLUTIONARY IMPACTS OF NATIVE AND INVASIVE INSECT HERBIVORES ON CIRSIUM CANESCENS , 2005 .

[14]  James S. Clark,et al.  HIERARCHICAL BAYES FOR STRUCTURED, VARIABLE POPULATIONS: FROM RECAPTURE DATA TO LIFE‐HISTORY PREDICTION , 2005 .

[15]  Tim Coulson,et al.  Estimating Density Dependence from Time Series of Population Age Structure , 2006, The American Naturalist.

[16]  S Pacala,et al.  Long-Term Studies of Vegetation Dynamics , 2001, Science.

[17]  M. J. Bayarri,et al.  Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models , 2007, 0802.0754.

[18]  Lu Lu,et al.  Bayesian Checking of the Second Levels of Hierarchical Models. Comment. , 2007 .

[19]  Xiao-Li Meng,et al.  Posterior Predictive $p$-Values , 1994 .

[20]  Mark Rees,et al.  Evolutionary demography of monocarpic perennials. , 2003 .

[21]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[22]  M. T. Rodríguez-Bernal,et al.  Posterior predictive p-values: what they are and what they are not , 2001 .

[23]  Claudio M. Ghersa,et al.  Weed Ecology: Implications for Management , 1984 .