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COMFAC is employed as a sequential simplification device in empirical analysis. Analysis of the finite‐sample statistical properties checked the power when a COMFAC representation of economic agents’ behaviour was valid. Improved test power response surfaces were proposed. Combined, the findings suggested using other model reduction devices, retaining COMFAC as a destructive testing device for invalid ‘autocorrelation correction’ claims. Diagnostic testing of the initial model was emphasized. Model selection (lag length, choice of simplification, and parameter) is investigated for highly seasonal data.

For almost 30 years, Lande and Arnold's approximation of individual fitness surfaces through multiple regression has provided a common framework for comparing the strength and form of phenotypic selection across traits, fitness components and sexes. This chapter provides an overview of the statistical and geometric approaches available for the multivariate analysis of phenotypic selection that build upon the Lande and Arnold approach. First, it details least squares based approaches for the estimation of multivariate selection in a single population. Second, it shows how these approaches can be extended for the statistical comparison of individual fitness surfaces among groups such as populations or experimental treatments, addressing the inferential differences between analyses of randomly chosen groups versus situations in which groups are experimentally fixed. In each case, it points out known issues and caveats associated with the approaches. Finally, using case studies, the chapter shows how these estimates of multivariate selection can be integrated with quantitative genetic analyses to better understand issues such as the maintenance of genetic variance under selection and how genetic constraints can bias evolutionary responses to selection.

Examines methods of testing for co‐integration in single equations via static regressions, and provides simulation estimates of the percentiles of the distributions of statistics used in these tests. The finite‐sample biases of the estimates of the co‐integrating vectors and powers of the tests based on static regressions are discussed within the framework of extensive Monte Carlo simulations. Dynamic models leading to an error‐correction mechanism based test (ECM test for co‐integration) and non‐parametrically modified estimators are also considered as better ways of estimating the co‐integrating relationships.

The population dynamics of the larch budmoth (LBM), Zeiraphera diniana, in the Swiss Alps are perhaps the best example of periodic oscillations in ecology (figure 7.1). These oscillations are characterized by a remarkably regular periodicity, and by an enormous range of densities experienced during a typical cycle (about 100,000-fold difference between peak and trough numbers). Furthermore, nonlinear time series analysis of LBM data (e.g., Turchin 1990, Turchin and Taylor 1992) indicates that LBM oscillations are definitely generated by a second-order dynamical process (in other words, there is a strong delayed density dependence—see also chapter 1). Analysis of time series data on LBM dynamics from five valleys in the Alps suggests that around 90% of variance in Rt is explained by the phenomenological time series model employing lagged LBM densities, R, =f(Ni-1,Ni-2,) (Turchin 2002). As discussed in the influential review by Baltensweiler and Fischlin (1988) about a decade ago, ecological theory suggests a number of candidate mechanisms that can produce the type of dynamics observed in the LBM (see also chapter 1). Baltensweiler and Fischlin concluded that changes in food quality induced by previous budmoth feeding was the most plausible explanation for the population cycles. During the last decade, the issue of larch budmoth oscillations was periodically revisited by various population ecologists looking for general insights about insect population cycles (e.g., Royama 1977, Bowers et al. 1993, Ginzburg and Taneyhill 1994, Den Boer and Reddingius 1996, Hunter and Dwyer 1998, Berryman 1999). These authors generally concurred with the view that budmoth cycles are driven by the interaction with food quality. A recent reanalysis of the rich data set on budmoth population ecology collected by Swiss researchers over a period of several decades, however, suggested that the role of parasitism is underappreciated (Turchin et al. 2002). Before focusing on the roles of food quality and parasitism in LBM dynamics, we briefly review the status of other hypotheses that were discussed in the literature on LBM cycles. First, the natural history of the LBM-larch system is such that food quantity is an unlikely factor to explain LBM oscillations.