Current theory on plant–animal interactions predicts that the outcome of herbivory on plant performance will be dependent on plant productivity. Thus, slow-growing plants should be less able to compensate for biomass losses than fast-growing plants, and therefore be more susceptible to herbivory if attacked. We simulated winter browsing by moose (Alcesalces (L.)) on Scots pine (Pinussylvestris L.) along a gradient of plant productivity and addressed the following questions: (1) Does herbivory affect growth independently of plant productivity? (2) Is herbivory a more important mortality factor for slow-growing than for fast-growing plants? (3) Is there any effect of herbivory on fecundity, and is it related to plant productivity? Two clipping regimes simulated different intensities of moose winter browsing. Mortality was followed annually, and after 4 years we measured tree growth and fecundity on control as well as on treatment pines. The effect of clipping on growth was related with both clipping intensity and plant productivity. In the light-clipping treatment mortality was restricted to the slow-growing pines, in contrast with the severe treatment, where it occurred across the whole range of plant growth. Moreover, in the light-clipping treatment most mortality occurred within 1 year after treatment, whereas tree death occurred over 2 or more years in the severe treatment. We found no effect of age on mortality within growth-rate classes. The proportion of trees with cones increased with growth rate for control trees but not for treated trees, indicating that herbivory more strongly affects fecundity on fast-growing than on slow-growing trees. Our results confirm the hypothesis that herbivory affects plant performance differently across a gradient of plant productivity. We suggest that mammalian herbivores can increase mortality of plant genets after the seedling stage primarily in stands on low-productivity sites, especially in combination with a high density of the herbivore.
SUMMARY
Maximum likelihood estimation of the generalized linear model under linear restrictions on the parameters is considered. Using a penalty function approach an iterative procedure for obtaining the estimates is proposed. The likelihood ratio test, the Wald test and the Lagrange multiplier test are considered as alternatives for testing a hypothesis about linear restrictions on the parameters. An application of the estimator and the tests is illustrated in a numerical example. The approach extends to a definition of a ridge estimator for generalized linear models and to a definition of piecewise regressions, including cubic spline functions and a nonparametric smoother.
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