Optimal Test for Parameter Instability When the Unstable Process and the Error Distribution are Unknown

This paper proposes asymptotically optimal tests for unstable parameter process under the feasible circumstance that the researcher has little information about the unstable parameter process and the error distribution, and suggests conditions under which the knowledge of those processes does not provide asymptotic power gains. I first derive a test under known error distribution, which is asymptotically equivalent to LR tests for correctly identified unstable parameter processes under suitable conditions. The conditions are weak enough to cover a wide range of unstable processes such as various types of structural breaks and time varying parameter processes. The test is then extended to semiparametric models in which the underlying distribution in unknown but treated as unknown infinite dimensional nuisance parameter. The semiparametric test is adaptive in the sense that its asymptotic power function is equivalent to the power envelope under known error distribution.

Ontogenetic Effects of Hatching Plasticity in the Spotted Salamander (Ambystoma maculatum) due to Egg and Larval Predators

The ability to respond plastically to the environment has allowed amphibians to evolve a response to spatial and temporal variation in predation threat (Benard 2004). Embroys exposed to egg predation are expected to hatch out earlier than their conspecifics. Larval predation can induce a suite of phenotypic changes including growing a larger tail area. When presented with cues from both egg and larval predators, embryos are expected to respond to the egg predator by hatching out earlier because the egg predator presents an immediate threat. However, hatching early may be costly in the larval environment in terms of development, morphology, and/or behavior. We created a laboratory experiment in which we exposed clutches of spotted salamander (Ambystoma maculatum) eggs to both egg (caddisfly larvae) and larval (A. opacum) predators to test this hypothesis. We recorded hatching time and stage and took developmental and morphological data of the animals a week after hatching. Larvae were entered into lethal predation trials with a larval predatory sunfish (Lepomis sp.) in order to study behavior. We found that animals exposed to the egg predator cues hatched out earlier and at earlier developmental stages than conspecifics regardless of whether there was a larval predator present. Animals exposed to larval predator cues grew relatively larger tails and survived longer in the lethal predation trials. However the group exposed to both predators showed a cost of early hatching in terms of lower tail area and shorter survival time in predation trials. The morphological and developmental effects measured of hatching plasticity were transient as there were no developmental or morphological differences between the treatment groups at metamorphosis. Hatching plasticity may be transient but it is important to the development and survival of many amphibians.