Evolutionary change is interpreted in terms of the near-universal ecological scenario of stressful environments. Consequently, there is a premium on the energetically efficient exploitation of resources in a resource-inadequate world. Under this environmental model, fitness can be approximated to energetic efficiency especially towards the limits of survival. Furthermore, fitness at one stage of the life-cycle should correlate with fitness at other stages, especially for development time, survival and longevity; ‘good genotypes’ under stress should therefore be at a premium. Conservation in the wild depends primarily on adaptation to abiotically changing habitats since towards the limits of survival, genomic variation is rarely restrictive. The balance between energetic costs under variable environments and energy from resources provides a model for interpreting evolutionary stasis, punctuational and gradual change, and specialist diversification. Ultimately, a species should be in an equilibrium between the physiology of an organism and its adaptation to the environment. The primary key to understanding evolutionary change should therefore be ecological, highlighting energy availability in a stressed world; this approach is predictive for various patterns of evolutionary change in the living and fossil biota.

We develop a test of evolutionary change that incorporates a null hypothesis of homogeneity, which encompasses time invariance in the variance and autocovariance structure of residuals from estimated econometric relationships. The test framework is based on examining whether shifts in spectral decomposition between two frames of data are significant. Rejection of the null hypothesis will point not only to weak nonstationarity but to shifts in the structure of the second-order moments of the limiting distribution of the random process. This would indicate that the second-order properties of any underlying attractor set has changed in a statistically significant way, pointing to the presence of evolutionary change. A demonstration of the test's applicability to a real-world macroeconomic problem is accomplished by applying the test to the Australian Building Society Deposits (ABSD) model.

We investigate the size and power properties of the AH test of evolutionary change. This involves examining whether the size results are sensitive to both the number of individual frequencies estimated and the spectral shape adopted under the null hypothesis. The power tests examine whether the test has good power to detect shifts in both spectral position (variance) and spectral shape (autocovariance structure).