To evaluate the potential of using surficial shell accumulations for paleoenvironmental studies, an extensive time series of individually dated specimens of the marine infaunal bivalve mollusk Semele casali was assembled using amino acid racemization (AAR) ratios (n = 270) calibrated against radiocarbon ages (n = 32). The shells were collected from surface sediments at multiple sites across a sediment-starved shelf in the shallow sub-tropical São Paulo Bight (São Paulo State, Brazil). The resulting 14C-calibrated AAR time series, one of the largest AAR datasets compiled to date, ranges from modern to 10,307 cal yr BP, is right skewed, and represents a remarkably complete time series: the completeness of the Holocene record is 66% at 250-yr binning resolution and 81% at 500-yr binning resolution. Extensive time-averaging is observed for all sites across the sampled bathymetric range indicating long water depth-invariant survival of carbonate shells at the sediment surface with low net sedimentation rates. Benthic organisms collected from active depositional surfaces can provide multi-millennial time series of biomineral records and serve as a source of geochemical proxy data for reconstructing environmental and climatic trends throughout the Holocene at centennial resolution. Surface sediments can contain time-rich shell accumulations that record the entire Holocene, not just the present.

Grade and age structures in manpower systems are often far from ideal. This fact raises the question of how the flows of people — and particularly the recruitment flow — should be controlled in order to attain and maintain a more desirable structure. The problem has received considerable attention from a deterministic point of view. This paper adopts a stochastic approach to the study of maintainability and shows, among other things, that the problem is more subtle than the deterministic analysis suggests.

Letting Z(t) be the number of objects alive at time t in a general supercritical age-dependent branching process generated by a single ancestor born at time 0, one achieves (Theorem 1) mean-square convergence of Z(t)/E[Z(t)] provided and , where N(t) is the number of offspring of the initial ancestor born by time t and α is the (positive) Malthusian parameter defined by . If the stronger conditions that (Theorem 2) and hold also, then the convergence is almost-sure. It is of interest that the embedded Galton-Watson process of successive generations need not have a finite mean for the conditions of the above theorems to hold. Similar results are obtained for the age-distribution as well.

Expressions are developed for the moments of age and remaining life in renewal processes, and from them, expressions for the moments of the last and next renewal epochs. The results for remaining life and next renewal epoch may be regarded as generalizations of theorems of Wald (1944) and others. The results for age and last renewal epoch do not fit into this sequential analysis framework. Both sets of results are obtained from partial differential equations developed for the distributions of age and of remaining life. These partial differential equations are of the “conservation” type familiar from statistical mechanics, and may have some independent interest for renewal theory.