The Inequality Process Versus the Saved Wealth Model: Which Is the More Likely to Imply an Analogue of Thermodynamics in Social Science?

The Inequality Process (IP) and the Saved Wealth Model (SW) are theories of income distribution. The IP's social science metatheory requires its stationary distribution to fit the distribution of labor income conditioned on education. The SW is a modification of the particle system model of the kinetic theory of gases (KTG), the basis of gas thermodynamics. The IP is a particle system similar to the SW and KTG. This article shows that the IP passes the empirical test required of it by social science theory better than the SW. The IP's advantage increases as the U.S. labor force becomes more educated. The IP may the better bet to imply an analogue of thermodynamics in social science.     

A General Model of Church Growth and Decline

An earlier model of church growth (Hayward, 1999 Hayward , J. ( 1999 ). Mathematical modeling of church growth . Journal of Mathematical Sociology , 23 ( 4 ): 255 – 292 . [CSA] [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) is extended to include long-term effects due to births, deaths and reversion from the church. It is proposed that only a subset of the church, the enthusiasts, is involved in the recruitment process, and only for a limited period of time after their conversion. It is found that the church reaches equilibrium in its proportion of society according to the potential of these enthusiasts to reproduce themselves, and the losses from the church. If this reproduction potential is below a threshold that depends on losses, then extinction occurs. If it is above a higher threshold, then the church sees rapid revival growth. The model is applied to a number of church denominations to examine their prospects for survival or revial growth. Generally, declining churches do so because their reproduction potential is inadequate, rather than due to excessive losses.     

MULTISPECIES MODELING FOR ADAPTIVE MANAGEMENT OF HORSESHOE CRABS AND RED KNOTS IN THE DELAWARE BAY

Abstract Adaptive management requires that predictive models be explicit and transparent to improve decisions by comparing management actions, directing further research and monitoring, and facilitating learning. The rufa subspecies of red knots (Calidris canutus rufa), which has recently exhibited steep population declines, relies on horseshoe crab (Limulus polyphemus) eggs as their primary food source during stopover in Delaware Bay during spring migration. We present a model with two different parameterizations for use in the adaptive management of horseshoe crab harvests in the Delaware Bay that links red knot mass gain, annual survival, and fecundity to horseshoe crab dynamics. The models reflect prevailing hypotheses regarding ecological links between these two species. When reported crab harvest from 1998 to 2008 was applied, projections corresponded to the observed red knot population abundances depending on strengths of the demographic relationship between these species. We compared different simulated horseshoe crab harvest strategies to evaluate whether, given this model, horseshoe crab harvest management can affect red knot conservation and found that restricting harvest can benefit red knot populations. Our model is the first to explicitly and quantitatively link these two species and will be used within an adaptive management framework to manage the Delaware Bay system and learn more about the specific nature of the linkage between the two species.     

OPTIMAL CONTROL OF MULTIPLE-USE PRODUCTS: THE CASE OF TIMBER,FORAGE AND WATER PRODUCTION

ABSTRACT. A thorough analysis of the optimal control of multiple-use forest management at the stand level reveals that the results of earlier studies, which seem to contradict each other, are in fact part of a common solution space. We provide an explanation for this result by showing that it is caused by the growth function and the interaction between the timber and forage production functions. We discuss the sensibility of the results using this new knowledge. Most optimal control models focusing on multiple-use forest management have applied production functions that are quadratic in the state variable. This makes explicit solutions easy because the first order derivative is linear. However, in reality, production is often better described by more complex nonlinear functions, but, unfortunately, such functions are difficult to handle in an optimal control framework. We illustrate how the convenience of the quadratic production function can be combined with better approximations to nonlinear production functions.