Power Theory of Exchange and Money

Modern exchange theories model a large market, but do not explain single exchanges. This paper considers the phenomenon of single exchange and formulates the general exchange problem in the form of a system of two equations, subjective and objective. Subjective equilibrium is given by the Walras–Jevons marginal utility equation. Objective equilibrium equations by Walras and Jevons are averaged over all transactions in the market and can only give a rough general picture without explaining the specific price of an individual exchange. An exchange micro-condition must be found that, when averaged, will give the Walras market equilibrium macro-condition. The study of the internal structure of exchange leads to the need to consider power. The concept of generalized power is introduced. It is generalized power that serves as the primary comparable and measurable objective basis of exchange. The power theory of exchange provides the objective price-equation. It is demonstrated that money is a measure of generalized power in exchange and a certification of generalized power in subsequent exchanges. This methodology is based on an interdisciplinary analysis of an abstract exchange model in the form of a system of equations. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.

Species losses, gains, and changes in persistent species are associated with distinct effects on ecosystem functioning in global grasslands

Global change drivers such as anthropogenic nutrient inputs simultaneously alter biodiversity, species composition, and ecosystem functions such as above ground biomass. These changes are interconnected by complex feedbacks among extinction, invasion, and shifting relative abundance. Here, we use a novel temporal application of the Price equation to separate species richness and biomass change through time and quantify the functional contributions of species that are lost, gained, and persist under ambient and experimental nutrient addition in 59 global grasslands. Under ambient conditions, compositional and biomass turnover was high, but species losses (i.e., local extinctions) were balanced by gains (i.e. colonization). Under fertilization, there was biomass loss associated with species loss. Few species were gained in fertilized conditions over time but those that were, and species that persisted, contributed to net biomass gains, outweighing biomass loss. These components of community change are associated with distinct effects on measures of ecosystem functioning.

Identifying Causes of Social Evolution: Contextual Analysis, the Price Approach, and Multilevel Selection

Kin selection theory and multilevel selection theory are distinct approaches to explaining the evolution of social traits. The latter claims that it is useful to regard selection as a process that can occur on multiple levels of organisation such as the level of individuals and the level of groups. This is reflected in a decomposition of fitness into an individual component and a group component. This multilevel view is central to understanding and characterising evolutionary transitions in individuality, e.g., from unicellular life to multicellular organisms, but currently suffers from the lack of a consistent, quantifiable measure. Specifically, the two major statistical tools to determine the coefficients of such a decomposition, the multilevel Price equation and contextual analysis, are inconsistent and may disagree on whether group selection is present. Here we show that the reason for the discrepancies is that underlying the multilevel Price equation and contextual analysis are two non-equivalent causal models for the generation of individual fitness effects (thus leaving different “remainders” explained by group effects). While the multilevel Price equation assumes that the individual effect of a trait determines an individual's relative success within a group, contextual analysis posits that the individual effect is context-independent. Since these different assumptions reflect claims about the causal structure of the system, the correct approach cannot be determined on general theoretical or statistical grounds but must be identified by experimental intervention. We outline interventions that reveal the underlying causal structure and thus facilitate choosing the appropriate approach. We note that kin selection theory with its focus on the individual is immune to such inconsistency because it does not address causal structure with respect to levels of organisation. In contrast, our analysis of the two approaches to measuring group selection demonstrates that multilevel selection theory adds meaningful (falsifiable) causal structure to explain the sources of individual fitness and thereby constitutes a proper refinement of kin selection theory. Taking such refined causal structure into account seems indispensable for studying evolutionary transitions in individuality because these transitions are characterised by changes in the selection pressures that act on the respective levels.

Power Theory of Exchange and Money

Modern exchange theories model a large market, but do not explain single exchange. The paper considers the phenomenon of single exchange and formulates the general exchange problem in the form of a system of two equations, subjective and objective. Subjective equilibrium is given by the Walras-Jevons marginal utility equation. Objective equilibrium equations by Walras and Jevons are averaged over all transactions in the market and can only give a rough general picture without explaining the specific price of an individual exchange. An exchange micro-condition must be found that, when averaged, will give the Walras market equilibrium macro-condition. The study of the internal structure of exchange leads to the need to consider power. The concept of generalized power is introduced. It is generalized power that serves as the primary comparable and measurable objective basis of exchange. The power theory of exchange provides the objective price-equation. It is demonstrated that money is a measure of generalized power in exchange and a certification of generalized power in subsequent exchanges. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.

Power Theory of Exchange and Money

Modern exchange theories model a large market, but do not explain single exchange. The paper considers the phenomenon of single exchange and formulates the general exchange problem in the form of a system of two equations, subjective and objective. Subjective equilibrium is given by the Walras-Jevons marginal utility equation. Objective equilibrium equations by Walras and Jevons are averaged over all transactions in the market and can only give a rough general picture without explaining the specific price of an individual exchange. An exchange micro-condition must be found that, when averaged, will give the Walras market equilibrium macro-condition. The study of the internal structure of exchange leads to the need to consider power. The concept of generalized power is introduced. It is generalized power that serves as the primary comparable and measurable objective basis of exchange. The power theory of exchange provides the objective price-equation. It is demonstrated that money is a measure of generalized power in exchange and a certification of generalized power in subsequent exchanges. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.

The extended Price equation: migration and sex

The Price equation provides a general partition of evolutionary change into two components. The first is usually thought to represent natural selection and the second, transmission bias. Here, we provide a new derivation of the generalised equation, which contains a largely ignored third term. Unlike the original Price equation, this extension can account for migration and mixed asexual and sexual reproduction. The derivation here expresses the generalised equation explicitly in terms of fitness, rendering this otherwise difficult third term more open to biological interpretation and use. This re-derivation also permits fundamental results, derived from the Price equation, to be more easily generalised. We take Hamilton's rule as a case study, and provide an exact, total expression that allows for population structures like haplodiploidy. Our analysis, more generally, makes clear the previously hidden assumptions in similar fundamental results, highlighting the caution that must be taken when interpreting them.

Towards a Pricean foundation for cultural evolutionary theory

The Price equation is currently considered one of the fundamental equations – or even the fundamental equation – of evolution. In this article, we explore the role of this equation within cultural evolutionary theory. More specifically, we use it to account for the explanatory power and the theoretical structure of a certain generalised version of dual-inheritance theory. First, we argue that, in spite of not having a definite empirical content, the Price equation offers a suitable formalisation of the processes of cultural evolution, and provides a powerful heuristic device for discovering the actual causes of cultural change and accumulation. Second, we argue that, as a consequence of this, a certain version of the Price equation is the fundamental law of cultural evolutionary theory. In order to support this claim, we sketch the ideal structure of dual-inheritance theory and we stress the unificatory role that the Price equation plays in it.

The mirror of physics: on how the price equation can unify evolutionary biology

Due to its high degree of complexity and its historical nature, evolutionary biology has been traditionally portrayed as a messy science. According to the supporters of such a view, evolutionary biology would be unable to formulate laws and robust theories, instead just delivering coherent narratives and local models. In this article, our aim is to challenge this view by showing how the Price equation can work as the core of a general theoretical framework for evolutionary phenomena. To support this claim, we outline some unnoticed structural similarities between physical theories (in particular, classical mechanics) and evolutionary biology. More specifically, we shall argue that the Price equation, in the same way as fundamental formalisms in physics, can serve as a heuristic principle to formulate and systematise different theories and models in evolutionary biology.