Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

Decision Making for Inconsistent Expert Judgments Using Negative Probabilities

In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular example, both the Bayesian and the quantum-like approaches have less normative power than the negative probabilities one.Comment: 14 pages, revised version to appear in the Proceedings of the QI2013 (Quantum Interactions) conferenc

Evolutionary diversity is associated with wood productivity in Amazonian forests

Higher levels of taxonomic and evolutionary diversity are expected to maximize ecosystem function, yet their relative importance in driving variation in ecosystem function at large scales in diverse forests is unknown. Using 90 inventory plots across intact, lowland, terra firme, Amazonian forests and a new phylogeny including 526 angiosperm genera, we investigated the association between taxonomic and evolutionary metrics of diversity and two key measures of ecosystem function: aboveground wood productivity and biomass storage. While taxonomic and phylogenetic diversity were not important predictors of variation in biomass, both emerged as independent predictors of wood productivity. Amazon forests that contain greater evolutionary diversity and a higher proportion of rare species have higher productivity. While climatic and edaphic variables are together the strongest predictors of productivity, our results show that the evolutionary diversity of tree species in diverse forest stands also influences productivity. As our models accounted for wood density and tree size, they also suggest that additional, unstudied, evolutionarily correlated traits have significant effects on ecosystem function in tropical forests. Overall, our pan-Amazonian analysis shows that greater phylogenetic diversity translates into higher levels of ecosystem function: tropical forest communities with more distantly related taxa have greater wood productivity

Carbon uptake by mature Amazon forests has mitigated Amazon nations' carbon emissions

BACKGROUND: Several independent lines of evidence suggest that Amazon forests have provided a significant carbon sink service, and also that the Amazon carbon sink in intact, mature forests may now be threatened as a result of different processes. There has however been no work done to quantify non-land-use-change forest carbon fluxes on a national basis within Amazonia, or to place these national fluxes and their possible changes in the context of the major anthropogenic carbon fluxes in the region. Here we present a first attempt to interpret results from ground-based monitoring of mature forest carbon fluxes in a biogeographically, politically, and temporally differentiated way. Specifically, using results from a large long-term network of forest plots, we estimate the Amazon biomass carbon balance over the last three decades for the different regions and nine nations of Amazonia, and evaluate the magnitude and trajectory of these differentiated balances in relation to major national anthropogenic carbon emissions. RESULTS: The sink of carbon into mature forests has been remarkably geographically ubiquitous across Amazonia, being substantial and persistent in each of the five biogeographic regions within Amazonia. Between 1980 and 2010, it has more than mitigated the fossil fuel emissions of every single national economy, except that of Venezuela. For most nations (Bolivia, Colombia, Ecuador, French Guiana, Guyana, Peru, Suriname) the sink has probably additionally mitigated all anthropogenic carbon emissions due to Amazon deforestation and other land use change. While the sink has weakened in some regions since 2000, our analysis suggests that Amazon nations which are able to conserve large areas of natural and semi-natural landscape still contribute globally-significant carbon sequestration. CONCLUSIONS: Mature forests across all of Amazonia have contributed significantly to mitigating climate change for decades. Yet Amazon nations have not directly benefited from providing this global scale ecosystem service. We suggest that better monitoring and reporting of the carbon fluxes within mature forests, and understanding the drivers of changes in their balance, must become national, as well as international, priorities

Biased-corrected richness estimates for the Amazonian tree flora

Amazonian forests are extraordinarily diverse, but the estimated species richness is very much debated. Here, we apply an ensemble of parametric estimators and a novel technique that includes conspecific spatial aggregation to an extended database of forest plots with up-to-date taxonomy. We show that the species abundance distribution of Amazonia is best approximated by a logseries with aggregated individuals, where aggregation increases with rarity. By averaging several methods to estimate total richness, we confirm that over 15,000 tree species are expected to occur in Amazonia. We also show that using ten times the number of plots would result in an increase to just ~50% of those 15,000 estimated species. To get a more complete sample of all tree species, rigorous field campaigns may be needed but the number of trees in Amazonia will remain an estimate for years to come

Contrasting Cases: The Lotka-Volterra Model Times Three

How do philosophers of science make use of historical case studies? Are their accounts of historical cases purpose-built and lacking in evidential strength as a result of putting forth and discussing philosophical positions? We will study these questions through the examination of three different philosophical case studies. All of them focus on modeling and on Vito Volterra, contrasting his work to that of other theoreticians. We argue that the worries concerning the evidential role of historical case studies in philosophy are partially unfounded, and the evidential and hermeneutical roles of case studies need not be played against each other. In philosophy of science, case studies are often tied to conceptual and theoretical analysis and development, rendering their evidential and theoretic/hermeneutic roles intertwined. Moreover, the problems of resituating or generalizing local knowledge are not specific to philosophy of science but commonplace in many scientific practices—which show similarities to the actual use of historical case studies by philosophers of science