Solving the Random Pielou Logistic Equation with the Random Variable Transformation Technique: Theory and Applications

[EN] The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.This work has been partially supported by the Ministerio de Economía y Competitividad grant MTM2017-89664-PCortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2019). Solving the Random Pielou Logistic Equation with the Random Variable Transformation Technique: Theory and Applications. Mathematical Methods in the Applied Sciences. 42(17):5708-5717. https://doi.org/10.1002/mma.5440S570857174217Kwasnicki, W. (2013). Logistic growth of the global economy and competitiveness of nations. Technological Forecasting and Social Change, 80(1), 50-76. doi:10.1016/j.techfore.2012.07.007Chen-Charpentier, B. M., & Stanescu, D. (2011). Biofilm growth on medical implants with randomness. Mathematical and Computer Modelling, 54(7-8), 1682-1686. doi:10.1016/j.mcm.2010.11.075Wolfram Research Inc.Mathematica. Version 11.2 Champaign IL;2018.CNMC Comisión Nacional de los Mercados y la Competencia.http://data.cnmc.es/datagraph/jsp/inf_anual.jsp Accessed: 2018‐07‐24 (in Spanish)

Competition between species can stabilize public-goods cooperation within a species

Competition between species is a major ecological force that can drive evolution. Here, we test the effect of this force on the evolution of cooperation within a species. We use sucrose metabolism of budding yeast, Saccharomyces cerevisiae, as a model cooperative system that is subject to social parasitism by cheater strategies. We find that when cocultured with a bacterial competitor, Escherichia coli, the frequency of cooperator phenotypes in yeast populations increases dramatically as compared with isolated yeast populations. Bacterial competition stabilizes cooperation within yeast by limiting the yeast population density and also by depleting the public goods produced by cooperating yeast cells. Both of these changes induced by bacterial competition increase the cooperator frequency because cooperator yeast cells have a small preferential access to the public goods they produce; this preferential access becomes more important when the public good is scarce. Our results indicate that a thorough understanding of species interactions is crucial for explaining the maintenance and evolution of cooperation in nature.United States. National Institutes of Health (GM085279‐02)National Science Foundation (U.S.) (PHY‐1055154)Alfred P. Sloan Foundation (BR2011‐066

Models of marine fish biodiversity : assessing predictors from three habitat classification schemes

Prioritising biodiversity conservation requires knowledge of where biodiversity occurs. Such knowledge, however, is often lacking. New technologies for collecting biological and physical data coupled with advances in modelling techniques could help address these gaps and facilitate improved management outcomes. Here we examined the utility of environmental data, obtained using different methods, for developing models of both uni- and multivariate biodiversity metrics. We tested which biodiversity metrics could be predicted best and evaluated the performance of predictor variables generated from three types of habitat data: acoustic multibeam sonar imagery, predicted habitat classification, and direct observer habitat classification. We used boosted regression trees (BRT) to model metrics of fish species richness, abundance and biomass, and multivariate regression trees (MRT) to model biomass and abundance of fish functional groups. We compared model performance using different sets of predictors and estimated the relative influence of individual predictors. Models of total species richness and total abundance performed best; those developed for endemic species performed worst. Abundance models performed substantially better than corresponding biomass models. In general, BRT and MRTs developed using predicted habitat classifications performed less well than those using multibeam data. The most influential individual predictor was the abiotic categorical variable from direct observer habitat classification and models that incorporated predictors from direct observer habitat classification consistently outperformed those that did not. Our results show that while remotely sensed data can offer considerable utility for predictive modeling, the addition of direct observer habitat classification data can substantially improve model performance. Thus it appears that there are aspects of marine habitats that are important for modeling metrics of fish biodiversity that are not fully captured by remotely sensed data. As such, the use of remotely sensed data to model biodiversity represents a compromise between model performance and data availability

Effects of trampling on in-stream macroinvertebrate communities from canyoning activity in the Greater Blue Mountains World Heritage Area

Perceived growth in the adventure recreation sport of canyoning in the Greater Blue Mountains World Heritage Area (Australia) has raised concerns with park management that such activity is resulting in unsustainable visitor impacts to canyon ecosystems. Three levels of trampling intensity were applied within an upland section of a canyon stream to assess the impact of trampling on benthic macroinvertebrate communities. After an initial detrimental effect from trampling, there was a rapid recovery of the macroinvertebrate community. Recovery occurred within one day of trampling ceasing, and overall community composition was similar among treatments after 15 days. However, by day 15 the untrampled sites showed a substantial decrease in animal abundance. This indicated that adjacent habitat contributed greatly to the recolonisation of animals into trampled areas