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)

To eat and not be eaten : optimal foraging behaviour in suspension feeding copepods

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of The Royal Society for personal use, not for redistribution. The definitive version was published in Journal of The Royal Society Interface 6 (2013): 20120693, doi:10.1098/rsif.2012.0693.Zooplankton feed on microscopic prey that they either entrain in a feeding current or encounter as they cruise through the water. They generate fluid disturbances as they feed and move, thus elevating their risk of being detected and encountered by predators. Different feeding modes generate different hydrodynamic signals to predators and different predator encounter speeds but may also differ in their efficiency; the optimal behaviour is that which maximizes the net energy gain over the predation risk. Here, we show by means of flow visualization and simple hydrodynamic and optimization models that copepods with a diversity of feeding behaviours converge on optimal, size-independent specific clearance rates that are consistent with observed clearance rates of zooplankton, irrespective of feeding mode, species and size. We also predict magnitudes and size-scaling of swimming speeds that are consistent with observations. The rationalization of the magnitude and scaling of the clearance rates of zooplankton makes it more suitable for development of models of marine ecosystems, and is particularly relevant in predicting the size structure and biomass of pelagic communities.The work was supported by grants from the Danish Council for Independent Research, The Niels Bohr Foundation and The Carlsberg Foundation to T.K., and by grants from the US National Science Foundation to H.J. (NSF OCE-1129496 and IOS-0718506)

A new mathematical model for environmental monitoring and assessment

Versão dos Autores para este artigo.In this paper we are concerned with a quantitative method of Landscape Ecology. More in details we consider an environmental system distributed in landscape units (ecological sectors) and we propose a new mathematical model in order to implement a method for the evaluation of the ecological state of the system under investigation. After having performed a stability analysis of the model, we apply the proposed procedure first by considering separately each landscape unit and then extending our investigation to the system as a whole, by taking into account the connections between all the landscape units themselves. Our investigation includes some numerical computations that were performed for a Northern district of the Turin Province, using an approximation procedure that should avoid stiffness problems.National Group GNFM of INdAM, Italyinfo:eu-repo/semantics/publishedVersio

Deciphering Network Community Structure by Surprise

The analysis of complex networks permeates all sciences, from biology to sociology. A fundamental, unsolved problem is how to characterize the community structure of a network. Here, using both standard and novel benchmarks, we show that maximization of a simple global parameter, which we call Surprise (S), leads to a very efficient characterization of the community structure of complex synthetic networks. Particularly, S qualitatively outperforms the most commonly used criterion to define communities, Newman and Girvan's modularity (Q). Applying S maximization to real networks often provides natural, well-supported partitions, but also sometimes counterintuitive solutions that expose the limitations of our previous knowledge. These results indicate that it is possible to define an effective global criterion for community structure and open new routes for the understanding of complex networks.Comment: 7 pages, 5 figure

Ability of Archival Tags to Provide Estimates of Geographical Position Based on Light Intensity

Key words: archival tags, ambient light level, geoposition algorithm, light attenuation, positional errors, crepuscular, Equinox, pelagic fishes Abstract: We tested the ability of archival tags and their associated algorithms to esti-mate geographical position based on ambient light intensity by attaching six tags (three tags each from Northwest Marine Technologies [NMT] and Wild-life Computers [WC]) at different depths to a stationary mooring line in the Pacific Ocean (approx. 166º42'W, 24º00'N), for approximately one year (29-Aug-98 to 16-Aug-99). Upon retrieval, one tag each from the two vendors had malfunctioned: from these no data (NMT) or only partial data (WC) could be downloaded. An algorithm onboard the NMT tag automatically calculated geographical positions. For the WC tags, three different algorithms were used to estimate geographical positions from the recorded light intensity data. Es-timates of longitude from all tags were significantly less variable than those for latitude. The mean absolute error for longitude estimates from the NMT tags ranged from 0.29 to 0.35º, and for the WC tags from 0.13 to 0.25º. Th

Cirsium species show disparity in patterns of genetic variation at their range-edge, despite similar patterns of reproduction and isolation

Genetic variation was assessed across the UK geographical range of Cirsium acaule and Cirsium heterophyllum. A decline in genetic diversity and increase in population divergence approaching the range edge of these species was predicted based on parallel declines in population density and seed production reported seperately. Patterns were compared with UK populations of the widespread Cirsium arvense.Populations were sampled along a latitudinal transect in the UK and genetic variation assessed using microsatellite markers. Cirsium acaule shows strong isolation by distance, a significant decline in diversity and an increase in divergence among range-edge populations. Geographical structure is also evident in C. arvense, whereas no such patterns are seen in C.heterophyllum. There is a major disparity between patterns of genetic variation in C. acaule and C. heterophyllum despite very similar patterns in seed production and population isolation in these species. This suggests it may be misleading to make assumptions about the geographical structure of genetic variation within species based solely on the present-day reproduction and distribution of populations

Composition and distribution of the peracarid crustacean fauna along a latitudinal transect off Victoria Land (Ross Sea, Antarctica) with special emphasis on the Cumacea

The following study was the first to describe composition and structure of the peracarid fauna systematically along a latitudinal transect off Victoria Land (Ross Sea, Antarctica). During the 19th Antarctic expedition of the Italian research vessel “Italica” in February 2004, macrobenthic samples were collected by means of a Rauschert dredge with a mesh size of 500 m at depths between 85 and 515 m. The composition of peracarid crustaceans, especially Cumacea was investigated. Peracarida contributed 63% to the total abundance of the fauna. The peracarid samples were dominated by amphipods (66%), whereas cumaceans were represented with 7%. Previously, only 13 cumacean species were known, now the number of species recorded from the Ross Sea increased to 34. Thus, the cumacean fauna of the Ross Sea, which was regarded as the poorest in terms of species richness, has to be considered as equivalent to that of other high Antarctic areas. Most important cumacean families concerning abundance and species richness were Leuconidae, Nannastacidae, and Diastylidae. Cumacean diversity was lowest at the northernmost area (Cape Adare). At the area off Coulman Island, which is characterized by muddy sediment, diversity was highest. Diversity and species number were higher at the deeper stations and abundance increased with latitude. A review of the bathymetric distribution of the Cumacea from the Ross Sea reveals that most species distribute across the Antarctic continental shelf and slope. So far, only few deep-sea records justify the assumption of a shallow-water–deep-sea relationship in some species of Ross Sea Cumacea, which is discussed from an evolutionary point of view

Maximum Likelihood Estimation of the Negative Binomial Dispersion Parameter for Highly Overdispersed Data, with Applications to Infectious Diseases

BACKGROUND: The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not highly overdispersed (i.e., those with k≥1), and the accuracy of confidence intervals estimated for k is typically not explored. METHODOLOGY: This article presents a simulation study exploring the bias, precision, and confidence interval coverage of maximum-likelihood estimates of k from highly overdispersed distributions. In addition to exploring small-sample bias on negative binomial estimates, the study addresses estimation from datasets influenced by two types of event under-counting, and from disease transmission data subject to selection bias for successful outbreaks. CONCLUSIONS: Results show that maximum likelihood estimates of k can be biased upward by small sample size or under-reporting of zero-class events, but are not biased downward by any of the factors considered. Confidence intervals estimated from the asymptotic sampling variance tend to exhibit coverage below the nominal level, with overestimates of k comprising the great majority of coverage errors. Estimation from outbreak datasets does not increase the bias of k estimates, but can add significant upward bias to estimates of the mean. Because k varies inversely with the degree of overdispersion, these findings show that overestimation of the degree of overdispersion is very rare for these datasets

A theory for ecological survey methods to map individual distributions

Spatially explicit approaches are widely recommended for ecosystem management. The quality of the data, such as presence/absence or habitat maps, affects the management actions recommended and is, therefore, key to management success. However, available data are often biased and incomplete. Previous studies have advanced ways to resolve data bias and missing data, but questions remain about how we design ecological surveys to develop a dataset through field surveys. Ecological surveys may have multiple spatial scales, including the spatial extent of the target ecosystem (observation window), the resolution for mapping individual distributions (mapping unit), and the survey area within each mapping unit (sampling unit). We developed an ecological survey method for mapping individual distributions by applying spatially explicit stochastic models. We used spatial point processes to describe individual spatial placements using either random or clustering processes. We then designed ecological surveys with different spatial scales and individual detectability. We found that the choice of mapping unit affected the presence mapped fraction, and the fraction of the total individuals covered by the presence mapped patches. Tradeoffs were found between these quantities and the map resolution, associated with equivalent asymptotic behaviors for both metrics at sufficiently small and large mapping unit scales. Our approach enabled consideration of the effect of multiple spatial scales in surveys, and estimation of the survey outcomes such as the presence mapped fraction and the number of individuals situated in the presence detected units. The developed theory may facilitate management decision-making and inform the design of monitoring and data gathering

Megafaunal Community Structure of Andaman Seamounts Including the Back-Arc Basin – A Quantitative Exploration from the Indian Ocean

Species rich benthic communities have been reported from some seamounts, predominantly from the Atlantic and Pacific Oceans, but the fauna and habitats on Indian Ocean seamounts are still poorly known. This study focuses on two seamounts, a submarine volcano (cratered seamount – CSM) and a non-volcano (SM2) in the Andaman Back–arc Basin (ABB), and the basin itself. The main purpose was to explore and generate regional biodiversity data from summit and flank (upper slope) of the Andaman seamounts for comparison with other seamounts worldwide. We also investigated how substratum types affect the megafaunal community structure along the ABB. Underwater video recordings from TeleVision guided Gripper (TVG) lowerings were used to describe the benthic community structure along the ABB and both seamounts. We found 13 varieties of substratum in the study area. The CSM has hard substratum, such as boulders and cobbles, whereas the SM2 was dominated by cobbles and fine sediment. The highest abundance of megabenthic communities was recorded on the flank of the CSM. Species richness and diversity were higher at the flank of the CSM than other are of ABB. Non-metric multi-dimensional scaling (nMDS) analysis of substratum types showed 50% similarity between the flanks of both seamounts, because both sites have a component of cobbles mixed with fine sediments in their substratum. Further, nMDS of faunal abundance revealed two groups, each restricted to one of the seamounts, suggesting faunal distinctness between them. The sessile fauna corals and poriferans showed a significant positive relation with cobbles and fine sediments substratum, while the mobile categories echinoderms and arthropods showed a significant positive relation with fine sediments only