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)

The Epidemics of Donations: Logistic Growth and Power-Laws

This paper demonstrates that collective social dynamics resulting from individual donations can be well described by an epidemic model. It captures the herding behavior in donations as a non-local interaction between individual via a time-dependent mean field representing the mass media. Our study is based on the statistical analysis of a unique dataset obtained before and after the tsunami disaster of 2004. We find a power-law behavior for the distributions of donations with similar exponents for different countries. Even more remarkably, we show that these exponents are the same before and after the tsunami, which accounts for some kind of universal behavior in donations independent of the actual event. We further show that the time-dependent change of both the number and the total amount of donations after the tsunami follows a logistic growth equation. As a new element, a time-dependent scaling factor appears in this equation which accounts for the growing lack of public interest after the disaster. The results of the model are underpinned by the data analysis and thus also allow for a quantification of the media influence

A Putative Plant Aminophospholipid Flippase, the Arabidopsis P4 ATPase ALA1, Localizes to the Plasma Membrane following Association with a β-Subunit

Plasma membranes in eukaryotic cells display asymmetric lipid distributions with aminophospholipids concentrated in the inner leaflet and sphingolipids in the outer leaflet. This unequal distribution of lipids between leaflets is, amongst several proposed functions, hypothesized to be a prerequisite for endocytosis. P4 ATPases, belonging to the P-type ATPase superfamily of pumps, are involved in establishing lipid asymmetry across plasma membranes, but P4 ATPases have not been identified in plant plasma membranes. Here we report that the plant P4 ATPase ALA1, which previously has been connected with cold tolerance of Arabidopsis thaliana, is targeted to the plasma membrane and does so following association in the endoplasmic reticulum with an ALIS protein β-subunit

Unmasking Chaotic Attributes in Time Series of Living Cell Populations

. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth.Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations.Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled

Demographic Diversity and Sustainable Fisheries

Fish species are diverse. For example, some exhibit early maturation while others delay maturation, some adopt semelparous reproductive strategies while others are iteroparous, and some are long-lived and others short-lived. The diversity is likely to have profound effects on fish population dynamics, which in turn has implications for fisheries management. In this study, a simple density-dependent stage-structured population model was used to investigate the effect of life history traits on sustainable yield, population resilience, and the coefficient of variation (CV) of the adult abundance. The study showed that semelparous fish can produce very high sustainable yields, near or above 50% of the carrying capacity, whereas long-lived iteroparous fish can produce very low sustainable yields, which are often much less than 10% of the carrying capacity. The difference is not because of different levels of sustainable fishing mortality rate, but because of difference in the sensitivity of the equilibrium abundance to fishing mortality. On the other hand, the resilience of fish stocks increases from delayed maturation to early maturation strategies but remains almost unchanged from semelparous to long-lived iteroparous. The CV of the adult abundance increases with increased fishing mortality, not because more individuals are recruited into the adult stage (as previous speculated), but because the mean abundance is more sensitive to fishing mortality than its standard deviation. The magnitudes of these effects vary depending on the life history strategies of the fish species involved. It is evident that any past high yield of long-lived iteroparous fish is a transient yield level, and future commercial fisheries should focus more on fish that are short-lived (including semelparous species) with high compensatory capacity

Maternal depressive symptoms, and not anxiety symptoms, are associated with positive mother–child reporting discrepancies of internalizing problems in children: a report on the TRAILS Study

Maternal internalizing problems affect reporting of child’s problem behavior. This study addresses the relative effects of maternal depressive symptoms versus anxiety symptoms and the association with differential reporting of mother and child on child’s internalizing problems. The study sample comprised a cohort of 1,986 10- to 12-year-old children and their mothers from the Dutch general population in a cross sectional setup. Children’s internalizing problems were assessed with the DSM-IV anxiety and affective problem scales of the Child Behavior Checklist (CBCL) and the Youth Self-Report (YSR). Current maternal internalizing problems were assessed with the depressive and anxiety symptom scales of the Depression Anxiety Stress Scale (DASS), while the TRAILS Family History Interview (FHI) measured lifetime maternal depression and anxiety. Results show that current and lifetime maternal depressive symptoms were associated with positive mother–child reporting discrepancies (i.e. mothers reporting more problems than their child). Considering the small amount of variance explained, we conclude that maternal depressive symptoms do not bias maternal reporting on child’s internalizing problems to a serious degree. Studies concerning long term consequences of mother–child reporting discrepancies on child’s internalizing problems are few, but show a risk for adverse outcome. More prognostic research is needed

Sex-specific effects of the local social environment on juvenile post-fledging dispersal in great tits

An individual’s decision to disperse from the natal habitat can affect its future fitness prospects. Especially in species with sex-biased dispersal, we expect the cost–benefit balance for dispersal to vary according to the social environment (e.g., local sex ratio and density). However, little is known about the social factors affecting dispersal decisions and about the temporal and spatial patterns of the dispersal process. In our study, we investigated experimentally the effects of the social environment on post-fledging dispersal of juvenile great tits by simultaneously manipulating the density and sex ratio of fledglings within forest plots. We expected young females in the post-fledging period mainly to compete for resources related to food and, as they are subordinate to males, we predicted higher female dispersal from male-biased plots. Juvenile males compete for vacant territories already in late summer and autumn; thus, we predicted increased male dispersal from high density and male-biased plots. We found that juvenile females had a higher probability to leave male-biased plots and had dispersed further from male-biased plots in the later post-fledging phase when juvenile males start to become territorial and more aggressive. Juvenile males were least likely to leave male-biased plots and had smallest dispersal distances from female-biased plots early after fledging. The results suggest that the social environment differentially affected the costs and benefits of philopatry for male and female juveniles. The local sex ratio of individuals is thus an important social trait to be considered for understanding sex-specific dispersal processes

The interplay between gonadal steroids and immune defence in affecting a carotenoid-dependent trait

The hypothesis that sexual ornaments are honest signals of quality because their expression is dependent on hormones with immune-depressive effects has received ambiguous support. The hypothesis might be correct for those signals that are carotenoid-dependent because the required carotenoid deposition in the signal, stimulated by testosterone, might lower the carotenoid-dependent immune defence of the organism. Two pathways underlying this androgen-dependent honest signaling have been suggested. Firstly, androgens that are needed for ornament expression may suppress immune defence, a cost that only high-quality animals can afford. Alternatively, immune activation may downregulate the production of androgens in low-quality individuals. Which of these alternatives is correct, and to what extent these effects are mediated by the different metabolites of androgens, remain open questions. To provide answers to these questions, we manipulated the levels of testosterone (T), 5α-dihydrotestosterone (DHT), and 17-β-estradiol (E2) in diamond doves Geopelia cuneata, a species in which both sexes exhibit a carotenoid-dependent, androgen-regulated red–orange periorbital ring of bare skin. On the first day of the experiment (day 0), we inserted steroid-releasing implants into groups of birds and on day 14, we subjected half of the birds to an immunological challenge by immunizing them with sheep red blood cells (SRBC). In females, but not in males, androgen but not estradiol treatments reduced antibody production to SRBC. In addition, the immunological challenge reduced redness and size of the trait as well as androgens levels in both sexes and in all treatments. This indicates that an immunological challenge can lower circulating T at the cost of the trait expression. These findings are in accordance with both pathways postulated in the immunocompetence-handicap hypothesis, but do not entirely support the idea that the immunosuppressive effect of androgens yields honest signaling since both T and DHT were not immunosuppressive in males, for which sexual signaling is supposed to be especially important

Prospective community study of family stress and anxiety in (pre)adolescents: the TRAILS study

For prevention of anxiety in children and adolescents, it is important to know whether family stress is a predictor of anxiety. We studied this in 1,875 adolescents from the Tracking Adolescents’ Individual Lives Survey (TRAILS) who were followed up for 2 years, from age 10–12 to 12–14 years. Adolescents reported anxiety and depression symptoms at both assessments, and parents reported family stress (family dysfunction and parenting stress) at the first assessment. Family dysfunction was not associated with future anxiety, whereas high parenting stress was. Furthermore, family dysfunction was more strongly associated with anxiety than with depression, whereas parenting stress was more strongly associated with depression. Level of parental psychopathology explained part of the association of family stress with anxiety. The associations were modest and the understanding of the origins of adolescents’ anxiety will require identifying other factors than family stress that account for more of the variance