An Application of the Z-Transform in Extracting the Density Regulation from the Periodic Output of an Age-Structured Population Model

The application of the Z-transform, a manipulation tool from the discrete signal processing (DSP) toolbox, on an ecological model was motivated by the mathematical similarities between an age-structured fish population model with a non linear density regulation and a linear time invariant (LTI) control system. Both models include a switching mechanism in regulating stock/signal throughput in accordance with a given density limitation/set value and both models can be expressed in terms of a negative feedback loop difference equations (Getz & Haight,1989; °Astr¨om & Murray, 2008). In the fish model, the switching mechanism is a density regulated stock-recruitment (SR) function which models the strategies implemented by the population in keeping the vulnerable egg-larvaejuvenile densities within an environmental limitation thereof (Subbey et al, 2014). A switching mechanism is also present in control engineering, for example, in the mechanism associated with cruise control in cars which keeps traveling speed close to a chosen set value midst varying weather and road conditions (Antsaklis and Gao, 2005). In both cases, the choosing of the control action and the tuning of its parameters requires careful consideration to avoid failures such as incorrectly timed switching actions in a control plant (see Kuphaldt (2019)) and errors in estimating total allowable catch (TAC) in the fishing industry (see Borlestean et al (2015), Skagen et al (2013) and Taboadai and R. Anadn (2016)). The Z-transform has proven itself useful in tuning LTI controlmodels for a desired control action (see Orfanidis, (2010) and Smith, (1999)) and it is on this account that its application was extended to the ecological model in pursuit of a more efficient way of estimating SR parameters to simulate an already existing output. It was however found that it could not be used for parameter tuning but rather for the extraction of the SR component hidden in the output together with components resulting from the age structure itself. Such an extraction can greatly assist in the mathematical identification of the SR, reducing the complexity of its choosing as there are many different types used in the fishing industry such as the classic Beverton-Holt model, the Ricker model and Shepherd model (Myers, 2001; Iles, 1994; Shepherd, 1982). It can also be used to monitor changes in the SR over time which can indicate the presence of strategy evolution (Apaloo et al, 2009; Br¨annstr¨om et al, 2013). In 1998 Schoombie and Getz investigated the latter by subjecting the Shepherd SR to strategy optimization with regards to a parameter associated with population interventions in regulating recruitment throughput and it is because of this versatility that the Shepherd SR is chosen for the intended extraction. In true control style, Simulink, a graphic environment for designing control simulations, is used to visualize the production of the output as well as the extraction of the SR from it. This paper showcases the versatility of the Z transform and the possibilities and unexpected finds when applied to similar systems designed to regulate signals or, in this case, recruitment densities.

Variations of intracellular density during the cell cycle arise from tip-growth regulation in fission yeast

Intracellular density impacts the physical nature of the cytoplasm and can globally affect cellular processes, yet density regulation remains poorly understood. Here, using a new quantitative phase imaging method, we determined that dry-mass density in fission yeast is maintained in a narrow distribution and exhibits homeostatic behavior. However, density varied during the cell cycle, decreasing during G2, increasing in mitosis and cytokinesis, and dropping rapidly at cell birth. These density variations were explained by a constant rate of biomass synthesis, coupled to slowdown of volume growth during cell division and rapid expansion post-cytokinesis. Arrest at specific cell-cycle stages exacerbated density changes. Spatially heterogeneous patterns of density suggested links between density regulation, tip growth, and intracellular osmotic pressure. Our results demonstrate that systematic density variations during the cell cycle are predominantly due to modulation of volume expansion, and reveal functional consequences of density gradients and cell-cycle arrests.

Insolation And Covid‑19: Protection From The Aggressor

The article reviews the importance of insolation as a factor of prevention and containment of infectious diseases and epidemics. The authors consider insolation not as a mean of curing the Сoronavirus Disease (WHO fairly calls such possibility “a myth”) but as a means to lower the risks of dissemination of the infection, to reduce viability of the virus in the environment, to support human protective immune mechanisms affecting susceptibility of the population as a whole, severity and recovery time, i.e. both sanitary and hygienic and prevention factors of the COVID‑19 epidemic containment. Apart from the germicidal and virucidal sanitising effects of solar rays, the article reviews anti-epidemic capabilities of insolation as a microclimate factor and a psychological and physiological regulator of human protective capabilities as well as the insolation standards as a mechanism of development density regulation. It is impossible to efficiently combat massive dissemination of highly contagious infections without concerted utilisation of all available means and measures: both medical and preventive and organisational. The unprecedented mobilisation of healthcare systems and large-scale restrictive quarantine measures are under special attention of the society. This article reviews the importance of insolation as a universal natural anti-epidemic factor which is undeservedly placed in the end of the list of effective infection combating measures.

The disproportionate effect of drift on a hypervariable master regulator of density

Symbiosis is a continuum of long-term interactions ranging from mutualism to parasitism, according to the balance between costs and benefits for the protagonists. The density of endosymbiont density is in both cases a key factor that determines both the transmission of symbiont and the host extended phenotype and is thus tightly regulated within hosts. However, the evolutionary and molecular mechanisms underlying bacterial density regulation are currently poorly understood. In this context, the symbiosis between the fruit fly and its intracellular bacteria Wolbachia (wMelPop strain) is particularly interesting to study. Although vertically-transmitted, the symbiont is pathogenic, and a positive correlation between virulence and wMelPop density is observed. In addition, the number of repeats of a bacterial genomic region -Octomom- varies between individuals, but most likely also within them, and is positively correlated to the Wolbachia density. Such genetic heterogeneity within the host could promote conflicts between partners by increasing within-host competition between symbiont genotypes through a process analogous to the tragedy of the common. To characterize the determinisms at play in the regulation of bacterial density, we first introgressed wMelPop in different genetic backgrounds of D. melanogaster. We found different density levels and Octomom copy numbers in each host lineage, suggesting a host influence on density regulation through Octomom copy number selection. To confirm this hypothesis, we performed new replicated introgressions on the two Drosophila populations that exhibited the most extreme density levels. However, we found no evidence of host influence on density regulation. Instead, we found instability in infection patterns across generations, which rather suggests an influence of drift. Moreover, using reciprocal crosses with the two extreme lineages, we confirmed the absence of host regulation on density levels and Octomom copy number, and a strong influence of drift. We then discuss how drift, both on the symbiont population during transmission and on the host population, could limit the efficiency of selection in such a symbiotic system, and the consequences of drift on the regulation of density and composition of bacterial populations.

Spatial and temporal variation in the generation time of a bird metapopulation: density regulation and the evolutionary potential of a pace-of-life measure

Generation time determines the pace of key demographic and evolutionary processes. Quantified as the weighted mean age at reproduction, it can be studied as a trait that varies within and among populations and may evolve in response to ecological conditions. We combined quantitative genetic analyses with age- and density-dependent models to study generation time variation in a bird metapopulation. Generation time was heritable, and males had longer generation times compared with females. Individuals with longer generation times had a higher lifetime reproductive success but not a higher expected population growth rate. Density regulation acted on recruit production, suggesting that longer generation times should be favored when populations are closer to carrying capacity. Furthermore, generation times were shorter when populations were growing, and longer when populations were closer to equilibrium or declining. These results support classic theory predicting that density regulation is an important driver of the pace of life-history strategies.

Bacterial density as an unexpected factor regulating decomposition by soil oligotrophs

Bacterial decomposition of organic matter in soils is generally believed to be mainly controlled by the accessibility of bacteria to their substrate. The influence of bacterial metabolic traits on this control has however received little attention in highly heterogeneous spatial conditions under advective-dispersive transport of bacteria and substrates. Here, we develop a biochemical transport model to screen the interactive impacts of dispersion and metabolic traits on mineralization. We compare the model results with two sets of previously performed cm-scale soil-core experiments in which the mineralization of the pesticide 2,4-D was measured under well-controlled initial distributions and transport conditions. Bacterial dispersion away from the source of substrate induced a significant increase in 2,4-D mineralization, revealing the existence of a control of decomposition by the bacterial density, in addition to the accessibility to the substrate. This regulation of degradation by density becomes dominant for bacteria with an efficient uptake of substrate at low substrate concentrations (i.e. oligotrophs). The model output suggests that the distance between bacteria adapted to oligotrophic environments is a stronger regulator of degradation than the distance between substrate source and these bacteria. Such oligotrophs, commonly found in soils, compete with each other for substrate even under remarkably low population densities. The ratio-dependent Contois growth model, which includes a density regulation in the expression of the uptake efficiency, appears more versatile and accurate than the substrate-dependent Monod model. In view of their strong interactions, biochemical and transport processes cannot be handled independently but should be integrated, in particular when biochemical processes of interest are carried out by oligotrophs.Abstract FigureHighlights–Biodegradation in soils results from strong biochemical and transport couplings–Biodegradation depends on bacterial density, in addition to substrate accessibility–Bacterial density regulation counterbalances substrate accessibility regulation–Density regulation is enhanced for oligotrophic bacteria–The ratio-dependent Contois model is relevant to represent this double regulation