The study was conducted in the raised bog Kusowo (Baltic region, West Pomerania, Poland). Along a transect line crossing two open mires affected by forest succession we analysed tree age ...distribution. One of those mires had been drained in the past years and still retained some open ditches, while the other one was located far from the ditches. Every 10 meters along the transect line one tree was drilled at the root collar in order to determine its age. We also conducted phytosociological analyses and short-term water level measurements in the sample plots. We expected faster tree encroachment in the undisturbed part of the open mire. The results showed, that there were no significant differences in water table level and in soil moisture indicator values between the formerly drained and undisturbed open mire. There were also no statistically significant differences in tree encroachment between the disturbed and undisturbed mires. Location and the age distribution of the trees suggest that changes in the tree growth conditions cannot be directly explained by the general decreasing of water level in the bog, although periods following drainage works were associated with more numerous establishment of young trees, in the drained part of the bog as well as in the part not directly affected by drainage ditches.
The study shows that the volumes and surfaces of n-balls, n-simplices, and n-orthoplices are holomorphic functions of n, which makes those objects omnidimensional, that is well defined in any complex ...dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about n-balls reveal previously unknown properties of these geometric objects. In particular, for 0<n<1, the volumes of the omnidimensional polytopes are larger than those of circumscribing n-balls, and both their volumes and surfaces are smaller than those of inscribed n-balls. The surface of an n-simplex circumscribing a unit diameter n-ball is spirally convergent to zero with real n approaching negative infinity but first has a local maximum at n=−3.5. The surface of an n-orthoplex circumscribing a unit diameter n-ball is spirally divergent with real n approaching negative infinity but first has a local minimum at n=−1.5, where its real and imaginary parts are equal to each other; similarly, is its volume, where the similar local minimum occurs at n=−3.5. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about n-balls are proposed. Symmetries of products and quotients of the volumes in complex dimensions n and −n and of the surfaces in complex dimensions n and 2−n are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between the volumes and surfaces in dimensions n=−1/2 and n=1/2.
We investigate the model of gene expression in the form of Iterated Function System (IFS), where the probability of choice of any iterated map depends on the state of the phase space. Random jump ...times of the process mark activation periods of the gene when pre-mRNA molecules are produced before mRNA and protein processing phases occur. The main idea is inspired by the continuous-time piecewise deterministic Markov process describing stochastic gene expression. We show that for our system there exists a unique invariant limit measure. We provide full probabilistic description of the process with a comparison of our results to those obtained for the model with continuous time.
Sample size estimation is a necessary and crucial step in clinical trial research. Statistical requirements, limited patient availability and high financial risk of a clinical trial necessitate the ...proper calculation of this measure. The aim of this paper is to discuss the reasons why the estimation of the sample size is important and, based on the obtained results, to show how this process may be completed in selected cases. Stochastic simulations based on the Monte Carlo methods approach are applied. Therefore, new challenges facing this area of research are mentioned.
Sample size estimation is a necessary and crucial step in clinical trial research. Statistical requirements, limited patient availability and high financial risk of a clinical trial necessitate the ...proper calculation of this measure. The aim of this paper is to discuss the reasons why the estimation of the sample size is important and, based on the obtained results, to show how this process may be completed in selected cases. Stochastic simulations based on the Monte Carlo methods approach are applied. Therefore, new challenges facing this area of research are mentioned.
In this paper we develop a model of stochastic gene expression, which is an extension of the model investigated in the paper T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A.R. Brasier, M. Kimmel, ...Transcriptional stochasticity in gene expression, J. Theor. Biol. 238 (2006) 348–367. In our model, stochastic effects still originate from random fluctuations in gene activity status, but we precede mRNA production by the formation of pre-mRNA, which enriches classical transcription phase. We obtain a stochastically regulated system of ordinary differential equations (ODEs) describing evolution of pre-mRNA, mRNA and protein levels. We perform mathematical analysis of a long-time behavior of this stochastic process, identified as a piece-wise deterministic Markov process (PDMP). We check exact results using numerical simulations for the distributions of all three types of particles. Moreover, we investigate the deterministic (adiabatic) limit state of the process, when depending on parameters it can exhibit two specific types of behavior: bistability and the existence of the limit cycle. The latter one is not present when only two kinds of gene expression products are considered.
•We model stochastic gene expression with pre-mRNA, mRNA and protein contribution.•This mechanism is mathematically based on Piece-wise Deterministic Markov Process.•We show that if the initial distribution of the process has a density, then it stabilizes in time with some invariant density.•We find a set on which the invariant density is supported.•We investigate bistability state and the existence of limit cycle in the adiabatic limit.
In this paper we analyse stochastic expression of a single gene with its dynamics given by the classical Goodwin model with mRNA and protein contribution. We compare the effect of the presence of ...positive and negative feedback on the transcription regulation. In such cases we observe two qualitatively different types of asymptotic behaviour. In the case of a negative feedback loop, under sufficient conditions, one can find a stationary density for mRNA and protein molecules. In the case of a positive feedback loop we observe extinction of both types of molecules with time.
•We investigate stochastic gene expression using classical Goodwin model.•The model is based on Piecewise Deterministic Markov Process.•We prove that the (long-time) behaviour of the process depends on the type of the feedback loop it exhibits.•We provide numerical simulations of the process for a wide variety of parameters.•We discuss biological interpretation of the process.
Key message
The disturbance of a research plot by a windstorm allowed us to study the role of the seedling bank in the regeneration processes. The released advance regeneration dominated among the ...saplings; taller individuals retained their position until the end of the study. Pioneer species occurred sporadically. Seven years after the disturbance, the windthrow was covered by a dense thicket of young trees.
Context
The dominant role played by advance regeneration in natural regeneration processes after intense wind disturbances is still a matter of dispute.
Aims
We took advantage of a windstorm in one of our research plots to study the role of the seedling bank released by the disturbance in the regeneration processes.
Methods
We collected data in 70 plots, recording the survivorship of seedlings, annual height growth, and signs of browsing. The height ranking was analyzed with Kendall’s concordance coefficient, and the height growth rates were compared using Dunn’s test.
Results
The density of seedlings increased from 6.7/m
2
in 2008 to 8.1/m
2
in 2010 and then decreased to 1.2/m
2
in 2015. The density of saplings increased continuously from 0.14 to 1.9/m
2
. The highest size differentiation occurred in sycamore maple; the individuals which were taller before the windstorm retained their position until the year 2015. The only species that was recruited mainly from germinants was European hornbeam.
Conclusion
The advance regeneration released by the windstorm played a major role in the regeneration process, while pioneer species occurred only sporadically. Seven years after the disturbance, the windthrow was already covered by a dense thicket of young trees.
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