The shade avoidance syndrome: A non-Markovian stochastic growth model

Plants at high population density compete for light, showing a series of physiological responses known as the shade avoidance syndrome. These responses are controlled by the synthesis of the hormone auxin, which is regulated by two signals, an environmental one and an internal one. Considering that the auxin signal induces plant growth after a time lag, this work shows that plant growth can be modelled in terms of an energy-like function extremization, provided that the Markov property is not applied. The simulated height distributions are bimodal and right skewed, as in real community of plants. In the case of isolated plants, theoretical growth dynamics and speed correctly fit Arabidopsis thaliana experimental data reported in literature. Moreover, the growth dynamics of this model is shown to be consistent with the biomass production function of an independent model. These results suggest that memory effects play a non-negligible role in plant growth processes.     

THE COMPONENTS OF KIN COMPETITION

It is well known that competition among kin alters the rate and often the direction of evolution in subdivided populations. Yet much remains unclear about the ecological and demographic causes of kin competition, or what role life cycle plays in promoting or ameliorating its effects. Using the multilevel Price equation, I derive a general equation for evolution in structured populations under an arbitrary intensity of kin competition. This equation partitions the effects of selection and demography, and recovers numerous previous models as special cases. I quantify the degree of kin competition, α, which explicitly depends on life cycle. I show how life cycle and demographic assumptions can be incorporated into kin selection models via α, revealing life cycles that are more or less permissive of altruism. As an example, I give closed‐form results for Hamilton's rule in a three‐stage life cycle. Although results are sensitive to life cycle in general, I identify three demographic conditions that give life cycle invariant results. Under the infinite island model, α is a function of the scale of density regulation and dispersal rate, effectively disentangling these two phenomena. Population viscosity per se does not impede kin selection.     

A spatially explicit model for an Allee effect: why wolves recolonize so slowly in Greater Yellowstone

A reduced probability of finding mates at low densities is a frequently hypothesized mechanism for a component Allee effect. At low densities dispersers are less likely to find mates and establish new breeding units. However, many mathematical models for an Allee effect do not make a distinction between breeding group establishment and subsequent population growth. Our objective is to derive a spatially explicit mathematical model, where dispersers have a reduced probability of finding mates at low densities, and parameterize the model for wolf recolonization in the Greater Yellowstone Ecosystem (GYE). In this model, only the probability of establishing new breeding units is influenced by the reduced probability of finding mates at low densities. We analytically and numerically solve the model to determine the effect of a decreased probability in finding mates at low densities on population spread rate and density. Our results suggest that a reduced probability of finding mates at low densities may slow recolonization rate.     

Interactions Between Pattern Formation and Domain Growth

In this paper we develop a theoretical framework for investigating pattern formation in biological systems for which the tissue on which the spatial pattern resides is growing at a rate which is itself regulated by the diffusible chemicals that establish the spatial pattern. We present numerical simulations for two cases of interest, namely exponential domain growth and chemically controlled growth. Our analysis reveals that for domains undergoing rapid exponential growth dilution effects associated with domain growth influence both the spatial patterns that emerge and the concentration of chemicals present in the domain. In the latter case, there is complex interplay between the effects of the chemicals on the domain size and the influence of the domain size on the formation of patterns. The nature of these interactions is revealed by a weakly nonlinear analysis of the full system. This yields a pair of nonlinear equations for the amplitude of the spatial pattern and the domain size. The domain is found to grow (or shrink) at a rate that depends quadratically on the pattern amplitude, the particular functional forms used to model the local tissue growth rate and the kinetics of the two diffusible species dictating the resulting behaviour.     

Analysis of Non-stationary Data for Heart-rate Fluctuations in Terms of Drift and Diffusion Coefficients

We describe a method for analyzing the stochasticity in non-stationary data for the beat-to-beat fluctuations in the heart rates of healthy subjects, as well as those with congestive heart failure. The method analyzes the return time series of the data as a Markov process, and computes the Markov time scale, i.e., the time scale over which the data are a Markov process. We also construct an effective stochastic continuum equation for the return series. We show that the drift and diffusion coefficients, as well as the amplitude of the return time series for healthy subjects are distinct from those with CHF. Thus, the method may potentially provide a diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, as it can distinguish small differences between the data for the two classes of subjects in terms of well-defined and physically-motivated quantities. PACS: 05.10.Gg 05.40.-a, 05.45.Tp, 87.19.Hh     

Estimation of the causal effects on survival of two-stage nonrandomized treatment sequences for recurrent diseases

In the treatment of cancer, patients commonly receive a variety of sequential treatments. The initial treatments administered following diagnosis can vary, as well as subsequent salvage regimens given after disease recurrence. This article considers the situation where neither initial treatments nor salvage treatments are randomized. Assuming there are no unmeasured confounders, we estimate the joint causal effects on survival of initial and salvage treatments, that is, the effects of two-stage treatment sequences. For each individual treatment sequence, we estimate the survival distribution function and the mean restricted survival time. Different treatment sequences are then compared using these estimates and their corresponding covariances. Simulation studies were conducted to evaluate the performance of the methods, including their sensitivity to the violation of the assumption of no unmeasured confounders. The methods are illustrated by a retrospective study of patients with soft tissue sarcoma, which motivated this research.     

Glass transition and enthalpy relaxation of amorphous lactose glass

The glass transition temperature, T(g), and enthalpy relaxation of amorphous lactose glass were investigated by differential scanning calorimetry (DSC) for isothermal aging periods at various temperatures (25, 60, 75, and 90 degrees C) below T(g). Both T(g) and enthalpy relaxation were found to increase with increasing aging time and temperature. The enthalpy relaxation increased approximately exponentially with aging time at a temperature (90 degrees C) close to T(g) (102 degrees C). There was no significant change observed in the enthalpy relaxation around room temperature (25 degrees C) over an aging period of 1month. The Kohlrausch-Williams-Watts (KWW) model was able to fit the experimental enthalpy relaxation data well. The relaxation distribution parameter (beta) was determined to be in the range 0.81-0.89. The enthalpy relaxation time constant (tau) increased with decreasing aging temperature. The observed enthalpy relaxation data showed that molecular mobility in amorphous lactose glass was higher at temperatures closer to T(g). Lactose glass was stable for a long time at 25 degrees C. These findings should be helpful for improving the processing and storage stability of amorphous lactose and lactose containing food and pharmaceutical products.