Measuring a mitotic oscillator: The ARC discontinuity

Mitosis occurs synchronously in up to 10⁸ nuclei in the syncytial plasmodium ofPhysarum polycephalum. Any two phases of the mitotic cycle may be mixed by fusing plasmodial pairs. A topological property of the synchronized phase of the fused pair as a function of parental phases, the arc discontinuity, characterizes the underlying oscillator, and indicates mitosis is controlled by a moderate relaxation oscillator which rotates more rapidly near its singularity than its limit cycle. A model oscillator is briefly described. Proceedings article from the Dissipative Structures Section of the Tenth Symposium on Biomathematics and Computer Science in the Life Sciences, University of Texas, Houston. March 29–31, 1973. Symposium Chairman: Stuart O. Zimmerman. Session Chairman and Proceedings Editors: Charles Walter and Hugo M. Martinez.     

Self‐recruitment in a Caribbean reef fish: a method for approximating dispersal kernels accounting for seascape

Characterizing patterns of larval dispersal is essential to understanding the ecological and evolutionary dynamics of marine metapopulations. Recent research has measured local dispersal within populations, but the development of marine dispersal kernels from empirical data remains a challenge. We propose a framework to move beyond point estimates of dispersal towards the approximation of a simple dispersal kernel, based on the hypothesis that the structure of the seascape is a primary predictor of realized dispersal patterns. Using the coral reef fish Elacatinus lori as a study organism, we use genetic parentage analysis to estimate self‐recruitment at a small spatial scale (<1 km). Next, we determine which simple kernel explains the observed self‐recruitment, given the influx of larvae from reef habitat patches in the seascape at a large spatial scale (up to 35 km). Finally, we complete parentage analyses at six additional sites to test for export from the focal site and compare these observed dispersal data within the metapopulation to the predicted dispersal kernel. We find 4.6% self‐recruitment (CI_95%: ±3.0%) in the focal population, which is explained by the exponential kernel y = 0.915^x (CI_95%: y = 0.865^x, y = 0.965^x), given the seascape. Additional parentage analyses showed low levels of export to nearby sites, and the best‐fit line through the observed dispersal proportions also revealed a declining function y = 0.77^x. This study lends direct support to the hypothesis that the probability of larval dispersal declines rapidly with distance in Atlantic gobies in continuously distributed habitat, just as it does in the Indo‐Pacific damselfishes in patchily distributed habitat.     

No-escape regions and oscillations in second order predator-prey recurrences

We are concerned with the second order recurrence x _n+1 = x _n f(x _n, y _n), y _n+1 = y _n g(x _n, y _n), where n N ₀, x ₀ > 0, y ₀ > 0, and the reproduction rates f and g simulate predator-prey interaction. Under conditions on the sign of f – 1 and g–1 we show the existence of a nontrivial no-escape region D, i.e. a compact set D {(x, y): x > 0, y > 0} which is invariant under the recurrence and has the property that every sequence enters D after finitely many steps. Under further conditions on the shape of the isoclines {f = 1} and {g = 1} and on the stationary points {f = 1} {g = 1} we are able to show the existence of sustained oscillations.This work has been supported by the Deutsche Forschungsgemeinschaft     

Multisubstrate kinetics of PAH mixture biodegradation: analysis in the double-logarithmic plot

The proposed method of kinetic analysis of aqueous-phase biodegradation of polycyclic aromatic hydrocarbons (PAH) mixture presupposes representation of kinetic curves for each pair of mixture components, S _x and S _y , in double-logarithmic coordinates (ln S _x ; ln S _y ). If PAH mixture conversion corresponds to the multisubstrate model with a common active site, then the graphs in double-logarithmic coordinates are straight lines with the angular coefficients equal to the ratio of respective first-order rate constants k_x^y = \fracV_y K_x K_y V_x k_{x}^{y} = {\frac{{V_{y} K_{x} }}{{K_{y} V_{x} }}} , where K _x and K _y are half-saturation constants, V _x and V _y are the maximum conversion rates for substrates S _x and S _y ; the graph slope does not depend on any concentrations and remains constant during the change of reaction rates as a result of inhibition, induction/inactivation of enzymes or biomass growth. The formulated method has been used to analyze PAH mixture conversion by the culture of Sphingomonas sp. VKM B-2434. It has been shown that this process does not satisfy the multisubstrate model with a single active site. The results suggest that the strain VKM B-2434 contains at least two dioxygenases of different substrate specificity: one enzyme converts phenanthrene and fluoranthene and the other converts acenaphthene and acenaphthylene. The ratios of first-order rate constants have been obtained for these pairs of substrates.     

The evolution of resource use

 The evolution of a consumer exploiting two resources is investigated. The strategy x under selection represents the fraction of time or energy an individual invests into extracting the first resource. In the model, a dimensionless parameter α quantifies how simultaneous consumption of both resources influences consumer growth; α<0 corresponds to hemi-essential resources, 0<α<1 corresponds to complementary resources, α=1 corresponds to perfectly substitutable resources, and α>1 corresponds to antagonistic resources. An analysis of the ecological and evolutionary dynamics leads to five conclusions. First, when α≤1, there is a unique singular strategy x ^* for the adaptive dynamics and it is evolutionarily stable and globally convergent stable. Second, when α=1, the singular strategy x ^* corresponds to the populations exhibiting an ideal free distribution and a population playing this strategy can invade and displace populations playing any other strategy. Third, when α>1, the strategies x=0 and x=1 are evolutionarily stable and convergent stable. Hence, if the populations initially specialize on one resource, evolution amplifies this specialization. Fourth, when α is slightly larger than one (i.e. the resources are slightly antagonistic), there is a convergent stable singular strategy whose basin of attraction is almost the entire strategy space (0,1). This singular strategy is evolutionarily unstable and serves as an evolutionary branching point. Following evolutionary branching, our analysis and numerical simulations suggest that evolutionary dynamics are driven toward an end state consisting of two populations specializing on different resources. Fifth, when α>>1, there is only one singular strategy and it is convergent unstable and evolutionarily unstable. Hence, if resources are overly antagonistic, evolutionary branching does not occur and ultimately only one resource is exploited. Received: 8 June 2002 / Revised version: 28 November 2002 / Published online: 23 April 2003 This work was supported by NSF Grant DMS-0077986 Key words or phrases: Consumer-resource interactions – Adaptive dynamics – Evolutionary branching     

Stability of stationary distributions in a space-dependent population growth process

We consider a spatial population growth process which is described by a reaction-diffusion equation c(x)u _t = (a ²(x)u _x ) _x +f(u), c(x) >0, a(x) > 0, defined on an interval [0, 1] of the spatial variable x. First we study the stability of nonconstant stationary solutions of this equation under Neumann boundary conditions. It is shown that any nonconstant stationary solution (if it exists) is unstable if a _xx0 for all x[0, 1], and conversely ifa _xx>0 for some x[0, 1], there exists a stable nonconstant stationary solution. Next we study the stability of stationary solutions under Dirichlet boundary conditions. We consider two types of stationary solutions, i.e., a solution u ₀(x) which satisfies u ₀ x0 for all x[0, 1] (type I) and a solution u ₀(x) which satisfies u _0x = 0 at two or more points in [0, 1] (type II). It is shown that any stationary solution of type I [type II] is stable [unstable] if a _xx 0 [a _xx 0] for all x[0, 1]. Conversely, there exists an unstable [a stable] stationary solution of type I [type II] if a _xx <0 [a _xx >0] for some x[0, 1].     

混合生物结皮对土壤养分的影响与群落结构之关联——以黄土丘陵区的生物结皮为例

自然条件下生物结皮是藻、藓及地衣等结皮类型以不同比例组成的混合群落,显著影响土壤养分含量,目前混合生物结皮对土壤养分的影响与其群落结构的关系尚不清楚,限制了混合生物结皮土壤养分的评估。为此,研究通过测定单一组成的藻结皮、藓结皮以及80%藻+20%藓、60%藻+40%藓、40%藻+60%藓和20%藻+80%藓4个不同藻藓比例的混合生物结皮土壤有机碳、全氮、全磷、速效磷、铵态氮和硝态氮含量,研究了混合生物结皮土壤养分与其群落结构之间的关联。结果显示：(1)藓结皮层土壤有机碳、全氮、速效磷、铵态氮和硝态氮含量显著高于藻结皮,分别高出166.4%、77.2%、55.1%、56.2%和42.2%。(2)藻藓混合生物结皮土壤有机碳、全氮、速效磷和铵态氮含量与组成和盖度等结构特征有关,可以通过单一类型生物结皮土壤养分含量与盖度加权预测混合生物结皮土壤养分储量。(3)混合生物结皮土壤有机碳、全氮、速效磷和铵态氮储量实测值(x)与预测值(y)拟合的线性函数分别为y=0.97x、y=0.96x、y=1.18x和y=0.92x。(4)混合生物结皮对全磷和硝态氮含量的影响与群落结构无关。生物结皮对下层0—5 ...     

A Further Problem of Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y = α + βx + ? (model I) of linear regression we dealt with in KUHNERT and HORN (1980) the determination of a confidence interval for that x₀ where the expectation Ey reaches a given value y₀. Here we start with realizations of random variables y (i = 1,…, m) being independent of x which are given in addition to the realizations of-y. Now y₀ denotes the unknown value of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^m $\end{document} ciEy and x₀ the x-value where the expectation Ey reaches that value y₀. For this x₀ we give a confidence interval. Applications stem from dose response assays.     

The effect of water depth on bacterial numbers,thymidine incorporation rates and C:N ratios in northeast Atlantic surficial sediments

The effect of water depth on bacterial biomass and their ability to synthesise DNA, by measuring their rate of [³H]-thymidine incorporation, was investigated in the northeast Atlantic at three sites of varying water depth (1100–3580 m) and sediment characteristics. Thymidine incorporation rates (y) in surficial sediments varied between 0.028 and 1.44 pmol h^–1 g^–1 and showed an exponential relationship with depth (x) according to the equation y= 2.05e^–0.0011x (r=0.9830 for n=7, P<0.001). However, this relationship failed when a layer of phytodetritus was found overlying the surface sediment and [³H]-thymidine incorporation rates increased by 80–339%. In contrast, bacterial numbers varied between 1.09 and 11.96 × 10⁸ cells g^–1 (dry weight) and showed no significant relationships with water depth or sediment POC/TN content. Significant exponential relationships were also found between water depth (x) and the POC (y ₁) and total nitrogen (TN, y ₂) content of surficial sediments according to the following equations: where y ₁ = 719e^–0.0003x (r=0.8700 for n=9, P<0.01) and y ₂ = 76e^–0.0002x(r=0.7582 for n=9 P<0.02). These relationships were irrespective of the presence or absence of an overlying layer of phytodetritus. This suggests that the POC and TN content of these surficial deep sea sediments is directly related to the flux of material through the water column, which significantly impacts bacterial production.     

Perfect harmony: the discrete dynamics of cooperation

We study the discrete model for cooperation as expressed through the dynamics of the family of noninvertible planar maps (x, y) (x exp(r(1 – x) + sy), y exp(r(1 – y) + sx)), with parameters r, s > 0. We prove that the map is proper in the open positive quadrant and describe its various stretching and folding actions. We determine conditions for a Hopf bifurcation — probably one of a cascade of double, quadruple, ... limit cycles, as a curve is followed in parameter space. For r > s an approximating version of the map is dissipative and permanent in the positive quadrant. We include the results of an extensive computer simulation, including a bifurcation diagram (y vs. r, with s fixed) through which is cut a number of x–y phase-plane plots; (an r–y curve penetrates each plot like a thread through cards). These indicate a complex dynamical evolution for cooperation, from stable cycle to strange attractor. A general conclusion is that the benefit of cooperation can be relatively high average values at the cost of oscillations of high amplitude.     

Calibration of FST-hemispheres against bottom shear stress in a laboratory flume*

SUMMARY.

• 1 Fliesswasserstammtisch (FST)-hemispheres of identical size but different densities were exposed on a horizontal plane on the pebble-covered bottom of a laboratory flume at streaming to shooting, turbulent and fully developed flow. The heaviest hemisphere moved was used as an indicator of shear stress, a flow force acting on the flume bottom.
• 2 The relationship between shear stress and hemisphere density was practically the same for three different sets of hemispheres, namely one prototype set newly prepared for the calibrations, one prototype set intensively used in the field prior to calibrations, and one randomly selected new set bought commercially.
• 3 Shear stress (y, dyn cm^?2) was related to hemisphere density (x, g cm^?3) by y= x^2.85 (n= 69; r²= 0.993). For lighter hemispheres this relationship was better explained by the linear model y= 7.32x– 6.60 (n= 35; r²=0.983).

     

Sequential Classification Based on Regression

Let us consider m general populations π₁, …,π_m. Each object belonging to these populations is represented by (p ± 1) characteristics x₁, x₂,…,x_p,y. A certain object, which is an element of one of the m general populations π₁,…,π_m has to be classified into the correct population. It will be assumed that knowledge of the value of the characteristic y would permit its correct classification, but that the observation of this characteristic is expensive, difficult or dangerous, as e.g. in medical applications. y is correlated with a set of p characteristics x₁,x₂,…,x_p, which are observed sequentially. The classification procedure is based on the division of the space of the observed value of characteristics x₁,x₂,…,x_p into nonintersecting areas determined so as to minimize the value of BAYES' risk given by equation (3).     

Genetic nets and dissipative structures: An algebraic approach

Genetic nets represent an attempt to model genome structure. Depending on the interaction dynamics assumed, they can constitute highly non-linear chemical systems having multiple steady states; hence their relevance to the theory of dissipative structures. Their typical size and possible complexity makes it difficult to study them by means of customary analytical techniques based on differential equations. We have therefore considered an algebraic approach derived from regarding the nets as finite-state automata. This view has revealed a surprisingly rich algebraic structure which can be used to investigate problems concerned with the relation between biological structure and function. This algebraic structure is described with particular reference to the genetic nets of Tsanev and Sendov. Proceedings article from the Dissipative Structures Section of the Tenth Symposium on Biomathematics and Computer Science in the Life Sciences, University of Texas, Houston. March 29–31, 1973. Symposium Chairman: Stuart O. Zimmerman. Session Chairman and Proceedings Editors: Charles Walter and Hugo M. Martinez.     

Three azido-, alk/phenoxido- and acetato-bridged tetranuclear nickel complexes featuring defective double-cubane

Three new tetranuclear nickel(II) complexes of general formula [Ni₄(L)₂(N₃)₂(CH₃COO)₂(CH₃O)₂]₂·xCH₃OH·yH₂O (HL = HL¹, HL² and HL³; x = 0, y = 1 for 1; x = 2, y = 0 for 2 and x = 2, y = 4 for 3) were synthesized and characterized by single crystal X-ray diffraction and magnetic measurements. Single crystal X-ray studies reveal that all three complexes exhibit similar tetranuclear face-shared defective double-cubane structure, having azido-, alk/phenoxido- and acetato-bridges. Magnetic susceptibility measurements on the complexes in the range of 300-2 K indicate ferromagnetic coupling between the metal ions. The slightly different magnetic behaviors observed are probably caused by subtle structural differences between the respective [Ni₄O₄N₂] cores induced by ligand variation.     

Relationships between phoma leaf spot and development of stem canker (Leptosphaeria maculans) on winter oilseed rape (Brassica napus) in southern England

Models were constructed to describe the relationships between incidence of phoma leaf spot at different growth stages in autumn/winter or early spring and incidence of stem canker (basal canker or stem lesions) in summer on winter oilseed rape in southern England. Model 1, describing the phoma leaf spot/basal canker relationship, was y₁=β₀+β₁x₁+β₂(x₂ ‐ x₁) if x₂ > x₁, and y₁=β₀+β₁x₁ if x₂≤x₁, in which y₁ was the incidence (% plants affected) of basal canker at harvest, x₁ was the maximum incidence of phoma leaf spot during the period from sowing to growth stage (G.S.) 1,6‐1,7 (about 100 days after sowing) and x₂ was the maximum incidence of phoma leaf spot between G.S. 1,7 and G.S. 2,0 (start of stem extension). Model 2, describing the phoma leaf spot/stem lesion relationship, was y₂=α₀+α₁x₃+α₂x₄, in which y₂ was the incidence of stem lesions at harvest, x₃ was the incidence of phoma leaf spot at G.S. 3,3–3,5 (flower buds visible) and x₄ was the incidence of phoma leaf spot at G.S. 4,5–5,5 (flower buds opening). Data from field experiments with four winter oilseed rape cultivars at Boxworth or Rothamsted in the 1992/93, 1993/94, 1996/97, 1997/98 or 1998/99 seasons were used to test the models. The values of R² for the regression equations testing model 1 for the phoma leaf spot/basal canker relationship were 0.75, 0.93, 0.91 and 0.89 for cvs Apex, Bristol, Capitol and Envol, respectively. The values of R² for the regression equations testing model 2 for the phoma leaf spot/stem lesion relationship were 0.58, 0.57, 0.54 and 0.71 for cvs Apex, Bristol, Capitol and Envol, respectively. The phoma leaf spot/basal canker relationship (model 1) could also be fitted to the combined data set for all four cultivars (R²= 0.65), whereas the phoma leaf spot/stem lesion relationship (model 2) could not to be fitted to the combined data set for the four cultivars. The relationships between incidence and severity of stem canker were examined and the values of R² for the regressions of severity on incidence were 0.91 for basal canker and 0.89 for stem lesions.     

A New Functional Equation Analogous to CAUCHT-PEXIDER Functional Equation and its Application

The CAUCHY-PEXIDER functional equation H (x±y)=F(x) G(y) is generalized to the form H ((x^c±y^c)^1/c) = F(x) G(y), c≠0, assuming the function H(x) possesses a measurable majorant on a set of positive measure. The result is used to obtain a characterization of WEIBULL distribution. This functional equation is generalized to functions of vector variables.     

Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?₀(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?₀(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?₀(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C₀(x).     

Diminished Confidence Levels in the Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y=β₀ + β₁ x + e (model I of linear regression) in the literature confidence estimators of an unknown position x₀ are given at which either the expectation of y is given (see FIELLER, 1944; FINNEY, 1952), or realizations of y are given (see GRAYBILL, 1961). These confidence regions with level 1—α need not be intervals. The occurrence of interval shape is a random event. Its probability is equal to the power of the t test for the examination of the hypothesis H: β₁ = 0. The papers mentioned above claim to provide confidence intervals with level 1 ? α. But because of the restriction of (1 —α)—confidence regions to intervals the true confidence probability is the conditional probability W_c: W_c = P (the confidence region covers x₀| the region has interval shape). Here this conditional probability is shown to be less than 1 —α. Evidence on the possible deviations from 1 —α has been obtained by simulations.     

Parnassius apollo last-instar larvae development prediction by analysis of weather condition as a tool in the species’ conservation

Parnassius apollo (Lepidoptera: Papilionidae) has already disappeared or is under threat of extinction in many of its former habitats. It has been documented that weather conditions – anomalies in particular – contributed to this process. In this study, we combined developmental data obtained previously for the last-instar Apollo larvae (collected in 1996, 1997, and 2003) with corresponding meteorological data to assess the effects of ambient temperature and rainfall episodes on the duration and the completion of the instar. For comparing the temperature effect, we applied the degree-day concept. We found significant positive correlation between the number of rainy days during the instar development (x) and its duration time (y): y = 8.293 + 0.936x (± 2.813) (r = 0.662, P < 10⁻⁷). Logarithmic transformation of the growth curves of the last-instar Apollo larvae revealed that there was no difference in growth among females; however, there was slower growth of males in 2003 in comparison to 1996. Growth (y) of female Apollo larvae as a function of instar duration (x) can by described by one common equation, irrespectively of the year: y = 317.6 + 502.3 lnx (± 263.3) (r = 0.82, P < 10⁻⁴).