On the option interpretation of rational harvesting planning

We consider the determination of the harvesting strategy maximizing the present expected value of the cumulative yield from the present up to extinction. By relying on a combination of stochastic calculus, ordinary nonlinear programming, and the classical theory of diffusions, we show that if the underlying population evolves according to a logistic diffusion subject to a general diffusion coefficient, then there is a single threshold density at which harvesting should be initiated in a singular fashion. We derive the condition which uniquely determines the threshold and show that harvesting should be initiated only when the option value of further preserving another individual falls below its opportunity cost. In this way, we present a real option interpretation of rational harvesting planning. We also consider the comparative static properties of the value of the harvesting opportunity and state a set of usually satisfied conditions under which increased stochastic fluctuations (demographic or environmental) decrease the expected cumulative yield from harvesting and increase the optimal harvesting threshold, thus postponing the rational exercise of the irreversible harvesting decision. Received: 19 January 1999 / Revised version: 2 July 1999 / Published online: 16 February 2000     

Spread rate for a nonlinear stochastic invasion

Despite the recognized importance of stochastic factors, models for ecological invasions are almost exclusively formulated using deterministic equations [29]. Stochastic factors relevant to invasions can be either extrinsic (quantities such as temperature or habitat quality which vary randomly in time and space and are external to the population itself) or intrinsic (arising from a finite population of individuals each reproducing, dying, and interacting with other individuals in a probabilistic manner). It has been long conjectured [27] that intrinsic stochastic factors associated with interacting individuals can slow the spread of a population or disease, even in a uniform environment. While this conjecture has been borne out by numerical simulations, we are not aware of a thorough analytical investigation. In this paper we analyze the effect of intrinsic stochastic factors when individuals interact locally over small neighborhoods. We formulate a set of equations describing the dynamics of spatial moments of the population. Although the full equations cannot be expressed in closed form, a mixture of a moment closure and comparison methods can be used to derive upper and lower bounds for the expected density of individuals. Analysis of the upper solution gives a bound on the rate of spread of the stochastic invasion process which lies strictly below the rate of spread for the deterministic model. The slow spread is most evident when invaders occur in widely spaced high density foci. In this case spatial correlations between individuals mean that density dependent effects are significant even when expected population densities are low. Finally, we propose a heuristic formula for estimating the true rate of spread for the full nonlinear stochastic process based on a scaling argument for moments. Received: 19 October 1998 / Revised version: 1 September 1999 / Published online: 4 October 2000     

Does increased stochasticity speed up extinction?

We consider the impact of increased stochastic fluctuations on the extinction date of an unstructured population subject to either environmental or demographical stochasticity (or both). By modelling the population density as a general linear diffusion, we state a set of typically satisfied conditions under which the decreasing minimal r-excessive mapping (and, therefore, the moment generating function) of the considered diffusion process is convex and, consequently, under which the impact of increased stochastic fluctuations on the expected date at which the density becomes arbitrarily small is unambiguously negative. In other words, we establish a set of sufficient conditions under which increased stochasticity speeds up the extinction process independently of whether stochasticity is environmental or demographic. In this way, we are able to confirm that increased stochasticity is detrimental for population growth. Received: 25 April 2000 / Revised version: 18 April 2001 / Published online: 12 October 2001     

Travelling front solutions of a nonlocal Fisher equation

We consider a scalar reaction-diffusion equation containing a nonlocal term (an integral convolution in space) of which Fisher‘s equation is a particular case. We consider travelling wavefront solutions connecting the two uniform states of the equation. We show that if the nonlocality is sufficiently weak in a certain sense then such travelling fronts exist. We also construct expressions for the front and its evolution from initial data, showing that the main difference between our front and that of Fisher‘s equation is that for sufficiently strong nonlocality our front is non-monotone and has a very prominent hump. Received: 8 August 1999 / Revised: 3 March 2000 / Published online: 14 September 2000     

An autoregressive method for the measurement of synchronization of interictal and ictal EEG signals

We propose a new measure of synchronization of multichannel ictal and interictal EEG signals. The measure is based on the residual covariance matrix of a multichannel autoregressive model. A major advantage of this measure is its ability to be interpreted both in the framework of stochastic and deterministic models. A preliminary analysis of EEG data from three patients using this measure documents the expected increased synchronization during ictal periods but also reveals that increased synchrony persists for prolonged periods (up to 2 h or more) in the postictal period. Received: 20 July 1997 / Accepted in revised form: 26 January 1999     

Consistency and fluctuation theorems for discrete time structured population models having demographic stochasticity

In this paper we prove a consistency theorem (law of large numbers) and a fluctuation theorem (central limit theorem) for structured population processes. The basic assumptions for these theorems are that the individuals have no statistically distinguishing features beyond their class and that the interaction between any two individuals is not too high. We apply these results to density dependent models of Leslie type and to a model for flour beetle dynamics. Received: 24 February 1999 / Revised version: 23 July 1999 / Published online: 14 September 2000     

Modeling and analysis of stochastic invasion processes

In this paper we derive spatially explicit equations to describe a stochastic invasion process. Parents are assumed to produce a random number of offspring which then disperse according to a spatial redistribution kernel. Equations for population moments, such as expected density and covariance averaged over an ensemble of identical stochastic processes, take the form of deterministic integro-difference equations. These equations describe the spatial spread of population moments as the invasion progresses. We use the second order moments to analyse two basic properties of the invasion. The first property is permanence of form in the correlation structure of the wave. Analysis of the asymptotic form of the invasion wave shows that either (i) the covariance in the leading edge of the wave of invasion asymptotically achieves a permanence of form with a characteristic structure described by an unchanging spatial correlation function, or (ii) the leading edge of the wave has no asymptotic permanence of form with the length scales of spatial correlations continually increasing over time. Which of these two outcomes pertains is governed by a single statistic, φ which depends upon the shape of the dispersal kernel and the net reproductive number. The second property of the invasion is its patchy structure. Patchiness, defined in terms of spatial correlations on separate short (within patch) and long (between patch) spatial scales, is linked to the dispersal kernel. Analysis shows how a leptokurtic dispersal kernel gives rise to patchiness in spread of a population. Received: 11 August 1997 / Revised version: 22 September 1998 / Published online: 4 October 2000     

Density-dependent vital rates and their population dynamic consequences

We explore a set of simple, nonlinear, two-stage models that allow us to compare the effects of density dependence on population dynamics among different kinds of life cycles. We characterize the behavior of these models in terms of their equilibria, bifurcations, and nonlinear dynamics, for a wide range of parameters. Our analyses lead to several generalizations about the effects of life history and density dependence on population dynamics. Among these are: (1) iteroparous life histories are more likely to be stable than semelparous life histories; (2) an increase in juvenile survivorship tends to be stabilizing; (3) density-dependent adult survival cannot control population growth when reproductive output is high; (4) density-dependent reproduction is more likely to cause chaotic dynamics than density dependence in other vital rates; and (5) changes in development rate have only small effects on bifurcation patterns. Received: 12 April 1999 / Published online: 3 August 2000     

Demographic and genetic invasion history of a 9-year-old roadside population of Bunias orientalis L. (Brassicaceae)

The population history of a 9-year-old roadside population of the invasive plant Bunias orientalis was reconstructed by demographic analysis including size, position, age (determined by herbchronology) and RAPD-PCR patterns of individual plants. We evaluated emerging patterns of population growth and genetic structure during a full period of population development under typical site conditions (anthropogenic disturbance) and their possible consequences for the invasion potential of the species. The population has grown rapidly and continuously (though with slowing geometric population increase) during the 9 years since its foundation, filling the space available in the study area. Genetic variation (RAPD markers) was already high in the founder cohorts and remained at the same level throughout population development (variance fluctuations <15%). Both results may be related to the mowing management at the site which seems to promote population growth of B. orientalis relative to other co-occuring species and to prevent the genetic drift and the development of spatial genetic structure that would be expected under isolation-by-distance models. Large founder plants had comparatively low genetic variance and were more closely related to younger cohorts than were small founder plants, indicating that selection acted during population development. Overall, the current anthropogenic disturbance regimes may contribute to high genetic variability by artificially increasing gene flow and thereby promoting the adaptability of invasive species to the often unpredictable conditions at disturbed sites. Our approach using retrospective demographic investigation allows the detection of spatio-temporal microscale patterns in genetic and phenotypic variation. Thus it allows a thorough understanding of local invasions of perennial herbaceous plants. Received: 23 November 1998 / Accepted: 14 April 1999     

Influence of the aeration rate on the yields of the biocontrol nematode Heterorhabditis megidis in monoxenic liquid cultures

The entomopathogenic nematode–bacterium complex Heterorhabditis megidis–Photorhabdus luminescens was cultured in 10-l internal loop bioreactors with marine impellers at aeration rates of 0.3 vvm and 0.7 vvm. Process parameters like impeller velocity and oxygen saturation were controlled at equal set points. The bacterial density was assessed at 24 h. Nematode dauer juveniles (DJ) were then inoculated and the development to adults after 8 days and final DJ yields after 16 days were recorded. The bacterial population density and the nematode inoculum development was variable and was not influenced by the aeration rate. A significant effect on the yield was recorded at the highest aeration rate. This result was confirmed by a direct comparison in two 5-l internal loop glass bioreactors at 0.3 vvm and 1.0 vvm, which were inoculated with nematode and bacterium pre-cultures from the same flask culture. Possible reasons for the positive correlation between aeration rate and DJ yield are discussed. Received: 27 September 1999 / Received revision: 21 January 2000 / Accepted: 23 January 2000     

Population and community responses of phytoplankton to fluctuating light

Light is a major resource in aquatic ecosystems and has a complex pattern of spatio-temporal variability, yet the effects of dynamic light regimes on communities of phytoplankton are largely unexplored. I examined whether and how fluctuating light supply affects the structure and dynamics of phytoplankton communities. The effect of light fluctuations was tested at two average irradiances: low, 25 μmol quanta m⁻² s⁻¹ and high, 100 μmol quanta m⁻² s⁻¹ in 2- and 18-species communities of freshwater phytoplankton. Species diversity, and abundances of individual species and higher taxa, depended significantly on both the absolute level and the degree of variability in light supply, while total density, total biomass, and species richness responded only to light level. In the two-species assemblage, fluctuations increased diversity at both low and high average irradiances and in the multispecies community fluctuations increased diversity at high irradiance but decreased diversity at low average irradiance. Species richness was higher under low average irradiance and was not affected by the presence or absence of fluctuations. Diatom abundance was increased by fluctuations, especially at low average irradiance, where they became the dominant group, while cyanobacteria and green algae dominated low constant light and all high light treatments. Within each taxonomic group, however, there was no uniform pattern in species responses to light fluctuations: both the magnitude and direction of response were species-specific. The temporal regime of light supply had a significant effect on the growth rates of individual species grown in monocultures. Species responses to the regime of light supply in monocultures qualitatively agreed with their abundances in the community experiments. The results indicate that the temporal regime of light supply may influence structure of phytoplankton communities by differentially affecting growth rates and mediating species competition. Received: 24 September 1997 / Accepted: 8 July 1998     

Persistence as an Optimal Hedging Strategy

Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where diversifying an investment portfolio protects against economic uncertainty. We provide a new, to our knowledge, theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest new opportunities for experimental investigation and design. Overall, we provide a new, to our knowledge, way of conceptualizing and modeling cellular decision making in volatile environments by explicitly unifying theory from mathematical biology and finance.     

Production of interferon-α in high cell density cultures of recombinant Escherichia coli and its single step purification from refolded inclusion body proteins

Escherichia coli TG1 transformed with a temperature-regulated interferon-α expression vector was grown to high cell density in defined medium containing glucose as the sole carbon and energy source, utilizing a simple fed-batch process. Feeding was carried out to achieve an exponential increase in biomass at growth rates which minimized acetate production. Thermal induction of such high cell density cultures resulted in the production of ∼4 g interferon-α/l culture broth. Interferon-α was produced exclusively in the form of insoluble inclusion bodies and was solubilized under denaturing conditions, refolded in the presence of arginine and purified to near homogeneity, utilizing single-step ion-exchange chromatography on Q-Sepharose. The yield of purified interferon-α was ∼300 mg/l with respect to the original high cell density culture broth (overall yield of ∼7.5% active interferon-α). The purified recombinant interferon-α was found by different criteria to be predominantly monomeric and possessed a specific bioactivity of ∼2.5 × 10⁸ IU/mg based on viral cytopathic assay. Received: 8 October 1999 / Received revision: 8 December 1999 / Accepted: 12 December 1999     

Stochastic epidemics in dynamic populations: quasi-stationarity and extinction

Empirical evidence shows that childhood diseases persist in large communities whereas in smaller communities the epidemic goes extinct (and is later reintroduced by immigration). The present paper treats a stochastic model describing the spread of an infectious disease giving life-long immunity, in a community where individuals die and new individuals are born. The time to extinction of the disease starting in quasi-stationarity (conditional on non-extinction) is exponentially distributed. As the population size grows the epidemic process converges to a diffusion process. Properties of the limiting diffusion are used to obtain an approximate expression for τ, the mean-parameter in the exponential distribution of the time to extinction for the finite population. The expression is used to study how τ depends on the community size but also on certain properties of the disease/community: the basic reproduction number and the means and variances of the latency period, infectious period and life-length. Effects of introducing a vaccination program are also discussed as is the notion of the critical community size, defined as the size which distinguishes between the two qualitatively different behaviours. Received: 14 February 2000 / Revised version: 5 June 2000 / Published online: 24 November 2000     

Analysis of recurrent cortico-basal ganglia-thalamic loops for working memory

 We analyse a simplified form of the frontal lobe architecture of cortico-basal ganglia-thalamo-cortical loops to determine the manner in which they can learn temporal sequences as part of working memory activity. In particular, we consider how the temporal duration of activity can arise in this setting. We start from a hard-wired version in which temporally extended activity is created by the `long' loop of cortex → basal ganglia → thalamus → cortex, and show it arises from a near saddle-node bifurcation. The manner in which the transition between patterns occurs is also considered. This is then extended to analyse the temporal sequence storage and regeneration abilities of trained networks with a similar architecture. The temporal dynamics of this activity is also analysed. Implications of this for other working memory activities and for understanding the architecture of the frontal lobes are discussed in conclusion. Received: 12 April 1999 / Accepted in revised form: 5 November 1999     

Analysis of clustered firing patterns in synaptically coupled networks of oscillators

Oscillators in networks may display a variety of activity patterns. This paper presents a geometric singular perturbation analysis of clustering, or alternate firing of synchronized subgroups, among synaptically coupled oscillators. We consider oscillators in two types of networks: mutually coupled, with all-to-all inhibitory connections, and globally inhibitory, with one excitatory and one inhibitory population of oscillators, each of arbitrary size. Our analysis yields existence and stability conditions for clustered states, along with formulas for the periods of such firing patterns. By using two different approaches, we derive complementary conditions, the first set stated in terms of time lengths determined by intrinsic and synaptic properties of the oscillators and their coupling and the second set stated in terms of model parameters and phase space structures directly linked to parameters. These results suggest how biological components may interact to produce the spindle sleep rhythm in thalamocortical networks. Received: 9 September 1999 / Revised version: 7 July 2000 / Published online: 24 November 2000     

Constructing the suitable initial configuration of the membrane-protein system in molecular dynamics simulations

A method for constructing the suitable initial configuration of the membrane-protein system for molecular dynamics (MD) simulations is presented. This method could provide some hydrated initial configurations and help us to determine the best surface area of the system by contracting the surface area and comparing the optimized lowest energy of the system by energy minimization. The gramicidin A (GA) channel in;the fully hydrated dimyristoylphosphatidylcholine (DMPC) bilayer was used as our model. Three configurations with different surface areas were selected and applied for one 400 ps and two 300 ps MD simulations at constant pressure and temperature. All simulations were fairly stable without any constraints. Through analysis of the MD trajectories we found that the system with the best surface area was more stable than the other two systems, whose sizes were changed in the simulations. Further analysis of the bilayer normal length and the order parameters of the lipid alkyl tails indicates that the system with the best surface area shows some characteristics of the L_α phase, while both the smaller and the larger size systems have distinct deviations from the L_α phase that we expect. This illustrates that the correct surface area and the suitable initial configuration have an important influence on the phase of the membrane in the MD simulation. In addition, by comparing the root mean square differences of GA relative to the initial structure and interaction energy between different components of the system for all three systems, we find that the state of the DMPC bilayer has exerted a significant influence on the structure of GA. All these results demonstrate the validity of our method for constructing the initial configuration of the membrane-protein system for MD simulations. Received: 10 September 1998 / Revised version: 19 March 1999 / Accepted: 19 March 1999     

Metabolic correlates of the circadian pattern of suckling-associated arousal in young rabbits

Young rabbits (Oryctolagus cuniculus) are only nursed for 3–5 min every 24 h. They show a circadian increase in activity in anticipation of this, which is entrained by suckling. Our aim was to determine whether serum and liver metabolites show diurnal fluctuations which could act to regulate this circadian pattern. Stomach weight, liver glycogen and serum metabolites were measured every 3 h in 7- to 8-day-old pups when normally nursed (up to 24 h after suckling) and fasted (up to 48 h after suckling). The results suggest: Accepted: 9 October 1999     

Solid-state fermentation for xylanase production by Thermoascus aurantiacus using response surface methodology

We investigated xylanase production by Thermoascus aurantiacus using semisolid fermentation. Multivariant statistical approaches were employed to evaluate the effects of several variables (initial moisture in the medium, cultivation time, inoculum level, and bagasse mass) on xylanase production. The initial moisture content and bagasse mass were the most important factors affecting xylanase activity. The xylanase activity produced by the fungus under the optimized conditions (81% moisture content and 17 g bagasse) was found to be 2700 U per gram of initial dry matter, whereas its value predicted by a polynomial model was 2400 U per gram of initial dry matter. Received: 4 December 1998 / Received revision: 15 March 1999 / Accepted: 16 May 1999     

Population structure of the sailfin sandfish, Arctoscopus japonicus (Trichodontidae), in the Sea of Japan

We analyzed patterns of genetic diversity in the sailfin sandfish (Arctoscopus japonicus), focusing on population subdivisions within the Sea of Japan. We observed 270 specimens from nine sampling sites in 1999–2000, i.e., seven sites in the Sea of Japan and two sites from the Pacific coast of Hokkaido. An additional site (30 specimens) was sampled from eastern Korea in the spawning season of 2004 for comparison. Forty haplotypes, compiled into three haplogroups (A–C), were detected based on the comparison of a 400-bp sequence of the anterior part of the mitochondrial control region. In accordance with previous hypotheses from morphological and molecular analyses, genetic discontinuity between the Sea of Japan and the Pacific coast of Hokkaido was conspicuous. Within the Sea of Japan, eight sampling sites were not genetically uniform, and most of the variations among sites were detected between eastern Korea [the “eastern Korea” (EK) population: distributed from the Korean Peninsula to Mishima, Yamaguchi Prefecture] and the other sites along the coast of Japan [the “western Japan” (WJ) population: from Oki Islands to western Hokkaido] (Φ _CT  = 0.096, P = 0.0183). The WJ population, having lower genetic variability, showed significant departure from neutrality, indicating influences through a recent population expansion. The period of the expansion can be estimated to have begun on the order of 10⁴ years ago. We consider that the present Japan Sea populations have been formed through the invasion of a small ancestral stock to the Sea of Japan and its population expansion during the last glacial period or later. On the other hand, we failed to detect distinct evidence of a population expansion in the EK population. Haplogroup C, detected in a high frequency in this population, was estimated to have mixed with haplogroup A after rapid differentiations of the latter. Therefore, the EK population, strongly influenced by such a mixture, might possess haplogroup C in a higher frequency and a different haplotype composition from the WJ population.