On the choice of the optimal periodic operation for a continuous fermentation process

In this contribution we investigate the impact of the forcing waveform on the productivity of a continuous bioreactor governed by an unstructured, nonlinear kinetic model. The (periodic) forcing is applied on the substrate concentration in the feed. To this end, some alternative waveforms commonly encountered in practice are evaluated and their performance is compared. An analytical/numerical approach is used. The preliminary analytical step is based on the π‐criterion that gives useful information for small amplitudes. The extension to larger amplitudes, when significant improvements are expected, is then performed through a continuation‐optimization procedure. It is found that the choice of the specific waveform has an impact on the performance of the process and there is no unique best forcing for any process condition, but its choice depends on the operating parameters and the forcing amplitude and frequency values. Further, the influence of the waveform functions on the wash‐out conditions are extensively examined. The analysis shows that all the waveforms examined in this work may lead to significant enlargement of the nontrivial regime with respect to a steady state operation. In particular, square‐wave forcing leads in practice to the extinction of the wash‐out conditions for any feed substrate concentration and for a well defined choice of the forcing parameters. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Plant litter feedback and population dynamics in an annual plant,<Emphasis Type="Italic"> Cardamine pensylvanica</Emphasis>

The presence of litter has the potential to alter the population dynamics of plants. In this paper, we explore the effects of litter on population dynamics using a simple experimental laboratory system with populations of the annual crucifer, Cardamine pensylvanica. Using a factorial experiment with four densities and three litter levels, we determined the effect of litter on biomass and plant fecundity, and the life stages responsible for these changes in yield. Although litter had significant effects on seed germination and on seedling survivorship, we show, using a population dynamics model, that these effects were not demographically significant. Rather, the potential effect of litter on population dynamics resulted almost entirely from its effect on biomass. Persistent litter suppressed plant biomass and apparently removed the direct density effect present in the absence of litter. Thus, litter changed the shape of the recruitment curve from slightly humped to asymptotic. In addition to changing the shape of the recruitment curve, litter reduced the carrying capacity of the populations. Thus, the population dynamics model indicated that not all statistically significant responses were dynamically significant. Given the potential complexity of litter effects, simple population models provide a powerful tool for understanding the potential consequences of short-term responses. Received: 8 September 1999 / Accepted: 5 April 2000     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

Abalone I: Analyzing Mark-Recapture-Recovery Data Incorporating Growth and Delayed Recovery

Abalone are semimobile marine gastropods that form the basis of Australia's second most valuable fishery. A site off the coast of Port Arthur, Tasmania, was visited on six occasions. On each occasion, any unmarked live abalone found were marked with a unique identification number and were recorded. Any previously marked abalone found had its identification number and whether or not it was still alive recorded. This results in integrated mark-recapture-recovery data, as in Catchpole et al. (1998, Biometrics 54, 33-46). During the study period, abalone grew in size, and we model the survival of individuals as a function of their size, estimated from a fitted growth curve. The shells of dead animals are long lasting, and we extend existing methodology to allow for the possibility that an animal found dead may have been dead but overlooked for several visits.     

Delayed inducible resistance against a leaf-chewing insect in four deciduous tree species

Summary Both mechanical damage to mountain birch foliage and rearing of moth larvae on the trees reduced the growth of Epirrita autumnata larvae reared on these trees in the following year. The effects of physical damage and some other cues from insects were additive. On bird cherry the performance of Epirrita larvae was equal on untreated trees and on trees artificially defoliated in the previous year, but larval growth was reduced on previously insect-damaged branches. With mountain ash just physical damage per se reduced the performance of Epirrita larvae. On Salix phylicifolia there were no significant differences in the growth or survival of Epirrita on untreated control bushes and on bushes with partial larval damage during the previous year. Among untreated control trees the growth and survivorship of Epirrita were higher on fast-growing willow and bird cherry than on the slow-growing mountain birch. Mountain birch and mountain ash, the two deciduous tree species adapted to nutrient-poor soils, showed delayed inducible resistance triggered by defoliation (artificial or insect-made). This supports the hypothesis that delayed inducible resistance may be a passive response due to nutrient-stress caused by defoliation. On the other hand, the additional increase in the resistance of mountain birch triggered by specific cues from insects suggests that this response may be an evolved defense against leaf-eating insects.     

Cycles in cannibalistic egg-larval interactions

A model of a cannibalistic larval-egg interaction such as occurs in Tribolium is developed which leads to a system of nonlinear Volterra integral equations. I determine the local stability properties of the unique equilibrium point of the model. A Hopf bifurcation analysis shows that the model always undergoes a subcritical bifurcation when stability is lost. Numerical solutions confirm the presence of multiple attractors over a range of parameter values. The form of the cycles observed in the numerical solutions is analogous to that observed in laboratory populations of Tribolium.     

Oscillations in a system with material cycling

We study a system of two integrodifierential equations which models the evolution of a biotic species feeding on an abiotic resource. We also consider nutrient recycling with time delay. By Hopf bifurcation theory we prove the existence of stable oscillations for a range of values of the input of nutrients.Work performed within the activity of the research group Evolution Equations and Physico-Mathematical Applications, M.P.I. (Italy), and under the auspices of G.N.F.M., C.N.R. (Italy)     

Cannibalism as a life boat mechanism

Under certain conditions a cannibalistic population can survive when food for the adults is too scarce to support a non-cannibalistic population. Cannibalism can have this lifeboat effect if (i) the juveniles feed on a resource inaccessible to the adults; and (ii) the adults are cannibalistic and thus incorporate indirectly the inaccessible resource. Using a simple model we conclude that the mechanism works when, at low population densities, the average yield, in terms of new offspring, due to the energy provided by one cannibalized juvenile is larger than one.     

Neuropathy Target Esterase: Rates of Turnover In Vivo Following Covalent Inhibition with Phenyl Di-n-Pentylphosphinate

Phenyl di-n-pentylphosphinate is a reasonably stable easily synthesized inhibitor of neuropathy target esterase (NTE) with low anticholinesterase activity. Like phenylmethylsulphonyl fluoride it protects hens against neuropathic effects of compounds such as diisopropylphosphorofluoridate. At intervals up to 15 days after dosing hens (10 mg/kg s.c. to inhibit 90% NTE) assays were made of catalytically active and of phosphinylated NTE in autopsy tissue. The sum of these components was always within the range of catalytic activity in undosed controls. However, the half-life of reappearance of active NTE was 2.07 days +/- 0.13 (SD, n = 6) for brain and 3.62 days +/- 0.23 (SD, n = 6) for spinal cord--shorter than after dosing with phenylmethylsulphonyl fluoride. It is proposed that: (1) The physiological turnover mechanism cannot distinguish between catalytically active and di-n-pentylphosphinylated NTE although initiation of organophosphate-induced delayed polyneuropathy might involve recognition of aged di-alkyl-phosphorylated NTE as "foreign". (2) The short half-lives indicate a slow spontaneous dephosphinylation of inhibited NTE occurs in vivo as well as de novo synthesis. The difference in half-lives for brain and spinal cord NTE may be due to different rates of synthesis de novo or (more likely) to different rates of spontaneous reactivation of the inhibited NTE in the two tissues.     

Some epidemiological models with nonlinear incidence

Epidemiological models with nonlinear incidence rates can have very different dynamic behaviors than those with the usual bilinear incidence rate. The first model considered here includes vital dynamics and a disease process where susceptibles become exposed, then infectious, then removed with temporary immunity and then susceptible again. When the equilibria and stability are investigated, it is found that multiple equilibria exist for some parameter values and periodic solutions can arise by Hopf bifurcation from the larger endemic equilibrium. Many results analogous to those in the first model are obtained for the second model which has a delay in the removed class but no exposed class.Research supported in part by Centers for Disease Control Contract 200-87-0515. Support services provided at University House Research Center at the University of IowaResearch supported in part by NSERC A-8965 and the University of Victoria President's Committee on Faculty Research and Travel