Chaos and population disappearances in simple ecological models

A class of truncated unimodal discrete-time single species models for which low or high densities result in extinction in the following generation are considered. A classification of the dynamics of these maps into five types is proven: (i) extinction in finite time for all initial densities, (ii) semistability in which all orbits tend toward the origin or a semi-stable fixed point, (iii) bistability for which the origin and an interval bounded away from the origin are attracting, (iv) chaotic semistability in which there is an interval of chaotic dynamics whose compliment lies in the origin’s basin of attraction and (v) essential extinction in which almost every (but not every) initial population density leads to extinction in finite time. Applying these results to the Logistic, Ricker and generalized Beverton-Holt maps with constant harvesting rates, two birfurcations are shown to lead to sudden population disappearances: a saddle node bifurcation corresponding to a transition from bistability to extinction and a chaotic blue sky catastrophe corresponding to a transition from bistability to essential extinction. Received: 14 February 2000 / Revised version: 15 August 2000 / Published online: 16 February 2001     

Classification of coupling patterns among spontaneous rhythms and ventilation in the sympathetic discharge of decerebrate cats

 The spontaneous low- and high-frequency rhythms in the sympathetic discharge of decerebrate artificially ventilated cats are affected by external ventilation. Two graphical methods (i.e. the space-time separation plot and the frequency tracking locus) are used to classify the non-linear interactions. The observed behaviours in the sympathetic discharge consist of phase-locked periodic dynamics (at various frequency ratios with ventilation), quasiperiodic and aperiodic patterns. They depend on the experimental condition. In control condition the sympathetic discharge appears more frequently locked to each ventilatory cycle (1 : 1 dynamics). However, some cases of quasiperiodic dynamics are found. A sympathetic activation stimulus, such as inferior vena cava occlusion, is able to synchronise slow rhythms in the sympathetic discharge to a subharmonic of ventilation. During a sympathetic inhibition stimulus, such as aortic constriction, 1 : 1 dynamics is detected but the amplitude of the sympathetic responses can be modulated by unlocked slow rhythms. Moreover, some cases of aperiodic dynamics are observed. Vagotomy reduces the 1 : 1 coupling between sympathetic outflow and ventilation. Vagotomy plus spinalisation disrupts periodic dynamics in the sympathetic discharge so that irregular and complex patterns are found. Received: 19 July 1995/Accepted in revised form: 20 May 1996     

Evidence for chaotic behavior in driven ventricles.

Toad ventricles were externally driven by periodic pulses while monophasic action potential (MAP) signals were recorded in seven excised and seven in situ ventricles. As the frequency was slowly increased in steps, the stimulated tissue displayed several dynamic characteristics. Hierarchies of periodic behavior, like phase-locking and period-doubling sequences leading to chaos, were observed. Results showed that subharmonic bifurcations (order one and two) and chaotic-like behavior may systematically occur in the MAP signal within a definite frequency interval in the 1:1 phase locking regime. The chaotic, or more cautiously expressed, chaotic-like behavior is characterized by the power spectrum, the autocorrelation function, the Poincaré map, and the reconstructed 2-D phase portrait. It is concluded that (a) bifurcations of order one and two and the characteristic irregular behavior are evidences of local universal chaotic dynamics in cardiac tissue; (b) there are no qualitative differences in the dynamics of the in situ and excised ventricles; and (c) fibrillation seems to be related to chaotic behavior, but whether they are similar or equivalent phenomena still remains to be seen.     

Dynamics of a physiologically structured population in a time-varying environment

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.     

The formation of 1-hydroxymethylnaphthalene and 6-hydroxymethylquinoline by both oxidative and reductive routes in Cunninghamella elegans

Extraction of medium after incubation of the fungus, Cunninghamella elegans, with 0.03% (w/v) 1-methylnaphthalene produced mainly 1-hydroxymethylnaphthalene together with some 1-naphthoic acid and hydroxynaphthoic acid. Higher concentrations of substrate were inhibitory to biotransformation. Similar incubations with 1-naphtoic acid as substrate resulted in reduction of the carboxyl group to give 1-hydroxymethylnaphthalene. When 6-methylquinoline was used, the main product was 6-hydroxymethylquinoline but also some quinoline-6-carboxylic acid and some 6-methylquinoline-N-oxide were identified. In a 2-l fermenter 2.5 g substrate was transformed in 324 h. The 6-hydroxymethylquinoline was also produced by reduction of quinoline-6-carboxylic acid by the organism. Received: 9 March 1998 / Received revision: 15 June 1998 / Accepted: 19 June 1998     

Intermediary sulfur compounds in pyrite oxidation: implications for bioleaching and biodepyritization of coal

Accumulation of elemental sulfur during pyrite oxidation lowers the efficiency of coal desulfurization and bioleaching. In the case of pyrite bioleaching by Leptospirillum ferrooxidans, an iron(II)-ion-oxidizing organism without sulfur-oxidizing capacity, from the pyritic sulfur moiety about 10% elemental sulfur, 2% pentathionate, and 1% tetrathionate accumulated by a recently described cyclic pyrite oxidation mechanism. In the case of pure cultures of Thiobacillus ferrooxidans and mixed cultures of L. ferrooxidans and T. thiooxidans, pyrite was nearly completely oxidized to sulfate because of the capacity of these cultures to oxidize both iron(II) ions and sulfur compounds. Pyrite oxidation in acidic solutions, mediated chemically by iron(III) ion, resulted in an accumulation of similar amounts of sulfur compounds as obtained with L. ferrooxidans. Changes of pH to values below 2 or in the iron ion concentration are not decisive for diverting the flux of sulfur compounds. The literature on pyrite bioleaching is in agreement with the findings indicating that the chemistry of direct and indirect pyrite leaching is identical. Received: 20 April 1998 / Received revision: 27 August 1998 / Accepted: 3 September 1998     

Seasonal variation of phytoplankton community structure and nitrogen uptake regime in the Indian Sector of the Southern Ocean

This study investigates the dynamics of phytoplankton communities and nitrogen uptake in the Indian sector of the Southern Ocean during spring and summer. The study area is oligotrophic (Chl a stocks <50 mg m⁻²); nevertheless, a large spatial variation of phytoplankton biomass and community structure was observed. During both seasons the phytoplankton community in the seasonal ice zone showed higher biomasses and was mainly composed of large diatom cells. However, in the permanently open ocean zone the community had low biomass and was chiefly composed of nano- and picoflagellates. In the polar front zone, although biomass was higher, the community structure was similar to the open ocean zone. The results suggest that the variation in phytoplankton community structure on a larger scale resonates with gradients in water column stability and nutrient distribution. However, significant changes in biomass and nutrient stocks but little change in community structure were observed. Absolute nitrogen uptake rates were generally low, but their seasonal variations were highly significant. During spring the communities displayed high specific nitrate uptake (mean rate = 0.0048 h⁻¹), and diatoms (in the seasonal ice zone) as well as nano- and picoflagellates (in the permanently open ocean zone and polar front zone) were mainly based on new production (mean ƒ-ratio = 0.69). The transition to summer was accompanied by a significant reduction in nitrate uptake rate (0.0048 h⁻¹ → 0.0011 h⁻¹) and a shift from predominantly new to regenerated production (ƒ-ratio 0.69 → 0.39). Ammonium played a major role in the seasonal dynamics of phytoplankton nutrition. The results emphasize that, despite a large contrast in community structure, the seasonal dynamics of the nitrogen uptake regime and phytoplankton community structure in all three subsystems were similar. Additionally, this study supports our previous conclusion that the seasonal shift in nitrogen uptake regime can occur with, as well as without, marked changes in community structure. Received: 2 December 1997 / Accepted: 20 April 1998     

An intracellular Ca2+ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory

We have developed a firing rate network model for working memory that combines Mexican-hat-like synaptic coupling with intrinsic or cellular dynamics that are conditionally bistable. While our approach is in the spirit of Camperi and Wang (1998) we include a specific and plausible mechanism for the cellular bistability. Modulatory neurotransmitters are known to activate second messenger signaling systems, and our model includes an intracellular Ca²⁺ handling subsystem whose dynamics depend upon the level of the second messenger inositol 1,4,5 trisphosphate (IP3). This Ca²⁺ subsystem endows individual units with conditional intrinsic bistability for a range of IP3. The full “hybrid” network sustains IP3-dependent persistent (“bump”) activity in response to a brief transient stimulus. The bump response in our hybrid model, like that of Camperi-Wang, is resistant to noise – its position does not drift with time. Action Editor: Upinder Bhalla     

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     

Biotransformation of citronellol by the basidiomycete Cystoderma carcharias in an aerated-membrane bioreactor

The basidiomycete Cystoderma carcharias transformed citronellol into 3,7-dimethyl-1,6,7-octanetriol as the main product. 3,7-Dimethyl-6,7-epoxy-1-octanol was identified as important intermediary product of the biotransformation, and the allylic diols 2,6-dimethyl-2-octene-1,8-diol, 3,7-dimethyl-5-octene-1,7-diol and 3,7-dimethyl-7-octene-1,6-diol were found to be minor products. Microbial formation of rose oxide, a flavour-impact component, was observed for the first time. The formation of the main products was inhibited by 70% after addition of 0.1 mmol l⁻¹ cytochrome monooxygenase inhibitors. Formation of 3,7-dimethyl-1,6,7-octanetriol was effective in a bioreactor with aeration over a coil of a hydrophobic microporous polypropene capillary membrane. Production rates of up to 150 mg l⁻¹ day⁻¹ were reached and led to a product concentration of 866 mg l⁻¹ (conversion rate: 52%). The total loss of the added volatile substrate via the exhaust air was 4.5% when this aeration method was used. Received: 30 July 1998 / Received revision: 2 November 1998 / Accepted: 7 November 1998     

A genetic linkage map of Quercus robur L. (pedunculate oak) based on RAPD, SCAR, microsatellite, minisatellite, isozyme and 5S rDNA markers

 A genetic map of Pedunculate oak (Quercus robur) was constructed based on one 5S rDNA, 271 RAPD, ten SCAR, 18 microsatellite, one minisatellite, and six isozyme markers. A total of 94 individuals from a full-sib family was genotyped. Two maps, including 307 markers, were constructed according to the “two-way pseudo-testcross” mapping strategy. Testcross markers segregating in the 1 : 1 ratio were first used to establish separate maternal (893.2 cM, 12 linkage groups) and paternal (921.7 cM, 12 linkage groups) maps. Both maps provided 85–90% genome coverage. Homologies between the male and female linkage groups were then identified based on 74 intercross markers segregating in the 3 : 1, 1 : 2 : 1 and 1 : 1 : 1 : 1 ratios (RAPDs, SCARs, SSRs, 5S rDNA and isozymes) in the hybrid progeny. In each map, approximately 18% of the studied markers showed segregation distortion. More than 60% of the skewed markers were due to an excess of heterozygote genotypes. This map will be used for: (1) studying the molecular organisation of genomic regions involved in inter- and intraspecific differentiation in oaks and (2) identification of QTLs for adaptive traits. Received: 30 January 1998 / Accepted: 12 May 1998     

Rich dynamics of a ratio-dependent one-prey two-predators model

The objective of this paper is to systematically study the qualitative properties of a ratio-dependent one-prey two-predator model. We show that the dynamics outcome of the interactions are very sensitive to parameter values and initial data. Specifically, we show the interactions can lead to all the following possible outcomes: 1) competitive exclusion; 2) total extinction, i.e., collapse of the whole system; 3) coexistence in the form of positive steady state; 4) coexistence in the form of oscillatory solutions; and 5) introducing a friendly and better competitor can save a otherwise doomed prey species. These results reveal far richer dynamics compared to similar prey dependent models. Biological implications of these results are discussed. Received: 14 November 2000 / Revised version: 18 February 2001 / Published online: 19 September 2001     

Complete transformation of 1,1,1-trichloroethane to chloroethane by a methanogenic mixed population

A methanogenic mixed population in a packed-bed reactor completely transformed 1,1,1-trichloroethane (10 μM) to chloroethane by a cometabolic process. Chloroethane was not further transformed. Acetate and methanol served as electron donors. Complete transformation of 1,1,1-trichloroethane to chloroethane only occurred when sufficient electron donor was fed into the reactor. Otherwise, besides chloroethane, 1,1-dichloroethane was also found as a product. The products of 1,1,1-trichloroethane transformation also depended on the type of electron donor present. With acetate, the degree of dechlorination was higher, i.e. more 1,1,1-trichloroethane was transformed to chloroethane than with methanol. In an enrichment culture obtained from the reactor contents, 1,1,1-trichloroethane was only transformed to 1,1-dichloroethane and was not further metabolized. Methanol, acetate, formate, ethanol, 2-propanol, trimethylamine and H₂, but not dimethylamine and methylamine, served as electron donors for 1,1,1-trichloroethane transformation by this enrichment culture. Both nitrate and nitrite inhibited 1,1,1-trichloroethane transformation; while nitrate completely inhibited 1,1,1-trichloroethane dechlorination, some conversion did occur in the presence of nitrite. The product(s) of this conversion remain unknown, since no chlorinated hydrocarbons were detected. Received: 19 June 1998 / Received revision: 14 September 1998 / Accepted: 17 September 1998     

Phytoplankton biomass in the sub-Antarctic area of the Straits of Magellan (53°S), Chile during spring-summer 1997/1998

In order to provide a better understanding of the dynamics of phytoplankton in the coastal regions of high latitudes, a study was carried out to estimate the dynamics of carbon biomass of autotrophic and heterotrophic algal groups over the austral spring-summer 1997/1998 period. At a fixed station located in the central basin (Paso Ancho) of the Straits of Magellan (53°S), surface water samples were collected at least once a week from September 1997 (early spring) to March 1998 (late summer). Quantitative analysis of biomass of phytoplankton was estimated from geometric volumes, using non-linear equations, and converted to biomass. The pattern of chlorophyll a showed a strong temporal variability, with maximum values (mean 2.8 mg m⁻³) at the austral spring phytoplankton increase or bloom (October/November) and minimum values during early spring (September: <0.5 mg m⁻³) and summer (January/March: 0.5–1.0 mg m⁻³). During the spring bloom, diatoms made up to 90% of the total phytoplankton carbon (0.01–189 μg l⁻¹), followed by a maximum of thecate dinoflagellates (0.08–34 μg l⁻¹), and sporadic high biomass of phytoflagellates during summer. Heterotrophic algal groups such as Gymnodinium and Gyrodinium spp. dominated (70%, in the 5- to 25-μm size range) shortly before the main diatom bloom, and small peaks were observed within spring and early summer periods (0–0.4 μg l⁻¹). Phytoflagellates dominated earlier (spring) with higher carbon biomass (8 μg l⁻¹) and post-bloom periods (summer) when carbon biomass ranged between 1 and 4 μg l⁻¹. Accepted: 6 September 2000     

Electroporation of, plasmid isolation from and plasmid conservation in Clostridium acetobutylicum DSM 792

Procedures have been developed allowing recombinant DNA work with Clostridium acetobutylicum DSM 792. Electroporation was used to introduce plasmid DNA into exponentially growing clostridial cells and 6 × 10² transformants/μg DNA could be obtained at a time constant of 5.5 ms, 1.8 kV, 50 μF, and 600 Ω. The method also allowed the taxonomic group IV strain NI-4082 to be transformed (10¹ transformants/μg DNA). Plasmid preparation from recombinant clostridia was optimal when a modification of the alkaline lysis method was employed. It was also important to use cells from the mid-logarithmic growth phase. Recombinant strains could be easily preserved as spore suspensions; under all conditions tested plasmids were maintained. Received: 17 March 1998 / Received revision: 17 August 1998 / Accepted: 26 August 1998     

Density-dependent birth rate, birth pulses and their population dynamic consequences

 In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose a single-species model with stage structure for the dynamics in a wild animal population for which births occur in a single pulse once per time period. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker functions or Beverton-Holt functions, and obtain the threshold conditions for their stability. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos. Received: 13 June 2001 / Revised version: 7 September 2001 / Published online: 8 February 2002     

Mannitol-enhanced survival of Lactococcus lactis subjected to drying

Survival of Lactococcus lactis subjected to different drying conditions was investigated. Mannitol most remarkably enhanced the survival of dried cells to a level almost equalling that of viable cells [log₁₀ (cfu ml⁻¹) = 9.42] as was found prior to the drying process (log₁₀ = 9.6). In the absence of mannitol, a survival was reduced by a factor of 10⁴. Drying of cells at 20 °C led to higher survival rates than drying at 30 °C. Mannitol enhanced the survival rate at both temperatures, and at both 20 °C and 30 °C the highest reduction in survival occurred when cells were dried at a water activity of 0.76. In the presence of mannitol, differences in survival after drying at different water activities were less pronounced. Rehydration of cells dried in the presence of mannitol resulted in an extended lag phase of 4 h compared to fresh cells. No growth or acidification of the culture medium was observed for 12 h in the case of rehydrated cells dried in the absence of mannitol. It was hypothesized that a radical scavenging activity of mannitol could partly explain these observations. Received: 28 August 1998 / Accepted: 2 October 1998     

An RFLP linkage map of Upland cotton, Gossypium hirsutum L.

 Ninety-six F₂.F₃ bulked sampled plots of Upland cotton, Gossypium hirsutum L., from the cross of HS46×MARCABUCAG8US-1-88, were analyzed with 129 probe/enzyme combinations resulting in 138 RFLP loci. Of the 84 loci that segregated as co-dominant, 76 of these fit a normal 1 :  2 : 1 ratio (non-significant chi square at P=0.05). Of the 54 loci that segregated as dominant genotypes, 50 of these fit a normal 3: 1 ratio (non-significant chi square at P=0.05). These 138 loci were analyzed with the MAPMAKER∖ EXP program to determine linkage relationships among them. There were 120 loci arranged into 31 linkage groups. These covered 865 cM, or an estimated 18.6% of the cotton genome. The linkage groups ranged from two to ten loci each and ranged in size from 0.5 to 107 cM. Eighteen loci were not linked. Received: 31 March 1998 / Accepted: 29 April 1998     

Rhamnose lipids – biosynthesis, microbial production and application potential

Biosurfactants containing rhamnose and β-hydroxydecanoic acid and called rhamnolipids are reviewed with respect to microbial producers, their physiological role, biosynthesis and genetics, and especially their microbial overproduction, physicochemical properties and potential applications. With Pseudomonas species, more than 100 g l⁻¹ rhamnolipids were produced from 160 g l⁻¹ soybean oil at a volumetric productivity of 0.4 g l⁻¹h⁻¹. The individual rhamnolipids are able to lower the surface tension of water from 72 mN m⁻¹ to 25–30 mN m⁻¹ at concentrations of 10–200 mg l⁻¹. After initial testing, rhamnolipids seem to have potential applications in combating marine oil pollution, removing oil from sand and in combating zoosporic phytopathogens. Rhamnolipids are also a source of l-rhamnose, which is already used for the industrial production of high-quality flavor components. Received: 1 July 1998 / Received revision: 11 September 1998 / Accepted: 13 September 1998     

Developments in destructive and non-destructive pathways for selective desulfurizations in oil-biorefining processes

Biocatalytic desulfurization is still not a commercial technology, but conceptual engineering and sensitivity analyses have shown that the approach is very promising. The purpose of this paper is to investigate further some aspects of the biodesulphurization pathways, discussing the non-destructive pathway with the well-known Rhodococcus rhodochrous IGTS8. Findings revealed byproducts, such as 2′-hydroxybiphenyl (HBP), sulfite and sulfate, obtained by the desulfurization of dibenzothiophene (DBT), to exert an inhibiting effect. The results suggest that IGTS8 may follow two different metabolic pathways in stationary-growth-phase cells or under growing conditions. The first pathway is characterized by oxidative steps, which convert DBT to DBT sulfoxide and to DBT sulfone. The sulfone is transformed to 2-(2′-hydroxyphenyl)benzene sulfinate and then to HBP and sulfite by a sulfinic acid hydrolase. In the second pathway the sulfone is further oxidized to 2-(2′-hydroxyphenyl)benzene sulfonate and then to HBP and sulfate by a sulfonic acid hydrolase. Experiments using benzene sulfonic acid suggest that the sulfonic acid hydrolase is an induced enzyme. Received: 8 June 1998 / Received revision: 1 October 1998 / Accepted: 2 October 1998