The global asymptotic stability of prey-predator systems with second-order dissipation

Models of biological development, evolution and control should take into account that very small numbers of cells or chemicals or individuals eventually grow into stable, large populations. The simplified two-component model used in these studies includes the following: (1) first-order decay; (2) first-order autocatalysis; (3) negative feedback; (4) positive feedback; (5) second-order decay; (6) second-order autocatalysis. A positive definite Lyapunov function is constructed and shown to have a negative definite total derivative. The stationary statex>0,y>0, therefore possesses global asymptotic stability. This means that sustained oscillations cannot occur. Another stationary state,x=y=0, is shown to be unstable. This means that infinitesimally small perturbations ofx=y=0 will result in evolution of the variables to the stable stationary state. This result contrasts with that obtained with the Lotka-Volterra model in that small perturbations ofx=y=0 for that model result in sustained, oscillating excursions; the smaller the initial perturbations, the larger these excursions will be. A simulation illustrates that stable populations of 10²⁰ x's andy's can arise from a singlex andy.x grows more or less continuously, buty remains extremely small for 80 per cent of the time interval required for the variables to approach their stable populations. 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.     

21st century zoo design

A review of Conservation Centres for the New Millennium. Proceedings of the 5^th International Symposium on Zoo Design, edited by Amy B. Plowman and Peter M.C. Stevens. Paignton, Devon, U.K.: Whitely Wildlife Conservation Trust, 1999, 181 pp., paperback.     

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.     

Book reviews

Book reviewed in this article: Marjory A. Hoy (Ed.): Recent Advances in Knowledge of the Phytoseiidae J. H. Visser and A. K. Minks (Eds.). Proceedings of the 5th International Symposium on Insect-Plant Relationships R. C. Rainey (Ed.): Biona Reports 1 & 2: Insect Flight.     

Book reviews

Book reviewed in this article: Fruit Flies of Economic Significance: Their Identification and Bionomics. By Ian M. White and Marlene M. Elson-Harris. Arthropods of Medical and Veterinary Importance . A checklist of preferred names and allied terms. Compiled by A.R. Pittaway. Behaviour and Impact of Aphidophaga [Proceedings of the 4th meeting of the IOBC working group ‘Ecology of Aphidophaga’], Edited by Polgar, L., R. J. Chambers, A. F. G. Dixon and I. Hodek. Proceedings of the 7^th International Symposium on Insect-Plant Relationships     

Chlamydomonas reinhardtii: duration of its cell cycle and phases at growth rates affected by temperature

Synchronized cultures of the green alga Chlamydomonas reinhardtii were grown photoautotrophically under a wide range of environmental conditions including temperature (15–37°C), different mean light intensities (132, 150, 264 μmol m⁻² s⁻¹), different illumination regimes (continuous illumination or alternation of light/dark periods of different durations), and culture methods (batch or continuous culture regimes). These variable experimental approaches were chosen in order to assess the role of temperature in the timing of cell division, the length of the cell cycle and its pre- and post-commitment phases. Analysis of the effect of temperature, from 15 to 37°C, on synchronized cultures showed that the length of the cell cycle varied markedly from times as short as 14 h to as long as 36 h. We have shown that the length of the cell cycle was proportional to growth rate under any given combination of growth conditions. These findings were supported by the determination of the temperature coefficient (Q ₁₀), whose values were above the level expected for temperature-compensated processes. The data presented here show that cell cycle duration in C. reinhardtii is a function of growth rate and is not controlled by a temperature independent endogenous timer or oscillator, including a circadian one.     

Starving with a full gut? Effect of suspended particles on the fitness of <Emphasis Type="Italic">Daphnia hyalina</Emphasis>

Suspended particles are abiotic factors that can affect the abundance of cladocerans such as daphnids. Ultra-oligotrophic Lake Brienz, situated in the front ranges of the Swiss Alps, is dominated by two major inflows that annually transport over 300,000 tons of suspended glacial material into the lake. A laboratory flow-through experiment was performed to test whether these suspended particles have an influence on the fitness of Daphnia hyalina from Lake Brienz, measured as body size, fecundity and juvenile growth rate, especially when they are simultaneously exposed to low food concentrations. Our results show that the concentration of suspended particles present in Lake Brienz does not reduce the fitness of daphnids, even at very low food concentration. In fact, a low concentration of suspended particles increased the fitness. Reduction of fitness could only be observed at a suspended particle concentration of over 25 mg l⁻¹, a level that has never been recorded in Lake Brienz. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera     

Light- and Clock-Controlled Leaflet Movements in Samanea saman*: A Physiological,Biophysical and Biochemical Analysis**

Leaflet movements in the legume Samanea saman are under joint control by light and a circadian oscillator. The movements are driven by massive fluxes of K⁺, Cl^?, and H⁺ through pulvinar motor cell membranes. Light and the oscillator affect leaflet movements by altering the activity of ion transport systems. Some effects of light on ion transport may be mediated by the phosphatidylinositol (PI) cycle, since brief irradiation of the pulvinus with white light accelerates PI turnover.     

Barnacle growth rate on artificial substrate in the Salton Sea,California

The Salton Sea is one of the few saline, inland lakes in the world with a population of barnacles, Balanus amphitrite. It is also one of California’s most impaired water bodies due to excessive nutrient loading which leads to phytoplankton blooms and low dissolved oxygen. Currently, B. amphitrite growth is limited due to lack of hard substrate in and around the Sea. We have hypothesized that artificial substrate could support the growth of B. amphitrite and their filter-feeding would lead to improved water quality. Periodic harvesting of the barnacles would result in the permanent removal of nitrogen and phosphorus from the Sea. A 44-day in-situ experiment was carried out in the Salton Sea to assess the rate of barnacle growth and phosphorus and nitrogen sequestration on burlap sheets suspended vertically from a floating line. Burlap panels were collected weekly and the barnacles analyzed for Ca, total-P, inorganic-P, total-N, total-C, CaCO₃, and organic matter content. After 44 days of growth, the barnacle mats weighed 7.4 kg m⁻² on a dry weight basis, with 80% of the mass as shell material. The nutrient sequestration was 9.4 g P m⁻² and 100 g N m⁻². Approximately half of the P was inorganic and appears to be coprecipitated with the calcium carbonate shell material. Results indicate that harvesting barnacles grown on artificial substrate in the Salton Sea would not be an effective method for removing N or P from the lake because of the relative proportions of shell material and organic material. Guest editor: S. H. Hurlbert The Salton Sea Centennial Symposium. Proceedings of a Symposium Celebrating a Century of Symbiosis Among Agriculture, Wildlife and People, 1905–2005, held in San Diego, California, USA, March 2005     

Models of ontogenetic allometry in cladoceran morphology studies

Ontogenetic variation of morphological traits in cladocerans is usually analysed by a simple allometry function. We found that common cyclomorphic and inducible traits in Bosmina and Daphnia sometimes deviate from simple allometry, however. Consequently, simple allometric analysis may at times be inadequate since important aspects of the ontogenetic development may not be revealed. We suggest that other allometric models should be used more extensively in ontogenetic studies of cladocerans morphology. Especially, complex allometric functions may help analyse the effects of size-selective predation on morphological defence traits when predators prefer prey of intermediate size. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera     

The species-area relationship of European Lumbricidae (Annelida,Oligochaeta)

Summary Studies throughout Europe reporting species lists of lumbricid earthworms and ranging from 100 m² to >500000 km² are analysed for the regression of species number S on size of area A [km²]. This species-area relation is described by: S=7.9*A ^0.09 (r=0.76).Revised version of a poster presented at the Wilhelm Michaelsen Memorial Symposium (International Symposium on Terrestrial Oligochaeta), Hamburg Sept. 14–18th 1987     

Potent synchronization of peripheral circadian clocks by glucocorticoid injections in PER2::LUC-Clock/Clock mice

In mammals, the central clock (the suprachiasmatic nuclei, SCN) is entrained mainly by the light-dark cycle, whereas peripheral clocks in the peripheral tissues are entrained/synchronized by multiple factors, including feeding patterns and endocrine hormones such as glucocorticoids. Clock-mutant mice (Clock/Clock), which have a mutation in a core clock gene, show potent phase resetting in response to light pulses compared with wild-type (WT) mice, owing to the damped and flexible oscillator in the SCN. However, the phase resetting of the peripheral clocks in Clock/Clock mice has not been elucidated. Here, we characterized the peripheral clock gene synchronization in Clock/Clock mice by daily injections of a synthetic glucocorticoid (dexamethasone, DEX) by monitoring in vivo PER2::LUCIFERASE bioluminescence. Compared with WT mice, the Clock/Clock mice showed significantly decreased bioluminescence and peripheral clock rhythms with decreased amplitudes and delayed phases. In addition, the DEX injections increased the amplitudes and advanced the phases. In order to examine the robustness of the internal oscillator, T-cycle experiments involving DEX stimulations with 24- or 30-h intervals were performed. The Clock/Clock mice synchronized to the 30-h T-cycle stimulation, which suggested that the peripheral clocks in the Clock/Clock mice had increased synchronizing ability upon DEX stimulation, to that of circadian and hour-glass type oscillations, because of weak internal clock oscillators.     

Low filtering rates of <Emphasis Type="Italic">Daphnia magna</Emphasis> in a hypertrophic lake: laboratory and in situ experiments using synthetic microspheres

Zooplankton grazing was measured in Albufera of València (Spain), a shallow turbid hypertrophic lagoon dominated by filamentous bluegreens, during the period of Daphnia magna growth, to evaluate the role of this cladoceran in maintaining a clear water phase which takes place after flushing for rice cultivation practices. We found extremely low ingestion and clearance rates (CR) on latex beads in situ, using a Haney trap suggesting potentially strong inhibition of grazing by the filamentous cyanobacteria, still flourishing in the lagoon. To test the effect of filaments, we undertook laboratory feeding experiments using six different dilutions of the lagoon water to vary filament concentrations, and four different bead concentrations. A highly significant power function between CR and water dilution associated with filament concentrations was found, indicating that the ability of Daphnia to exploit smaller edible algae and thereby control phytoplankton growth would depend on filament concentration levels in the lagoon. From our results only the two more diluted treatments, 9 × 10³ and 18 × 10³ filament ml⁻¹ showed CRs not far from the range of what would be normally expected on the basis of the general relationship of feeding rate as a function of total food concentration. This means that at lower food concentrations, filaments reduce D. magna CR by increasing total food concentration beyond the incipient limiting level, as well as by moderate mechanical interference with the animal’s feeding. However, at lagoon water concentrations above 25% (corresponding to filament concentrations of 75 × 10⁵ filaments ml⁻¹), extremely low CR’s, which did not respond to any food addition, were obtained for D. magna. From these results we can infer that at concentrations beyond the above-mentioned critical level, feeding inhibition by filamentous cyanobacteria is most probably due entirely to mechanical interference. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera     

GRAIN COUNT THRESHOLD DEPENDENCE OF FLM CURVE PATTERN AND CELL CYCLE PARAMETERS OF HEPATOCYTES IN VIVO

FLM curves from hepatocytes of regenerating rat liver in vivo were compared at different grain count thresholds. Estimates of cell cycle phases derived from curves with thresholds decreasing from 15 to 1 grain (background 0.2 grains per nuclear area) revealed a prolongation of t_s from 6.6 to 9.5 hr, at the expense of t_G2M, and t_G1, whereas t_c remained constant. A similar pattern was observed in FLM curves at various threshold levels for hepatocytes localized in subunits of the liver lobule along the vascular axis from afferent to efferent pole. The shapes of these FLM curves indicated an intralobular gradient of reutilizable labelled material. The use of two different threshold levels is crucial for proper selection of FLM curves to evaluate cell cycle phases in regenerating rat liver: first, a threshold to exclude the autoradiographic background, and a second one to avoid errors due to reutilization of labelled DNA precursors. Each threshold has its own implications for the estimation of cell cycle phases.     

A Detailed Study of the Complex Cell Cycle of the Dinoflagellate Crypthecodinium cohnii Biecheler and Evidence for Variation in Histone H1 Kinase Activity

ABSTRACT By adding the protein synthesis inhibitor, emetine (10^-4 M) to a highly synchronized population of Crypthecodinium cohnii Biecheler 1938 at different phases of its cycle, we were able to determine: 1. The existence and the lengthening of the G2-Phase (30 min) in the first cycle (cycle with swimming G1 phase). 2. The time of the second cell cycle phases (cycle in the cyst): G1, 30 min; S, 1.5 h; G2, 2 h and M, 2 h. These results, together with the estimation of the cell volume of the two and four swimming daughter cells emerging from the cysts, allowed us to state the existence of two transition points: G1/S and G2/M, which are necessary for completion of mitosis. We completed this refined approach of the cell cycle in studying the activities of the histone H1 kinase either in dividing or in non-dividing Crypthecodinium cohnii cells with either total soluble proteins or the isolated mitotic kinase complex. The H1 kinase activity of this purified complex is noticeably higher (twice as high) in the dividing cells than in the non-dividing ones. These data are discussed in the light of the basic characteristics of the dinokaryon, and also compared with recent biochemical observations on the same organism and studies on other higher eukaryotic protists and metazoa.     

Effects of cGMP,calcium and reversible methylation on sensory signal processing in halobacteria

Cyclic GMP and Ca²⁺ change the following parameters of sensory behavior of Halobacterium halobium in opposite directions: the interval between two spontaneous reversals of the swimming direction, the phases of increasing and decreasing responsiveness to light stimuli during an interval and the length of the refractory period. Inhibition of the methylation of membrane proteins by blocking the methyltransferase increases the attractant response and prolongs the time during which successive stimuli are integrated. A decrease of the external Ca²⁺ concentration, which activates methylation, has the opposite effect. Inhibition of methylation also prevents the entrainment of the reversal frequency by rhythmic repellent stimuli. The result suggest that cGMP and Ca²⁺ may be antagonistic components of an oscillator, which generates the autonomous rhythm of flagellar reversals, while methylation determines the life-time of sensory signals at an integration link prior to the oscillator, and thereby allows adaptation. Ca²⁺ is thought to act on the methylation system in a feedback loop.     

Reproduction strategies of <Emphasis Type="Italic">Daphnia pulicaria</Emphasis> population in a high mountain lake of Southern Spain

For three consecutive years, a population study of Daphnia pulicaria was undertaken in Río Seco Lake, a small high-mountain lake, in order to elucidate the reproductive strategies adopted by Daphnia in this system. Daphnia appears to colonize this lake every spring by hatching from ephippia and reproduce by means of subitaneous (non-diapausing) and ephippial (diapausing) eggs. D. pulicaria in this lake is an obligate parthenogenetic population. There is a short time period for subitaneous egg production and a much longer period for ephippial egg production. The contribution of subitaneous eggs to Daphnia population density and structure appears to be low. Diapause onset showed a high temporal synchronization in the three studied years in Río Seco Lake, and day-length emerged as the main cue triggering diapause onset and the main explanatory factor for the proportion of ephippial females observed. The development and reproduction of D. pulicaria in Río Seco Lake involves taking a gamble on resting forms to guarantee inter-annual Daphnia persistence in the lake, giving priority to investment in future generations. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera     

The effect of lead on the cell cycle in the root meristem ofAllium cepa L.

Summary Allium cepa (L.) adventitious roots were treated with lead (2.5 mg of Pb²⁺ [from Pb(NO₃)₂] per dm³) for 30–72 h. The cell cycle was studied by pulse labeling with [³H]thymidine. Mitotic activity kinetics, occurrence of disturbed mitoses (c-mitoses), and level of DNA synthesis were examined. It was found that lead prolonged the cell cycle and that cells in two phases of the cycle, G₂ and S, differed in their sensitivity to lead. Cells in G₂ were more sensitive; lead lengthened their cycle by 216% and disturbed the course of cell division by causing c-mitoses. Cells in S phase were less sensitive. Their cell cycle was longer by 55%. They went through their G₂ phase without major disturbances, mitosis in these cells was normal. During treatment ofA. cepa with lead, its destructive effects on cells were exerted only during the first few hours (around 6 h) of incubation. That is when the inhibition of mitotic activity, numerous disturbances of cell division, a decline in the number of cells synthesizing DNA, and a lower level of DNA synthesis were observed. As the incubation continued, the above processes were found to return to normal. In the discussion, data are presented supporting the hypothesis that during the initial period of exposure ofA. cepa to lead, this metal enters both the root apoplast and symplast, exerting a destructive effect on cells, while later, lead penetrates only into the root apoplast, and in this way remains harmless to cells.     

Life history responses of <Emphasis Type="Italic">Daphnia longispina</Emphasis> to mosquitofish (<Emphasis Type="Italic">Gambusia holbrooki</Emphasis>) and pumpkinseed (<Emphasis Type="Italic">Lepomis gibbosus</Emphasis>) kairomones

In the present study, the effect of chemical cues from two fish species (mosquitofish and pumpkinseed), at different concentrations, was tested in life history experiments with Daphnia longispina. The two fish species used represent the most abundant planktivores of many Mediterranean shallow lakes (SW Europe), where the indigenous fish communities have been replaced by such exotic assemblages. Results have shown a similar response of D. longispina to both fish species: kairomones stimulated daphnids to produce more offspring, which resulted in higher fitness (r), relatively to a fishless control. Fish presence also induced an earlier first reproduction, a smaller size at maturity of daphnids, and the production of smaller-sized neonates. Significant correlations with fish concentration (indirect measure of fish kairomone concentration) were found for size at maturity and neonate size, for both fish species. These results are in accordance to the “positive response” observed by other authors, which represents a defence mechanism to face losses caused by fish predators. The chemically mediated size reduction of mature females and neonates is an adaptive response to the size-selective predation exerted by fish. Pumpkinseed introduction is very recent in the lake of origin of the daphnids used in the experiments and its kairomone produced similar effects to mosquitofish in the life history of D. longispina. These results are contrary to the existence of a species-specific kairomone and support the hypothesis of a general fish kairomone. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera     

Biochemical adaptation for dormancy in subitaneous and dormant eggs of <Emphasis Type="Italic">Daphnia magna</Emphasis>

Daphnia can reproduce through subitaneous and dormant eggs. The production of dormant eggs is induced by stimuli associated with deteriorating growth conditions, and enable Daphnia populations to survive temporarily harsh environmental conditions. Dormant eggs are expected to have developed special biochemical adaptations to bridge this long unfavourable period, but little comparative biochemical data are available for dormant and subitaneous eggs. We compared levels of the following molecules between subitaneous and dormant eggs: (a) triglycerides, which are the most abundant energy storage molecules in Daphnia, (b) glycerol, a cryoprotectant also involved in energy storage, and (c) the heat shock protein Hsp60, a molecular chaperone that may assist in maintaining protein structural integrity and inhibiting cell metabolism during diapause. Unexpectedly, no difference in triglycerides content between egg types was found. As expected, dormant eggs contained more glycerol and relatively more Hsp60 than subitaneous eggs. The biochemical composition of dormant eggs can therefore be seen as an adaptation to the harsh environmental conditions these eggs encounter. Guest editor: Piet Spaak Cladocera: Proceedings of the 7th International Symposium on Cladocera