Permanent coexistence in general models of three interacting species

We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x _i = X _i f _i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f _i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.     

Seasonal dynamics of rotifer and crustacean zooplankton populations in a eutrophic,monomictic lake with a note on rotifer sampling techniques

The abundances, biomass, and seasonal succession of rotifer and crustacean zooplankton were examined in a man-made, eutrophic lake, Lake Oglethorpe, over a 13 month period. There was an inverse correlation between the abundance of rotifers and crustaceans. Rotifers were most abundant and dominated (>69%) the rotifer-crustacean biomass during summer months (June–September) while crustacean zooplankton dominated during the remainder of the year (>89%). Peak biomasses of crustaceans were observed in the fall (151 µg dry wt l^–1 in October) and spring (89.66 µg dry wt l^–1 in May). Mean annual biomass levels were 46.99 µg dry wt l^–1 for crustaceans and 19.26 µg dry wt l^–1 for rotifers. Trichocerca rousseleti, Polyarthra sp., Keratella cochlearis and Kellicottia bostoniensis were the most abundant rotifers in the lake. Diaptomus siciloides and Daphnia parvula were the most abundant crustaceans. Lake Oglethorpe is distinct in having an unusually high abundance of rotifers (range 217–7980 l^–1). These high densities can be attributed not only to the eutrophic conditions of the lake but also to the detailed sampling methods employed in this study.The research was supported by National Science Foundation grants DEB 7725354 and DEB 8005582 to Dr. K. G. Porter. It is lake Oglethorpe Limnological Association Contribution No. 25 and Contribution No. 371 of the Harbor Branch Foundation, Inc.     

Oxygen demand and long term changes of profundal zoobenthos

The paper attempts to combine the low oxygen content of the hypolimnion during stratification and the oxygen uptake of zoobenthos. Data of declining oxygen content in the hypolimnion and critical limits of respiration are combined for Chironomus anthracinus, Potamothrix hammoniensis and three species of Pisidium, P. casertanum, P. subtruncatum and P. henslowanum. The respiratory adaptation to low oxygen content influences both growth and population dynamics of the different species. The results have important bearing on eutrophication of the Lake Esrom ecosystem and temperate eutrophic lakes in general as well as the composition of profundal zoobenthos and its population dynamics.Publication No. 389 from Freshwater-Biological Laboratory, University of Copenhagen.     

Climate and plant distribution at global and local scales

This paper investigates, with predictive models, the utility of ecophysiological responses to climate as predictors of plant distribution. At the global scale responses to extreme minimum temperatures and to the hydrological budget effectively predict the distribution limits of the major vegetation types of the World. A minimum temperature of -15°C, for example, appears critical in controlling the poleward spread of vegetation that is dominated by evergreen broadleaved species; however, the presence or absence of more frost resistant species, such as those that are deciduous broadleaved, is not obviously explained in terms of extremes of climate. In such cases, predicting the competitive relationships between species is necessary and dependent on the climatic sensitivity of population dynamics.We are grateful to Hans de Kroon for discussions on the application of matrices to ecology.     

Density fluctuations in populations (1982–1986) and biological observations ofPotamopyrgus Jenkinsi in two trophically differing lakes

The hydrobiid snailPotamopyrgus jenkinsi (E.A. Smith), characterized by parthenogenesis and ovovivipary, was quantitatively sampled monthly between June, 1982, and December, 1986, on sandy bottoms in the shallow zones of the meso-oligotrophic Lake Maarsseveen I and the eutrophic Lake Maarsseveen II. The snail demonstrated a very clumped distribution in both lakes. The mean numbers of juveniles and adults taken together fluctuated strongly. Organisms in Lake I showed relatively high densities (up to 25,000 per m²) in 1982, followed by a sudden drop to values approaching zero in December, 1982, with a subsequent rapid increase in densities, fluctuating between 2,000 and 200 per m². In Lake II, densities of snails fluctuated between 13,000 and 300 per m² with decreases in the spring of 1985 and 1986. The various types of decreases in the lakes are extensively discussed, but no explanation is presently available. The reduction in Lake I was of catastrophic proportions, but the speed of recovery of the population was remarkable.Floating was observed only in Lake I, and only during the occurrence of the highest densities on the sediment. Burrowing behaviour was very common, but strongly suppressed under an uninterrupted dark regime. A shift of temperature from 15 to 22°C had the same effect. A number of submerged macrophyte species from Lake I proved to attractP. jenkinsi in the absence of sandy substrate, though these plants were only covered by the snail during the period of the highest densities in 1982. Temperatures of 20°C or lower were well tolerated, unlike temperatures of 25 and 30°C. Growth was distinct at 10, 15 and 20°C. Keeled individuals were encountered in much higher numbers in Lake I than in Lake II.     

Biotic regionalization and climatic controls in western North America

New methods of weather analysis accompanied by microhabitat ‘bioassays’ have been applied in several case studies to demonstrate effects of atmospheric processes on patterns of community composition and structure and potential species evolution. Average spatial and seasonal airmass dynamics which determine regional and elevational patterns of relative microhabitat favorability, were found to vary between a recent global warming trend (ca 1900 to 1940) and the subsequent global cooling trend (ca 1940 to 1970). These apparently systematic spatial and temporal shifts in weather were related to plant establishment patterns and community composition and structure. The proposed causal mechanisms function, in part, through regional shifts in microhabitat size. These effects are similar to larger scale, longer term shifts deduced from the late Quaternary fossil record. By modifying the spatial approach, month-to-month and year-to-year variability of weather has been examined for the last 130 years at individual points in southwestern North America. Three climatic regimes (the end of the Little Ice Age, the recent warming trend and the recent cooling trend) exhibited distinct year-to-year patterns of weather that can be related to the establishment of different kinds of plants (e.g., C₄ grasses versus C₃ shrubs). Oscillations between different temporal climatic regimes appear to promote the episodic establishment of different life forms, but not necessarily their local extinction. The two methods of weather analysis have been combined in a regional assessment of climatic controls of different biomes in space and time with a primary focus on the Chihuahuan desert. Natural ecotones between the Chihuahuan desert and neighboring biomes are clearly related to large scale airmass dynamics associated with seasonal oscillations in jetstream position. The weather patterns controlling ecotonal positions result from seasonal topographic influences on the general circulation of the atmosphere. The apparent stability of these patterns allows causal hypotheses of biogeographic dynamics and the evolution of physiological traits and life history characteristics.     

Population structure and dynamics of Pinus massoniana Lamb. on mount Jinyun,Sichuan, China

Masson Pine (Pinus massoniana Lamb.) is a pioneer in forest succession in the subtropics of East Asia. However, the species persits, though with decreasing abundance, throughout the various successional phases. Agestructure, spatial pattern, density, population biomass, and their dynamics are described for a population in Sichuan, China, on the basis of a census of all individuals in the population while substituting space with time. In the course of succession, the population density increases and its rate of growth decreases until self-thinning starts; during the phase of self-thinning density decrease and continues to decrease even afterwards, but the rate of growth increase markedly after self-thinning has stopped. The development of population biomass (Bp) during the early succession from shrub-grassland to the early stages of mixed pine and broad-leaved forest can be described by a logistic equation. Later, Bp decrease rapidly. These changes are governed partly by inherent biological features of P. massoniana and partly by the invasion, establishment and development of shade-tolerant evergreen broad-leaved trees. Both self- and alien-thinning occur. Soil conditions affect the rates of these processes.     

Noise-induced neural impulses

The firing pattern of neural pulses often show the following features: the shapes of individual pulses are nearly identical and frequency independent; the firing frequency can vary over a broad range; the time period between pulses shows a stochastic scatter. This behaviour cannot be understood on the basis of a deterministic non-linear dynamic process, e.g. the Bonhoeffer-van der Pol model. We demonstrate in this paper that a noise term added to the Bonhoeffer-van der Pol model can reproduce the firing patterns of neurons very well. For this purpose we have considered the Fokker-Planck equation corresponding to the stochastic Bonhoeffer-van der Pol model. This equation has been solved by a new Monte Carlo algorithm. We demonstrate that the ensuing distribution functions represent only the global characteristics of the underlying force field: lines of zero slope which attract nearby trajectories prove to be the regions of phase space where the distributions concentrate their amplitude. Since there are two such lines the distributions are bimodal representing repeated fluctuations between two lines of zero slope. Even in cases where the deterministic Bonhoeffer-van der Pol model does not show limit cycle behaviour the stochastic system produces a limit cycle. This cycle can be identified with the firing of neural pulses.     

Protein folding kinetics by combined use of rapid mixing techniques and NMR observation of individual amide protons

A method to be used for experimental studies of protein folding introduced by Schmid and Baldwin (J. Mol. Biol. 135: 199-215, 1979), which is based on the competition between amide hydrogen exchange and protein refolding, was extended by using rapid mixing techniques and 1H NMR to provide site-resolved kinetic information on the early phases of protein structure acquisition. In this method, a protonated solution of the unfolded protein is rapidly mixed with a deuterated buffer solution at conditions assuring protein refolding in the mixture. This simultaneously initiates the exchange of unprotected amide protons with solvent deuterium and the refolding of protein segments which can protect amide groups from further exchange. After variable reaction times the amide proton exchange is quenched while folding to the native form continues to completion. By using 1H NMR, the extent of exchange at individual amide sites is then measured in the refolded protein. Competition experiments at variable reaction times or variable pH indicate the time at which each amide group is protected in the refolding process. This technique was applied to the basic pancreatic trypsin inhibitor, for which sequence-specific assignments of the amide proton NMR lines had previously been obtained. For eight individual amide protons located in the beta-sheet and the C-terminal alpha-helix of this protein, apparent refolding rates in the range from 15 s-1 to 60 s-1 were observed. These rates are on the time scale of the fast folding phase observed with optical probes.     

Ion-specific diffusion rates through transmembrane protein channels. A molecular dynamics study

The migration of different alkali metal cations through a transmembrane model channel is simulated by means of the molecular dynamics technique. The parameters of the model are chosen in close relation to the gramicidin A channel. Coulomb- and van der Waals-type potentials between the ions and flexible carbonyl groups of the pore-forming molecule are used to describe the ion channel interaction. The diffusion properties of the ions are obtained from three-dimensional trajectory calculations. The diffusion rates for the different ions Li+, Na+, K+ and Rb+ are affected not only by the mass of the particles but also very strongly by their size. The latter effect is more pronounced for rigid channels, i.e., for binding vibrational frequencies of the CO groups with v greater than 400 cm-1. In this range the selectivity sequence for the diffusion rates is the inverse of that expected from normal rate theory but agrees with that found in experiments for gramicidin A.