Patch dynamics and metapopulation theory: the case of successional species

We present a mathematical framework that combines extinction-colonization dynamics with the dynamics of patch succession. We draw an analogy between the epidemiological categorization of individuals (infected, susceptible, latent and resistant) and the patch structure of a spatially heterogeneous landscape (occupied-suitable, empty-suitable, occupied-unsuitable and empty-unsuitable). This approach allows one to consider life-history attributes that influence persistence in patchy environments (e.g., longevity, colonization ability) in concert with extrinsic processes (e.g., disturbances, succession) that lead to spatial heterogeneity in patch suitability. It also allows the incorporation of seed banks and other dormant life forms, thus broadening patch occupancy dynamics to include sink habitats. We use the model to investigate how equilibrium patch occupancy is influenced by four critical parameters: colonization rate? extinction rate, disturbance frequency and the rate of habitat succession. This analysis leads to general predictions about how the temporal scaling of patch succession and extinction-colonization dynamics influences long-term persistence. We apply the model to herbaceous, early-successional species that inhabit open patches created by periodic disturbances. We predict the minimum disturbance frequency required far viable management of such species in the Florida scrub ecosystem. (C) 2001 Academic Press.

Patch dynamics in grazed subtropical native pastures in south-east Queensland

Patch formation is common in grazed grasslands but the mechanisms involved in the formation and maintenance of patches are not clear. To increase our knowledge on this subject we examined possible reasons for patch formation and the influence of management on changes between patch states in three experiments in native pasture communities in the Crows Nest district, south-east Queensland. In these communities, small-scale patches (tall grassland (dominated by large and medium tussock grasses), short swards (dominated by short tussock grasses and sedges), and lawns (dominated by stoloniferous and/or rhizomatous grasses)) are readily apparent. We hypothesized that the formation of short sward and lawn patches in areas of tall grassland was due to combinations of grazing and soil fertility effects. This was tested in Experiment 1 by applying a factorial combination of defoliation, nutrient application and transplants of short tussock and stoloniferous species to a uniform area of tall grassland. Total species density declined during the experiment, was lower with high nutrient applications, but was not affected by defoliation. There were significant changes in abundance of species that provided support for our hypotheses. With light defoliation and low nutrients, the tall grassland remained dominated by large tussock grasses and contained considerable amounts of forbs. With heavy defoliation, the pastures were dominated by medium tussock grasses and there were significant decreases in forbs and increases in sedges (mainly with low nutrients) and stoloniferous grasses (mainly with high nutrients). Total germinable seed densities and those of most species groups were significantly lower in the heavy defoliation than the light defoliation plots. Total soil seed numbers were not affected by nutrient application but there were fewer seeds of the erect forbs and more sedge seeds in plots with high nutrients. The use of resting from grazing and fire to manage transitions between patches was tested. In Experiment 2, changes in species density and abundance were measured for 5 years in the three patch types with and without grazing. Experiment 3 examined the effects of fire, grazing and resting on short sward patches over 4 years. In Experiment 2, total species density was lower in lawn than short sward or tall grassland patches, and there were more species of erect forbs than other plant groups in all patch types. The lawn patches were originally dominated by Cynodon spp. This dominance continued with grazing but in ungrazed patches the abundance of Cynodon spp. declined and that of forbs increased. In the short sward patches, dominance of short tussock grasses continued with grazing but in ungrazed plots their abundance declined while that of large tussock grasses increased. The tall grassland patches remained dominated by large and medium tussock species. In Experiment 3, fire had no effect on species abundance. On the grazed plots the short tussock grasses remained dominant but where the plots were rested from grazing the small tussock grasses declined and the large tussock grasses increased in abundance. The slow and relatively small changes in these experiments over 4 or 5 years showed how stable the composition of these pastures is, and that rapid changes between patch types are unlikely.

The role of habitat disturbance and recovery in metapopulation persistence

Classical metapopulation theory assumes a static landscape. However, empirical evidence indicates many metapopulations are driven by habitat succession and disturbance. We develop a stochastic metapopulation model, incorporating habitat disturbance and recovery, coupled with patch colonization and extinction, to investigate the effect of habitat dynamics on persistence. We discover that habitat dynamics play a fundamental role in metapopulation dynamics. The mean number of suitable habitat patches is not adequate for characterizing the dynamics of the metapopulation. For a fixed mean number of suitable patches, we discover that the details of how disturbance affects patches and how patches recover influences metapopulation dynamics in a fundamental way. Moreover, metapopulation persistence is dependent not only oil the average lifetime of a patch, but also on the variance in patch lifetime and the synchrony in patch dynamics that results from disturbance. Finally, there is an interaction between the habitat and metapopulation dynamics, for instance declining metapopulations react differently to habitat dynamics than expanding metapopulations. We close, emphasizing the importance of using performance measures appropriate to stochastic systems when evaluating their behavior, such as the probability distribution of the state of the. metapopulation, conditional on it being extant (i.e., the quasistationary distribution).

Undular tidal bore dynamics in the Daly Estuary, Northern Australia

Measurements in the macro-tidal Daly Estuary show that the presence of an undular tidal bore contributed negligibly to the dissipation of tidal energy. No recirculation bubble was observed between a trough and the following wave crest in the lee waves following the undular bore. This differs to stationary undular bores in laboratory experiments at larger Froude numbers where a recirculation bubble exists. Secondary motions and the turbulence generated by the undular bore had no measurable influence on the sediment transport. This situation contrasts with the intense sediment resuspension observed in breaking tidal bores. The tidally averaged sediment budget in the Daly Estuary was controlled by the asymmetry of tidal currents. The undular bore may widen the river by breaking along the banks that it undercuts, leading to bank slippage. A patch of river-wide macro-turbulence of 3-min duration occurred about 20 min after the passage of the bore during accelerating tidal currents. (C) 2004 Elsevier Ltd. All rights reserved.

Time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultracold atomic Bose-Einstein condensates to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to 6.022×1023 (Avogadro's number) of particles. This system is realizable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.

Superchemistry: dynamics of coupled atomic and molecular Bose condensates

We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas coupled to a diatomic molecular Bose gas by coherent Raman transitions. This system is shown to result in a new type of “superchemistry,” in which giant collective oscillations between the atomic and the molecular gas can occur. The phenomenon is caused by stimulated emission of bosonic atoms or molecules into their condensate phases.

Quantum dynamics of three coupled atomic Bose-Einstein condensates

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.

Substructure and Dynamics of the Fornax Cluster

We present the first dynamical analysis of a galaxy cluster to include a large fraction of dwarf galaxies. Our sample of 108 Fornax Cluster members measured with the UK Schmidt Telescope FLAIR-II spectrograph contains 55 dwarf galaxies (15.5 > b(j) > 18.0 or -16 > M-B > -13.5). H alpha emission shows that of the dwarfs are star forming, twice the fraction implied by morphological classifications. The total sample has a mean velocity of 1493 +/- 36 kms s(-1) and a velocity dispersion of 374 +/- 26 km s(-1). The dwarf galaxies form a distinct population: their velocity dispersion (429 +/- 41 km s(-1)) is larger than that of the giants () at the 98% confidence level. This suggests that the dwarf population is dominated by infalling objects whereas the giants are virialized. The Fornax system has two components, the main Fornax Cluster centered on NGC 1399 with cz = 1478 km s(-1) and sigma (cz) = 370 km s(-1) and a subcluster centered 3 degrees to the southwest including NGC 1316 with cz = 1583 km s(-1) and sigma (cz) = 377 km s(-1). This partition is preferred over a single cluster at the 99% confidence level. The subcluster, a site of intense star formation, is bound to Fornax and probably infalling toward the cluster core for the first time. We discuss the implications of this substructure for distance estimates of the Fornax Cluster. We determine the cluster mass profile using the method of Diaferio, which does not assume a virialized sample. The mass within a projected radius of 1.4 Mpc is (7 +/- 2) x 10(13) M-., and the mass-to-light ratio is 300 +/- 100 M-./L-.. The mass is consistent with values derived from the projected mass virial estimator and X-ray measurements at smaller radii.

Evolution of Wolbachia pipientis transmission dynamics in insects

Wolbachia pipientis is an intracellular bacterial parasite of arthropods that enhances its transmission by manipulating host reproduction, most commonly by inducing cytoplasmic incompatibility. The discovery of isolates with modified cytoplasmic incompatibility phenotypes and others with novel virulence properties is an indication of the potential breadth of evolutionary strategies employed by Wolbachia.

Dependence of transient dynamics in a class-C laser upon variation of inversion with time

The transient statistics of a gain-switched coherently pumped class-C laser displays a linear correlation between the first passage time and subsequent peak intensity. Measurements are reported showing a positive or negative sign of this linear correlation, controlled through the switching time and the laser detuning. Further measurements of the small-signal laser gain combined with calculations involving a three-level laser model indicate that this sign fundamentally depends upon the way the laser inversion varies during the gain switching, despite the added dynamics of the laser polarization in the class-C laser. [S1050-2947(97)07112-6].

Spin-glass dynamics

Spin glasses are magnetic systems with conflicting and random interactions between the individual spins. The dynamics of spin glasses, as of structural glasses, reflect their complexity. Both in experimental and numerical work the relaxation below the freezing temperature depends strongly on the annealing conditions (aging) and, above the freezing point, relaxation in equilibrium is slow and non-exponential, In this Forum, observed characteristics of the dynamics were summarized and the physical models proposed to explain them were outlined. (C) 1998 Elsevier Science B.V. All rights reserved.

A study of the stability of subcycling algorithms in structural dynamics

Algorithms for explicit integration of structural dynamics problems with multiple time steps (subcycling) are investigated. Only one such algorithm, due to Smolinski and Sleith has proved to be stable in a classical sense. A simplified version of this algorithm that retains its stability is presented. However, as with the original version, it can be shown to sacrifice accuracy to achieve stability. Another algorithm in use is shown to be only statistically stable, in that a probability of stability can be assigned if appropriate time step limits are observed. This probability improves rapidly with the number of degrees of freedom in a finite element model. The stability problems are shown to be a property of the central difference method itself, which is modified to give the subcycling algorithm. A related problem is shown to arise when a constraint equation in time is introduced into a time-continuous space-time finite element model. (C) 1998 Elsevier Science S.A.

Ecosystem dynamics at disturbed and undisturbed sites in North Queensland wet tropical rain forest. III. Nutrient returns to the forest floor through litterfall

The nutrient contents and accessions in litterfall over a period of 3 y are reported for undisturbed areas and at two sites disturbed by selective harvesting in tropical rain forest in North Queensland, Australia. Mean concentrations (mg g(-1) dry weight) of nutrients in litterfall ranged from 10 to 12 for nitrogen; 0.33 to 0.43 for phosphorus; 3.6 to 4.3 for potassium; 6.0 to 10.5 for calcium and 1.7 to 2.6 for magnesium. These concentrations are in the middle to lower part of the spectrum of values recorded for tropical forest. Accessions of nutrients in litterfall (kg ha(-1) y(-1)) ranged from 59 to 64 N; 1.9 to 2.4 P; 20 to 24K; 34 to 63 Ca; and 9 to 16 Mg. These rates, particularly for IN and P, are among the lowest recorded for tropical forests. There were no consistent between-site differences in total nutrient accessions in small litterfall. In terms of the contribution of litterfall to the accessions of nutrients to the forest floor, this suggests that the logged sites have recovered from the effects of selective harvesting within 25 y. Nutrient accessions at each site were distinctly seasonal, with maximum accessions occurring in the late dry season to late in the wet season. Leaf-fall accounted for the largest proportion of nutrient accessions over the study period, although at certain times accessions in both reproductive material and wood were significant. A cyclone which crossed the coast near the study sites resulted in large nutrient accessions over a short period but had little effect on the total annual accession. A comparison with previous studies of litterfall in Australian tropical rainforests indicates that nutrient return in litterfall is directly related to soil fertility.

The influence of joint position on the dynamics of perception-action coupling

Six right-handed subjects performed rhythmic flexion and extension movements of the index finger in time with an auditory metronome. On each block of trials, the wrist of the response hand was placed in a extended, neutral or flexed position. In the flex-on-the-beat condition, subjects were instructed to coordinate maximum excursion in the direction of finger flexion with each beat of the metronome. In the extend-on-the-beat condition, subjects were instructed to coordinate maximum excursion in the direction of finger extension with each beat of the metronome. The frequency of the metronome was increased from 2.00 Hz to 3.75 Hz in 8 steps (8 s epochs) of 0.25 Hz. During trials prepared in the extend-on-the-beat pattern, all subjects exhibited transitions to either a flex-on-the-beat pattern or to phase wandering as the frequency of pacing was increased. The time at which these transitions occurred was reliably influenced by the position of the wrist. Four subjects exhibited qualitative departures from the flex-on-the-beat pattern at pacing frequencies that were greater than those at which the extend-on-the-beat pattern could be maintained. The lime at which these departures occurred was not influenced by the position of the wrist. These results are discussed with reference to the constraints imposed on the coordination dynamics by the intrinsic properties of the neuromuscular-skeletal system.