Metapopulation-level adaptation of insect host plant preference and extinction-colonization dynamics in heterogeneous landscapes

Species living in highly fragmented landscapes typically occur as metapopulations with frequent turnover of local populations. The turnover rate depends on population sizes and connectivities, but it may also depend on the phenotypic and genotypic composition of populations. The Glanville fritillary butterfly (Melitaea cinxia) in Finland uses two host plant species, which show variation in their relative abundances at two spatial scales: locally among individual habitat patches and regionally among networks of patches. Female butterflies in turn exhibit spatial variation in genetically determined host plant preference within and among patch networks. Emigration, immigration and establishment of new populations have all been shown to be strongly influenced by the match between the host plant composition of otherwise suitable habitat patches and the host plant preference of migrating butterflies. The evolutionary consequences of such biased migration and colonization with respect to butterfly phenotypes might differ depending on spatial configuration and plant species composition of the patches in heterogeneous patch networks. Using a spatially realistic individual-based model we show that the model-predicted evolution of host plant preference due to biased migration explains a significant amount of the observed variation in host plant use among metapopulations living in dissimilar networks. This example illustrates how the ecological extinction-colonization dynamics may be linked with the evolutionary dynamics of life history traits in metapopulations.     

Peak-to-peak dynamics in food chain models

We show in this paper that the chaotic regimes of many food chain models often enjoy a very peculiar property, known as peak-to-peak dynamics. This means that the maximum (peak) density of the populations of any trophic level can be easily forecasted provided the last two peaks of the same population are known. Moreover, extensive simulation shows that only the last peak is needed if the forecast concerns the population at the top of the food chain and that peaks variability often increases from bottom to top. All these findings bring naturally to the conclusion that top populations should be sampled in order to have higher chances to detect peak-to-peak dynamics. The analysis is carried out by studying ditrophic food chain models with seasonally varying parameters, tritrophic food chain models with constant parameters, and more complex food chain and food web models.     

Metapopulation theory for fragmented landscapes

We review recent developments in spatially realistic metapopulation theory, which leads to quantitative models of the dynamics of species inhabiting highly fragmented landscapes. Our emphasis is in stochastic patch occupancy models, which describe the presence or absence of the focal species in habitat patches. We discuss a number of ecologically important quantities that can be derived from the full stochastic models and their deterministic approximations, with a particular aim of characterizing the respective roles of the structure of the landscape and the properties of the species. These quantities include the threshold condition for persistence, the contributions that individual habitat patches make to metapopulation dynamics and persistence, the time to metapopulation extinction, and the effective size of a metapopulation living in a heterogeneous patch network.     

Cross-correlation suppressed T1 and NOE experiments for protein side-chain 13CH2 groups

Relaxation measurements of side-chain ¹³CH₂-groups of uniformly ¹³C labeled human ubiquitin were performed at 600 MHz and 800 MHz magnetic field strength at 30°C. Dipole-dipole cross-correlated relaxation effects in T₁ experiments were suppressed by the combination of radio-frequency pulses and pulsed field gradients during the relaxation delay leading to monoexponential relaxation decays that allow a more accurate extraction of the ¹³C T₁ relaxation times. Heteronuclear ¹H-¹³C NOEs obtained by using different proton saturation schemes indicate that the influence of cross-correlation is small. The experimental T₁ and NOE data were interpreted in a model-free way in terms of a generalized order parameter and an internal correlation time.     

Cross correlations between 13C-1H dipolar interactions and 15N chemical shift anisotropy in nucleic acids

Two sets of cross-correlated relaxation rates involving chemical shift anisotropy and dipolar interactions have been measured in an RNA kissing complex. In one case, both the CSA and dipolar interaction tensors are located on the same nucleotide base and are rigidly fixed with respect to each other. In the other case, the CSA tensor is located on the nucleotide base whereas the dipolar interaction is located on the adjoining ribose unit. Analysis of the measured rates in terms of isotropic or anisotropic rotational diffusion has been carried out for both cases. A marked difference between the two models is observed for the cross-correlation rates involving rigidly fixed spin interactions. The influence of internal motions about the glycosidic linkage between the nucleotide base and the ribose unit on cross-correlated relaxation rates has been estimated by applying a model of restricted rotational diffusion. Local motions seem to have a more pronounced effect on cross-correlated relaxation rates when the two spin interactions are not rigidly fixed with respect to each other.     

Population dynamics of phytophagous and predatory mites (Acari: Tetranychidae, Eriophyidae, Phytoseiidae) on bamboo plants in Fujian, China

The seasonal cycle and population dynamics of Schizotetranychus nanjingensis Ma and Yuan, Aponychus corpuzae Rimando (Tetranychidae), Aculus bambusae Kuang (Eriophyidae) and their natural enemy Typhlodromus bambusae Ehara (Phytoseiidae) were studied during 1996–1998 in moso bamboo forests in Nanping, Fujian, China. Damage to bamboo leaves was often caused by mixed populations of the three phytophagous species, which displayed different seasonal dynamics: S. nanjingensis fed actively and reproduced in May and from late July to late October (aestivating from June to mid July), Ap. corpuzae was active and reproduced from mid July to late November, and Ac. bambusae from July to next February. During Spring S. nanjingensis was the dominant species with the greatest niche width, but in Summer Ac. bambusae and Ap. corpuzae became dominant and had greater niche widths. In Autumn, Ac. bambusae decreased but both S. nanjingensis and Ap. corpuzae mites increased and the latter became dominant. In winter all species decreased sharply in number. The two spider mite species (S. nanjingensis and Ap. corpuzae) had high niche overlaps in all four seasons. Niche overlaps between the eriophyid Ac. bambusae and the two spider mites were similarly high except during the spring when Ac. bambusae was absent. The predatory mite (T. bambusae) had higher niche overlap with Ap. corpuzae than with others during Autumn and Winter, but during Spring and Summer niche overlap was higher with S. nanjingensis.     

Is DNA a nonlinear dynamical system where solitary conformational waves are possible?

DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA’s nonlinear properties.     

Persistent solutions for age-dependent pair-formation models

Conditions on the vital rates and the mating function are derived which imply existence or nonexistence of exponentially growing persistent age-distributions for age-dependent pair-formation models.     

Parametric analysis of the ratio-dependent predator–prey model

We present a complete parametric analysis of stability properties and dynamic regimes of an ODE model in which the functional response is a function of the ratio of prey and predator abundances. We show the existence of eight qualitatively different types of system behaviors realized for various parameter values. In particular, there exist areas of coexistence (which may be steady or oscillating), areas in which both populations become extinct, and areas of "conditional coexistence" depending on the initial values. One of the main mathematical features of ratio-dependent models, distinguishing this class from other predator-prey models, is that the Origin is a complicated equilibrium point, whose characteristics crucially determine the main properties of the model. This is the first demonstration of this phenomenon in an ecological model. The model is investigated with methods of the qualitative theory of ODEs and the theory of bifurcations. The biological relevance of the mathematical results is discussed both regarding conservation issues (for which coexistence is desired) and biological control (for which extinction is desired).     

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