Spatial patterns are a subfield of spatial ecology, and these patterns modify the temporal dynamics and stability properties of population densities at a range of spatial scales. Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer–resource interactions, localized disturbance–recovery processes, and scale-dependent feedback. However, in this paper, our main aim is to study the effect of tide on the pattern formation of a spatial plant-wrack model. We discuss the changes of the wavelength, wave speed, and the conditions of the spatial pattern formation, according to the dispersion relation formula. Both the mathematical analysis and numerical simulations reveal that the tide has great influence on the spatial pattern. More specifically, typical traveling spatial patterns can be obtained. Our obtained results are consistent with the previous observation that wracks exhibit traveling patterns, which is useful to help us better understand the dynamics of the real ecosystems.

Herbivore outbreaks, a major form of natural disturbance in many ecosystems, often have devastating impacts on their food plants. Understanding those factors permitting herbivore outbreaks to occur is a long-standing issue in conventional studies of plant-herbivore interactions. These studies are largely concerned with the relative importance of intrinsic biological factors and extrinsic environmental variations in determining the degree of herbivore outbreaks. In this paper, we illustrated that how the time delay associated with plant defense responses to herbivore attacks and the spatial diffusion of herbivore jointly promote outbreaks of herbivore population. Using a reaction-diffusion model, we showed that there exists a threshold of time delay in plant-herbivore interactions; when time delay is below the threshold value, there is no herbivore outbreak. However, when time delay is above the threshold value, periodic outbreak of herbivore emerges. Furthermore, the results confirm that during the outbreak period, plants display much lower density than its normal level but higher in the inter-outbreak periods. Our results are supported by empirical findings. © 2013.

Evidence for significant losses of species richness or biodiversity, even within protected natural areas, is mounting. Managers are increasingly being asked to monitor biodiversity, yet estimating biodiversity is often prohibitively expensive. As a cost-effective option, we estimated the spatial and temporal distribution of species richness for four taxonomic groups (birds, mammals, herpetofauna (reptiles and amphibians), and plants) within Sequoia and Kings Canyon National Parks using only existing biological studies undertaken within the Parks and the Parks' long-term wildlife observation database. We used a rarefaction approach to model species richness for the four taxonomic groups and analyzed those groups by habitat type, elevation zone, and time period. We then mapped the spatial distributions of species richness values for the four taxonomic groups, as well as total species richness, for the Parks. We also estimated changes in species richness for birds, mammals, and herpetofauna since 1980. The modeled patterns of species richness either peaked at mid elevations (mammals, plants, and total species richness) or declined consistently with increasing elevation (herpetofauna and birds). Plants reached maximum species richness values at much higher elevations than did vertebrate taxa, and non-flying mammals reached maximum species richness values at higher elevations than did birds. Alpine plant communities, including sagebrush, had higher species richness values than did subalpine plant communities located below them in elevation. These results are supported by other papers published in the scientific literature. Perhaps reflecting climate change: birds and herpetofauna displayed declines in species richness since 1980 at low and middle elevations and mammals displayed declines in species richness since 1980 at all elevations.