Spatially-explicit Modeling Approach Research Articles

In-stream surface water quality in China: A spatially-explicit modelling approach for nutrients

Nutrient pollution is a widespread problem in rivers in China. Managing nutrient pollution requires better knowledge of in-stream processes governing the surface water quality. As current nutrient models for China mainly focus on river export of nutrients to seas, in-stream surface water quality and their contributing sources and processes are, therefore not well understood. This requires accounting for combined effects of nutrient inputs to rivers from produced waste, biochemistry of different forms of nutrients and their transport by river network. Moreover, improvements can be made in evaluating the model performance of large-scale nutrient models based on water quality measurements in China (using the surface water quality classes from 1 to 6). The objective of this study is to quantify the spatial variation in in-stream water quality for nutrients, and associated sources, for water quality classes in China. Our new Model to Assess River Inputs of Nutrients to seAs (MARINA 3.0) for in-stream water quality distinguishes different nutrient forms including dissolved inorganic (DIN, DIP) and organic (DON, DOP) nitrogen and phosphorus and was applied for the year 2012. Our model simulations compare reasonably well with measurements across 155 river sections. Results show that between 12% and 66% of the streams are highly polluted (exceeding water quality class 3) and depending on nutrient form. Diffuse sources dominate in 76% of the streams for DIN. Point sources such as direct discharges of animal manure dominate in 46%–59% of the streams for DON, DIP and DOP. The dominant sources vary considerably between rivers and nutrient forms. This indicates the need account for nutrient forms in models and national monitoring programs. Our model results could support effective management to reduce nutrient pollution in China.

Community consequences of foraging under fear

Non-consumptive effects of predators within ecosystems can alter the behavior of individual prey species, and have cascading effects on other trophic levels. In this context, an understanding of non-consumptive predator effects on the whole prey community is crucial for predicting community structure and composition, hence biodiversity patterns. We used an individual-based, spatially-explicit modelling approach to investigate the consequences of landscapes of fear on prey community metrics. The model spans multiple hierarchical levels from individual home range formation based on food availability and perceived predation risk to consequences on prey community structure and composition. This mechanistic approach allowed us to explore how important factors such as refuge availability and foraging strategy under fear affect prey community metrics. Fear of predators affected prey space use, such as home range formation. These adaptations had broader consequences for the community leading to changes in community structure and composition. The strength of community responses to perceived predation risk was driven by refuge availability in the landscape and the foraging strategy of prey animals. Low refuge availability in the landscape strongly decreased diversity and total biomass of prey communities. Additionally, body mass distributions in prey communities facing high predation risk were shifted towards small prey animals. With increasing refuge availability the consequences of non-consumptive predator effects were reduced, diversity and total biomass of the prey community increased. Prey foraging strategies affected community composition. Under medium refuge availability, risk-averse prey communities consisted of many small animals while risk-taking prey communities showed a more even body mass distribution. Our findings reveal that non-consumptive predator effects can have important implications for prey community diversity and should therefore be considered in the context of conservation and nature management.

Assessing wild bees in perennial bioenergy landscapes: effects of bioenergy crop composition, landscape configuration, and bioenergy crop area

Wild bee populations are currently under threat, which has led to recent efforts to increase pollinator habitat in North America. Simultaneously, U.S. federal energy policies are beginning to encourage perennial bioenergy cropping (PBC) systems, which have the potential to support native bees. Our objective was to explore the potentially interactive effects of crop composition, total PBC area, and PBC patches in different landscape configurations. Using a spatially-explicit modeling approach, the Lonsdorf model, we simulated the impacts of three perennial bioenergy crops (PBC: willow, switchgrass, and prairie), three scenarios with different total PBC area (11.7, 23.5 and 28.8% of agricultural land converted to PBC) and two types of landscape configurations (PBC in clustered landscape patterns that represent realistic future configurations or in dispersed neutral landscape models) on a nest abundance index in an Illinois landscape. Our modeling results suggest that crop composition and PBC area are particularly important for bee nest abundance, whereas landscape configuration is associated with bee nest abundance at the local scale but less so at the regional scale. Strategies to enhance wild bee habitat should therefore emphasize the crop composition and amount of PBC.

Assessing conditions influencing the longitudinal distribution of exotic brown trout (Salmo trutta) in a mountain stream: a spatially-explicit modeling approach

Trout species often segregate along elevational gradients, yet the mechanisms driving this pattern are not fully understood. On the Logan River, Utah, USA, exotic brown trout (Salmo trutta) dominate at low elevations but are near-absent from high elevations with native Bonneville cutthroat trout (Onchorhynchus clarkii utah). We used a spatially-explicit Bayesian modeling approach to evaluate how abiotic conditions (describing mechanisms related to temperature and physical habitat) as well as propagule pressure explained the distribution of brown trout in this system. Many covariates strongly explained redd abundance based on model performance and coefficient strength, including average annual temperature, average summer temperature, gravel availability, distance from a concentrated stocking area, and anchor ice-impeded distance from a concentrated stocking area. In contrast, covariates that exhibited low performance in models and/or a weak relationship to redd abundance included reach-average water depth, stocking intensity to the reach, average winter temperature, and number of days with anchor ice. Even if climate change creates more suitable summer temperature conditions for brown trout at high elevations, our findings suggest their success may be limited by other conditions. The potential role of anchor ice in limiting movement upstream is compelling considering evidence suggesting anchor ice prevalence on the Logan River has decreased significantly over the last several decades, likely in response to climatic changes. Further experimental and field research is needed to explore the role of anchor ice, spawning gravel availability, and locations of historical stocking in structuring brown trout distributions on the Logan River and elsewhere.

Field Margins, Foraging Distances and Their Impacts on Nesting Pollinator Success

The areas of wild land around the edges of agricultural fields are a vital resource for many species. These include insect pollinators, to whom field margins provide both nest sites and important resources (especially when adjacent crops are not in flower). Nesting pollinators travel relatively short distances from the nest to forage: most species of bee are known to travel less than two kilometres away. In order to ensure that these pollinators have sufficient areas of wild land within reach of their nests, agricultural landscapes need to be designed to accommodate the limited travelling distances of nesting pollinators. We used a spatially-explicit modelling approach to consider whether increasing the width of wild strips of land within the agricultural landscape will enhance the amount of wild resources available to a nesting pollinator, and if it would impact differently on pollinators with differing foraging strategies. This was done both by creating field structures with a randomised geography, and by using landscape data based upon the British agricultural landscape. These models demonstrate that enhancing field margins should lead to an increase in the availability of forage to pollinators that nest within the landscape. With the exception of species that only forage within a very short range of their nest (less than 125 m), a given amount of field margin manipulation should enhance the proportion of land available to a pollinator for foraging regardless of the distance over which it normally travels to find food. A fixed amount of field edge manipulation should therefore be equally beneficial for both longer-distance nesting foragers such as honeybees, and short-distance foragers such as solitary bees.

Distance-decay patterns of nutrient loading at watershed scale: Regression modeling with a special spatial aggregation strategy

The effect of distance-decay on nutrient flux usually plays an important role in nutrient retention from non-point sources to surface waters. However, the distance-decay effect has been inappropriately neglected in many studies that adopted regression modeling method to quantify the relationship between watershed landscape and in-stream nutrient loading level. The goal of this study was to develop non-linear regression models that better quantify the role of distance on non-point source nutrient loads in rivers by using simulation results of a spatially-explicit model applied to the watersheds in the Upper Chattahoochee River Basin, Georgia. Because a detailed spatially-explicit modeling approach typically simulates the nutrient flux across the entire watershed, it provides opportunities to examine the nutrient decay patterns at watershed scale. The simulation results confirmed that regarding the effect of flow distance on nutrient loading, the exponential decay setting in the spatially-explicit model performs well. Other heterogeneous factors including slope and soil conditions do affect the decay results but not strongly enough to change the general exponential patterns. The nutrient contribution from areas that were greater than 300 meters to the river network was negligible. It was also found that the decay rate for urban lands is lower than that for other land-covers. Based on these findings, a spatial aggregation strategy in the lateral dimension of the river network was adopted and eight non-linear regression models which explicitly addressed the effects of distance-decay were designed to estimate the nutrient annual average loads. The model validation results showed that three of them can well estimate the nutrient loads. This study shows the usage of stream-lateral-dimension aggregation strategy in addressing nutrient distance-decay patterns and developing simple regression models of nutrient loading. This study also illustrates the advantages of using comprehensive spatially-explicit models to design and configure simpler regression models for improving our understanding of nutrient export from land to water.

A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics.

In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explictly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

Allee effects, adaptive evolution, and invasion success.

The mechanisms that facilitate success of an invasive species include both ecological and evolutionary processes. Investigating the evolutionary dynamics of founder populations can enhance our understanding of patterns of invasiveness and provide insight into management strategies for controlling further establishment of introduced populations. Our aim is to analyze the evolutionary consequences of ecological processes (i.e., propagule pressure and threshold density effects) that impact successful colonization. We address our questions using a spatially-explicit modeling approach that incorporates dispersal, density dependent population growth, and selection. Our results show that adaptive evolution may occur in small or sparse populations, providing a means of mitigating or avoiding inverse density dependent effects (i.e., Allee effects). The rate at which this adaptation occurs is proportional to the amount of genetic variance and is a crucial component in assessing whether natural selection can rescue a population from extinction. We provide theoretical evidence for the importance of recognizing evolution in predicting and explaining successful biological invasions.