A spatial optimisation model for multi-period landscape level fuel management to mitigate wildfire impacts

Elevated fuel loads are contributing to an increase in the occurrence of, and area burned by, severe wildfires in many regions across the globe. In an attempt to reverse this trend, fire and land management agencies are investing in extensive fuel management programs. However, the planning of fuel treatment activities poses complicated decision-making problems with spatial and temporal dimensions. Here, we present a mixed integer programming model for spatially explicit multi-period scheduling of fuel treatments. The model provides a flexible framework that allows for landscape heterogeneity and a range of ecological and operational considerations and constraints. The model’s functionality is demonstrated on a series of hypothetical test landscapes and a number of implementation issues are discussed.     

Wildfire fuel management: Network-based models and optimization of prescribed burning

Wildfires are a common phenomenon on most continents. They have occurred for an estimated 60 million years and are part of a regular climatic cycle. Nevertheless, wildfires represent a real and continuing problem that can have a major impact on people, wildlife and the environment. The intensity and severity of wildfires can be reduced through fuel management activities. The most common and effective fuel management activity is prescribed burning. We propose a multi-period optimization framework based on mixed integer programming (MIP) techniques to determine the optimal spatial allocation of prescribed burning activities over a finite planning horizon. In contrast to the existing fuel management optimization literature, we model fuel accumulation with Olson’s equation. To capture potential fire spread along with irregular landscape connectivity considerations, we use a graph-theoretical approach that allows us to exploit graph connectivity measures (e.g., the number of connected components) as optimization objectives. The resulting mathematical programs can be tackled by general purpose MIP solvers, while for handling larger instances we propose a simple heuristic. Our computational experiments with test instances constructed based on real-life data reveal interesting insights and demonstrate the advantages and limitations of the proposed approaches.     

On the effects of migration and spatial heterogeneity on single and multiple species

We first investigate in a logistic model the effects of migration and spatial heterogeneity of the environment on the total population size at equilibrium of a single species. Our study shows that (i) the total population size is maximized at some intermediate migration rate, and hence is a non-monotone function of the migration rate; (ii) heterogeneity of the environment increases the population size. In the second part of this paper, these findings are applied to ecological invasions. For a two-species Lotka-Volterra competition model with migration, we show that (i) without migration, the invading species eliminates the resident species at every point of the habitat, whereas when migration is present, for certain ranges of migration rates the invader may be eliminated when it is rare; and (ii) without migration, the two species can coexist at every point of the habitat, whereas when migration is present, for some ranges of migration rates one of the species is extinguished for all initial conditions.     

Evolution of dispersal in a spatially periodic integrodifference model

An integrodifference model describing the reproduction and dispersal of a population is introduced to investigate the evolution of dispersal in a spatially periodic habitat. The dispersal is determined by a kernel function, and the dispersal strategy is defined as the probability of population individuals’ moving to a different habitat. Both conditional and unconditional dispersal strategies are investigated, the distinction being whether dispersal depends on local environmental conditions. For competing unconditional dispersers, we prove that the population with the smaller dispersal probability always prevails. Alternatively, for conditional dispersers, it is shown that the strategy known as ideal free dispersal is both sufficient and necessary for evolutionary stability. These results extend those in the literature for discrete diffusion models in finite patchy landscapes and from reaction–diffusion models.     

Endangered species,real options,and forest management

We use a real option approach to determine optimally when a social planner has to stop or resume logging in situations where an endangered species relies on forest habitat for its survival, and that habitat evolves stochasticly. The model incorporates economic, ecological and social features, and is calibrated to generate an optimal forest management rule that balances the benefits from commercial forest exploitation with the risks of extinction facing the endangered species. For the reasonable parameters used in our application to the Rangifer tarandus caribou, an endangered species in Central Labrador (Canada), the policy of banning logging temporarily is quite attractive as it does not require long banning periods while it drastically reduces the extinction risk and increases forest value. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling forest core area with integer programming

Abundant and continuous old forest tend to be fragmented into isolated and small patches because of human harvest activities. Dispersive and isolated old forest patches cannot provide abundant interior habitat to wildlife, which is a fatal threat for specific plant communities and wildlife species. In this paper, an Integer Programming model for forest planning is designed to maximize the economical benefit of the forest and to guarantee a minimum area of interior old forest for wildlife habitat, the so-called core area satisfying minimum mature age requirements. The minimum core area constraints, to some degree, can help mitigate the negative impact of harvest activities to divide forest habitat into many small patches. The model is implemented in a commercial Integer Programming solver and it is applied to several hypothetical landscapes. The results show the possibility of incorporating a core area requirement into a forest planning model, and the possibility to obtain solutions within a reasonable computational time. Instances with up to 1600 management units have been solved in seconds to an optimality gap of 1% (0.1% in some cases).     

A stochastic approach to optimize Maritime pine (Pinus pinaster Ait.) stand management scheduling under fire risk. An application in Portugal

The paper discusses research aiming at the development of a management scheduling model for even-aged stands that may take into consideration fuel treatments to address the risk of wildfires. A Stochastic dynamic programming (SDP) approach is proposed to determine the policy (e.g. the fuel treatment and thinning schedules and the rotation age) that produces the maximum expected discounted net revenue. Fuel treatment activities encompass shrub cleanings. Emphasis was on combining a deterministic stand-level growth and yield model with wildfire occurrence and damage models to design a SDP network. SDP stages are defined by age and state variables include both the stand basal area and the number of years since the last fuel treatment. Fire occurrence and damage scenarios are addressed at each stage. Results from an application to Maritime pine (Pinus pinaster Ait.) stand management scheduling in Leiria National Forest, Portugal, are presented. Results suggest that the modeling strategy may help assess the impact of wildfire risk on the optimal stand management schedule. They confirm that the maximum expected discounted net revenues decreases. Further, albeit some timber may be salvaged after the wildfire, rotation age also decreases when the risk of fire is considered. Finally, they provide interesting insights about the role of thinning and fuel treatment policies in mitigating risk.     

Dynamical effects of biocontrol on the ecosystem: Benefits or harm?

Motivated by recent field studies on the effects of biocontrol beetle on invasive plants (Tamarix) on riparian ecosystems, we develop a simple three-species (the native consumer, the biocontrol agent, and their predator) model to explore potential dynamical benefits and harm of introducing a non-indigenous species into varied ecosystems with different habitat structures. Our proposed model assumes that (1) habitat consists of both native plants that are main food resources of the native consumer and invasive plants which are targeted food resources of the biocontrol agents; (2) the habitat structure is stable which has a fixed ratio of invasive plants; (3) biocontrol agents can defoliate invasive plants whose defoliations provide as additional food resources for the native consumer that could potentially increase the native consumer’s abundance; and (4) the predators feed on both the native consumer and the biocontrol agents. Our study shows that introducing biocontrol agents into the ecosystem can generate complicated dynamics that could be beneficial or harmful to the ecosystem depending on the environments: biocontrol agents could be beneficial by promoting its biodiversity such that all species could coexist; on the other hand, biocontrol agents could also be harmful by eliminating the native consumer or the predator. In addition, biocontrol agents could stabilize or destabilize the ecosystem depending on the habit structure and the local ecological environments. These theoretical results provide us potential decision-making tools that allow managers to better predict both safety and efficacy of candidate biological control agents are needed.     

PROTECTING A FOREST AGAINST FIRE: OPTIMAL PROTECTION PATTERNS AND HARVEST POLICIES

A model for determining the optimal level of expenditure on fire protection for a forest, through time, is developed. The model requires the specification of a function relating the probability of fire at a given age to the current level of expenditure. Use of the Pontryagin Maximum Principle enables the determination of the optimal protection schedule for a single rotation with a fixed cutting age. The optimal cutting age and protection schedule for an ongoing succession of stands on a site can be determined numerically by an iterative technique.     

Basis Reduction for the Shakedown Problem for Bounded Kinematic Hardening Material

Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto–plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient conditions stated in the corresponding static shakedown theorem. The finite element dicretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening.     

THE TRANSFORMATION OF LANDSCAPE: MODELING POLICY AND SOCIAL IMPACTS ON THE AGRICULTURAL LANDSCAPE OF LESVOS

ABSTRACT. The term landscape is more and more used as an “umbrella‘ concept, covering a series of cultural, productive and ecological processes. In order to uncover mechanisms, monitor transformations and predict changes, a complicated set of interacting factors has to be taken into account. This paper presents a model for estimating social and policy impacts on agricultural landscapes, based on the assumption that agricultural landscapes are shaped at” macro “(landscape) level by” micro “interventions at farm level. The model consists of three parts: an” ecological processes “part, which deals with processes that shape the ecological and aesthetic value of a landscape, a” population dynamics “part, which examines farmer population dynamics and a” policy impact “part, which deals with direct or indirect impacts on farming systems and farmer dynamics and refers to CAP Rural Development Measures. The model is applied for the olive and graze land agricultural landscapes of Lesvos (Greece). Results, apart from revealing landscape change patterns; help to illustrate some mechanisms behind this change and indicate that Rural Development Measures are inherent with minor but important malfunctions that cannot lead to sustainable landscape management and rural development in the area.     

Schedule execution for two-machine flow-shop with interval processing times

This paper addresses the issue of how to best execute the schedule in a two-phase scheduling decision framework by considering a two-machine flow-shop scheduling problem in which each uncertain processing time of a job on a machine may take any value between a lower and upper bound. The scheduling objective is to minimize the makespan. There are two phases in the scheduling process: the off-line phase (the schedule planning phase) and the on-line phase (the schedule execution phase). The information of the lower and upper bound for each uncertain processing time is available at the beginning of the off-line phase while the local information on the realization (the actual value) of each uncertain processing time is available once the corresponding operation (of a job on a machine) is completed. In the off-line phase, a scheduler prepares a minimal set of dominant schedules, which is derived based on a set of sufficient conditions for schedule domination that we develop in this paper. This set of dominant schedules enables a scheduler to quickly make an on-line scheduling decision whenever additional local information on realization of an uncertain processing time is available. This set of dominant schedules can also optimally cover all feasible realizations of the uncertain processing times in the sense that for any feasible realizations of the uncertain processing times there exists at least one schedule in this dominant set which is optimal. Our approach enables a scheduler to best execute a schedule and may end up with executing the schedule optimally in many instances according to our extensive computational experiments which are based on randomly generated data up to 1000 jobs. The algorithm for testing the set of sufficient conditions of schedule domination is not only theoretically appealing (i.e., polynomial in the number of jobs) but also empirically fast, as our extensive computational experiments indicate.     

HOW BIG AND HOW CLOSE? HABITAT PATCH SIZE AND SPACING TO CONSERVE A THREATENED SPECIES

Abstract. We present results of a spatially explicit, individual‐based stochastic dispersal model (HexSim) to evaluate effects of size and spacing of patches of habitat of Northern Spotted Owls (NSO; Strix occidentalis caurina) in Pacific Northwest, USA, to help advise recovery planning efforts. We modeled 31 artificial landscape scenarios representing combinations of NSO habitat cluster size (range 4–49 NSO pairs per cluster) and edge‐to‐edge cluster spacing (range 7–101 km), and an all‐habitat landscape. We ran scenarios using empirical estimates of NSO dispersal dynamics and distances and stage class vital rates (representing current population declines) and under adult survival rates adjusted to achieve an initially stationary population. Results suggested that long‐term (100‐yr) habitat occupancy rates are significantly higher with habitat clusters supporting ≥25 NSO pairs and ≤15 km spacing, and with overall landscapes of ≥35–40% habitat. Although habitat provision is key to NSO recovery, no habitat configuration provided for long‐term population persistence when coupled with currently observed vital rates. Results also suggested a key role of floaters (unpaired, nonterritorial, dispersing owls) in recolonizing vacant habitat, and that the floater population segment becomes increasingly depleted with greater population declines. We suggest additional areas of modeling research on this and other threatened species.     

Bond graph modelling of marine power systems

The main motivation for writing this article is to develop a model library for an All-Electric Ship that gives an opportunity to simulate both existing and new machinery systems without having to remodel the entire system each time. The model library should support the process of modelling and reuse, while also emphasizing openness to brace the modeller during the development and refinement phase. The bond graph approach is good when it comes to the physical modelling of systems and is a good tool for combining different energy domains to better help in understanding the system. In addition, a bond graph is a powerful method to find dependencies between various components. Using a causal analysis, any problems in the model, for example, algebraic constrains or dependent system variables, will be detected, and the necessary remodelling may be performed to handle such problems. The bond graph approach is therefore used when developing the component library. The component library consists of selected power producers such as diesel and gas engines, fuel cell and synchronous generator and power consumers such as asynchronous motor with a voltage source converter in addition to a generic load used for hotel and auxiliary loads. The library also consists of a ship model and propeller models.     

A model for fire propagation in arrays

Fire propagation through arrays of vertically mounted fuel elements is considered. Simple experiments and the work of Vogel and Williams [1] suggests a geometrical model for fire propagation from one element of the array to another. The advantages of a geometrical model are that an inclined base can easily be accommodated, and that a physical model for simulation of fire propagation naturally appears. From the former, a critical slope can be found beyond which heat transfer is no longer rate limiting.     

Asymptotic Profile of Species Migrating on a Growing Habitat

This paper deals with a diffusive logistic equation on one dimensional isotropically growing domain. The model equation on growing domains is first presented, and the comparison principle is then proved. The asymptotic behavior of temporal solutions to the reaction-diffusion problem is given by constructing upper and lower solutions. Our result shows that when the domain grows slowly, the species successfully spreads to the whole habitat and stabilizes at a positive steady state, while it dies out in the long run if the domain grows fast. Numerical simulations are also presented to illustrate the analytical result.     

具有连续时滞的非自治扩散Lotka-volterra模型的渐近性

持续生存概念是种群生态系统稳定性的一个重要描述,而研究竞争种群共存的问题是种群生态学的一个重要问题,考虑非自治的两种群L otka-vo lterra周期系数的时滞扩散摸型,通过构造李亚普诺夫泛函,微分不等式等获得了其一致持续生存及正周期解存在与全局渐近稳定的充分条件.     

Unveiling connectivity patterns of categories in complex systems: An application to human needs in urban places

We present a methodology based on weighted networks and dependence coefficients aimed at revealing connectivity patterns between categories. As a case study, it is applied to an urban place and at two spatial levels—neighborhood and square—where categories correspond to human needs. Our results show that diverse spatial levels present different and nontrivial patterns of need emergence. A numerical model indicates that these patterns depend on the probability distribution of weights. We suggest that this way of analyzing the connectivity of categories (human needs in our case study) in social and ecological systems can be used to define new strategies to cope with complex processes, such as those related to transition management and governance, urban-making, and integrated planning.