A Markov model for assessing ecological stability properties

Ecological systems are frequently modeled as dynamic systems. It is natural then to use the techniques of dynamic systems theory to analyze such models. However, the methods and results that are produced by dynamic systems theory do not always capture the aspects of ecological systems that are of greatest interest to managers and decision-makers. We identify some of the challenges of using dynamic systems theory to explore ecological systems and propose an alternative approach that emphasizes the understanding of transient effects in light of uncertainty and variability. We illustrate this method by an examination of a model for phosphorus levels in fresh water lakes.     

The pattern of species turnover resulting from stochastic population dynamics: The model and field data

The model of random population dynamics in a sampling site returns geometric distribution of longevities of continuous presence (=persistence) and Poisson distribution of the presence–absence transitions. This discrete-time stochastic process describes the presence–absence pattern observed in the beetles surveyed 6 years on Mount Carmel, Israel. Homogeneous pools of species mostly on the Families rank, exhibit the predicted by the model patterns. Conformity to an ergodic hypothesis is the criterion of ecological homogeneity. This criterion assumes the equivalence of short-term behavior of entire pool and long-term behavior of any species from this pool. The pool of all 801 species of Order Coleoptera does not match the model. Thus a taxon of an arbitrary rank may not be considered a priory as a unit of ecological study. Determined from field data parameters of the model are biased and magnitude of the bias depends on longevity of the survey. Parameter of distribution depends also on species tolerance, which is the level adaptation of given species to given environment in given time interval. Random process of species turnover may be considered as a game of species to gain their presence against deteriorative fluctuations of environmental conditions.     

Testing the Stochastic Dynamic Methodology (StDM) as a management tool in a shallow temperate estuary of south Europe (Mondego, Portugal)

A long-term monitoring program has been carried out since the early 1990s in the Mondego estuary, on Portugal's west coast, which is presently under heavy human pressure. In this shallow warm-temperate estuary, a significant macroalgal proliferation has been observed, which is a clear sign of nutrient enrichment. As a result of competition with algae, the extension of the seagrass meadows (mainly Zostera noltii) has been reduced. The present paper examined the applicability of a holistic Stochastic Dynamic Methodology (StDM) in predicting the tendencies of trophic key-components (macrophytes, macroalgae, benthic macroinvertebrate and wading birds) as a response to the changes in estuarine environmental conditions. The StDM is a sequential modelling process developed in order to predict the ecological status of changed ecosystems, from which management strategies can be designed. The data used in the dynamic model construction included true gradients of environmental changes and was sampled from January 1993 to September 1995 and from December 1998 to December 2005. The dynamic model developed was preceded by a conventional multivariate statistical procedure performed to discriminate the significant relationships between the selected ecological components. The model validation was based on independent data collected from January 1996 to January 1997 and from February 1999 to April 2000 for all the state variables considered. Overall, the simulation results are encouraging since they seem to demonstrate the StDM reliability in capturing the trophic dynamics of the studied estuary, by predicting the behavioural pattern for the most part of the components selected, with a focus on the Zostera noltii meadows recovery after the implementation of important management measures.     

感潮河段水污染控制的随机方法

根据Liouville定理,推导了一个随机动态水质模型,并提出了相应的数值求解方法,该模型用于感潮河段的水质模拟及控制,获得污染物浓度变化的主要趋势、波动范围、浓度超标风险率及其与超标时间长的关系等,较好地揭示了污染物浓度的不确定性变化对水污染控制的影响.     

Energetic state and the performance of dawn chorus in silvereyes (Zosterops lateralis)

Stochastic dynamic programming (SDP) models predict that males singing to attract a mate should concentrate singing in what has been termed the dawn chorus. This is because male birds should have a variable surplus of fat in the morning that can be used to fuel singing, with the amount of fat available dependent upon such factors as his quality, foraging success and risk of predation. In this manner, the dawn chorus can act as an indicator of male quality in the context of female mate choice. We test a key prediction of SDP models of singing behaviour that males with greater fat levels should sing more. We conducted an experiment where we recorded the dawn chorus of male silvereyes (Zosterops lateralis) on three consecutive days. Each male received supplementary food on the second day, which enabled us to sample his dawn chorus before, during and after food supplementation. We also collected data on the effect of supplementary food on the body mass of silvereyes. As predicted by SDP models, we found that silvereyes sang for a greater proportion of the time after receiving supplementary food. Supplementary food also had a significant effect on the complexity of a male song, indicating that males not only increased the quantity of their song but also the quality of their song when they received extra food. As the provision of supplementary food significantly increased the mass of fed birds, our results support a causal link between male energy reserves and his ability to perform the dawn chorus.     

The Effect of Jump on Evaluating Natural Resource Investments

Abstract

The evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices. It is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing managing. This paper describes a model for evaluating natural resource investments under uncertainty from a new perspective. The previous works in this field mostly regard the movements of natural resource prices as a continuous GBM process, which pays few attentions to the shock of unexpected bad news. Our model provides the first theoretical method to analyze the impact of such “jump” on investment decisions. It concludes that the more frequently bad news happens, the earlier a project will be invested.     

Implications of network particle tracking (NPT) for ecological model interpretation

Network particle tracking (NPT), building on the foundation of network environ analysis (NEA), is a new development in the definition of coherence relations within and between connected systems. This paper evaluates three ecosystem models in a comparison of throughflow- and storage-based NEA and NPT. Compartments in models with high indirect effects and Finn cycling showed low correlation of NEA storage and throughflow with particle repeat visits and numbers of particles in compartments at steady state. Conversely, the correlation between NEA and NPT results was high with two models having lower indirect effects and Finn cycling. Analysis of ecological orientors associated with NEA showed NPT to fully support conventional NEA results when the common conditions of donor control and steady state are satisfied. Particle trajectories are recorded in the new concept of a particle “passport”. Ability to track and record particle in-system histories enables views of multiple scales and opens the possibility of making pathway-dependent modeling decisions. NPT may also enable modeling of time, allowing integration of Newtonian, organismal and stochastic modeling perspectives in a single comprehensive analysis.     

The theoretical value of encounters with parasitized hosts for parasitoids

A female parasitoid searching for hosts in a patch experiences a diminishing encounter rate with unparasitized and thus suitable hosts. To use the available time most efficiently, it constantly has to decide whether to stay in the patch and continue to search for hosts or to search for and travel to another patch in the habitat. Several informational cues can be used to optimize the searching success. Theoretically, encounters with unparasitized hosts should lead to a prolonged search in a given patch if hosts are distributed contagiously. The results of empirical studies strongly support this hypothesis. However, it has, to date, not been investigated theoretically whether encounters with already parasitized hosts (which usually entail time costs) provide a parasitoid with valuable information for the optimization of its search in depletable patches, although the empirical studies concerning this question so far have produced ambiguous results. Building on recent advances in Bayesian foraging strategies, we approached this problem by modeling a priori searching strategies (which differ in the amount of information considered) and then testing them in computer simulations. By comparing the strategies, we were able to determine whether and how encounters with already parasitized hosts can yield information that can be used to enhance a parasitoid’s searching success.

A STOCHASTIC DYNAMIC PROGRAMMING MODEL FOR THE OPTIMUM OPERATION OF A MULTI-PURPOSE RESERVOIR1

ABSTRACT: The main objective of this paper is to present a stockastic dynamic programming model useful in determining the optimal operating policy of a single multipurpose surface reservoir. It is the unreliability of forecasting the amount of future streamflow which makes the problem of a reservoir operation a stochastic process. In this paper the stochastic nature of the streamflow is taken into account by considering the correlation between the streamflows of each pair of consecutive time intervals. This interdependence is used to calculate the probability of transition from a given state and stage to its succeeding ones. A dynamic programming model with a physical equation and a stochastic recursive equation is developed to find the optimum operational policy. For illustrative purposes, the model is applied to a real surface water reservoir system.