Deterministic in contrast to stochastic modeling.

The first attempt to model a process is often a deterministic setup with differential equations. The existing stochastic influence is suppressed and hopefully negligible. However, sometimes the stochastic component is important. We demonstrate and clarify this for a growth process. The deterministic approach is given by Yn + 1 = Yn + g(Yn) or dYt = g(Yt)dt, Y0 = 1, g a positive function. The corresponding stochastic equation is Xn + 1 = Xn + g(Xn)(1 + xi n) or dXt = g(Xt)dt + f(Xt)dWt, xi some random variable, W the Brownian motion. We compare the asymptotic behavior of the deterministic solution versus the stochastic solution.     

Deterministic and stochastic features of rhythmic human movement

The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method’s merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.     

Phylogenetic distance can predict susceptibility to attack by natural enemies

If related species share enemies, variation in the damage experienced by species within a community may be predictable based on phylogeny. We examined the hypothesis that plant species more closely related to other community members experience greater herbivory by assessing leaf damage to native and exotic plants in two North American communities: an Eastern hardwood forest and a Rocky Mountain montane community. Pairwise phylogenetic distances between focal species and the hundreds of other native species in each community were calculated. We examined the influence of four measures of relatedness within each community: NND (phylogenetic distance to the nearest native neighbor), MPD (mean phylogenetic distance to the native species in the community), and two new metrics, MIPD (mean inverse phylogenetic distance) and INND (inverse nearest neighbor distance). These new metrics assume a nonlinear increase in interaction strength with relatedness; in the context of natural enemies, they posit that the sharing of enemies between any two species increases nonlinearly with their relatedness. Using regression models, we found that herbivore damage decreased with decreasing phylogenetic similarity of focal species to native species (as measured by MIPD) in both sites, although the pattern was significant only for native focal species in the montane community and exotic focal species in the hardwood forest. Similar decreases in herbivory with decreasing relatedness were detected using INND (montane natives) and MPD (hardwood forest exotics). There was no significant relationship between NND and herbivory for any of the four site by focal plant origin combinations. Our results are the first to support the hypothesis that native species can escape attack as a function of their phylogenetic dissimilarity to the larger community of native species, and to demonstrate that exotic species show these patterns in the wild (as opposed to in common gardens). We suggest that phylogenetic distance metrics assuming a nonlinear increase in interaction strength with relatedness show promise for broader application.     

Deterministic or stochastic choices in retinal neuron specification

There are two views on vertebrate retinogenesis: a deterministic model dependent on fixed lineages and a stochastic model in which choices of division modes and cell fates cannot be predicted. In this issue of Neuron, He et?al. (2012) address this question in zebrafish using live imaging and mathematical modeling.     

居竹伪角蚜及其3种主要天敌的空间格局研究

对危害孝顺竹Bambusa multiplex的居竹伪角蚜Pseudoregma bambusicola及其3种主要天敌的卒间分布进行调查,聚集度指标表明竹蚜在竹林问为聚集分布,其种群密度在一定时间内较为稳定.天敌蚜厌蝶Taraka hama-da、赤星瓢虫Lemnia sauciaia和食蚜虻Asilichae.sp.在竹林中主要符合负二项式分布和P-E核心分布,为小均匀的聚集分布,存在由点片向四周扩散的现象,频次分析和聚集度指标的分析结果基本一致,其中瓢虫的聚集程度不及另外2种天敌的明显.对竹蚜和天敌的相关关系分析表明,仪食蚜虻的分布与竹蚜之间表现为负相关(r=-0.6341),食蚜虻的活动受蚜群分布的影响最大,而其余2种天敌的取食范围不受限制.     

A stochastic approach to predator-prey models

A deterministic investigation of a linear differential equation system which describes predator vs prey behavior as a function of equilibrium densities and reproductive rates is given. A more realistic structure of this model in a stochastic framework is presented. The reproductive rates and initial population sizes are considered to be random variables and their probabilistic behavior characterized by various joint probability distributions. The deterministic behaviors of the prey and predator species as functions of time are compared with the mean behaviors in the stochastic model.     

Attractiveness of Michigan native plants to arthropod natural enemies and herbivores

The use of plants to provide nectar and pollen resources to natural enemies through habitat management is a growing focus of conservation biological control. Current guidelines frequently recommend use of annual plants exotic to the management area, but native perennial plants are likely to provide similar resources and may have several advantages over exotics. We compared a set of 43 native Michigan perennial plants and 5 frequently recommended exotic annual plants for their attractiveness to natural enemies and herbivores for 2 yr. Plant species differed significantly in their attractiveness to natural enemies. In year 1, the exotic annual plants outperformed many of the newly established native perennial plants. In year 2, however, many native perennial plants attracted higher numbers of natural enemies than exotic plants. In year 2, we compared each flowering plant against the background vegetation (grass) for their attractiveness to natural enemies and herbivores. Screening individual plant species allowed rapid assessment of attractiveness to natural enemies. We identified 24 native perennial plants that attracted high numbers of natural enemies with promise for habitat management. Among the most attractive are Eupatorium perfoliatum L., Monarda punctata L., Silphium perfoliatum L., Potentilla fruticosa auct. non L., Coreopsis lanceolata L., Spiraea alba Duroi, Agastache nepetoides (L.) Kuntze, Anemone canadensis L., and Angelica atropurpurea L. Subsets of these plants can now be tested to develop a community of native plant species that attracts diverse natural enemy taxa and provides nectar and pollen throughout the growing season.     

Survival of three commercially available natural enemies exposed to Michigan wildflowers

Flowering plants are often used in habitat management programs to conserve the arthropod natural enemies of insect pests. In this study, nine species of flowering plants representing six families commonly found in North America east of the Rocky Mountains were evaluated based on how much they extended the lifespans of three commercially available natural enemy species in cages with cut flower stems compared with cages containing water only. The natural enemies used in the experiments were a lady beetle (Coleoptera: Coccinellidae: Hippodamia convergens Guérin-Méneville), a predatory bug (Heteroptera: Anthocoridae: Orius insidiosus (Say)), and an aphid parasitoid (Hymenoptera: Braconidae: Aphidius colemani Viereck). The plant species that most extended the lifespans of all three natural enemies were Monarda fistulosa L. (Lamiaceae), Solidago juncea Aiton (Asteraceae), and Daucus carota L. (Apiaceae). Agastache nepetoides (L.) Kuntze (Lamiaceae), Lobelia siphilitica L. (Campanulaceae), and Trifolium pratense L. (Fabaceae) were intermediate in their support of natural enemies. One plant species, Penstemon hirsutus (L.) Willdenow (Scrophulariaceae), did not contribute to the longevity of natural enemies any more than water alone. These results emphasize the need for multi-species evaluations of flowering plants for conservation biocontrol programs, and the variability in plant value for natural enemies.     

On the role of spatial stochastic models in understanding landscape indices in ecology

Spatial stochastic models play an important role in understanding and predicting the behaviour of complex systems. Such models may be implemented with explicit knowledge of only a limited number of parameters relating to spatial relationships among locations. Consequently, they are often used instead of deterministic‐mechanistic models, which may potentially require an unrealistically large number of parameters. Currently, in contrast to spatial stochastic models, the parameterization of the joint spatial distribution of objects in landscape models is more often implicit than explicit. Here, we investigate the similarities and differences between bona fide spatial stochastic models and landscape models by focusing mostly on the relationships between processes, their realizations (patterns), representation and measurement, and their use in exploratory as well as confirmatory data analysis. One of the most important outcomes of recognizing the importance of stochastic processes is the acknowledgement that the spatial pattern observed in a landscape is only one realization of that process. Hence, while ecologists have been using landscape pattern indices (LPIs) to characterize landscape heterogeneity and/or make inferences about processes shaping the landscape, no stochastic modelling framework has been developed for their proper statistical elucidation. Consequently, several (mis)uses of LPIs draw conclusions about landscapes which are suspect. We show that several reports about sensitivities of LPIs to measurements have common roots that can be made explicitly manageable by adopting stochastic models of spatial structure. The key parameters of these stochastic models are composition and configuration, which, in general, cannot be estimated independently from each other. We outline how to develop the stochastic framework to interpret observations and make some recommendations to practitioners about everyday usage. The conceptual linkages between patterns and processes are particularly important in light of recent efforts to bridge the static‐structural and the dynamic‐analytic traditions of ecology.     

Deterministic genetic models in varying environments

Summary J. B. S. Haldane and S. D. Jayakar [J. Genet. 58, 237–242 (1963)] argue that, when genotype fitnesses fluctuate from generation to generation, if the geometric and arithmetic means of the fitnesses satisfy certain inequalities, there will be a protected polymorphism. Their assertions are biologically interesting, but their mathematical analysis is not sufficient to support their conclusions. We present a firm mathematical analysis and several examples that demonstrate the need for stronger hypotheses and, in some cases, weaker conclusions.Journal Paper No. J-10136 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project 1669. Partial support by National Institutes of Health, Grant GM 13827     

Using network models to approximate spatial point-process models

Spatial effects are fundamental to ecological and epidemiological systems, yet the incorporation of space into models is potentially complex. Fixed-edge network models (i.e. networks where each edge has the same fixed strength of interaction) are widely used to study spatial processes but they make simplistic assumptions about spatial scale and structure. Furthermore, it can be difficult to parameterize such models with empirical data. By comparison, spatial point-process models are often more realistic than fixed-edge network models, but are also more difficult to analyze. Here we develop a moment closure technique that allows us to define a fixed-edge network model which predicts the prevalence and rate of epidemic spread of a continuous spatial point-process epidemic model. This approach provides a systematic method for accurate parameterization of network models using data from continuously distributed populations (such as data on dispersal kernels). Insofar as point-process models are accurate representations of real spatial biological systems, our example also supports the view that network models are realistic representations of space.     

Deterministic analysis of stochastic bifurcations in multi-stable neurodynamical systems

Many perceptual and cognitive processes, like decision-making and bistable perception, involve multistable phenomena under the influence of noise. The role of noise in a multistable neurodynamical system can be formally treated within the Fokker–Planck framework. Nevertheless, because of the underlying nonlinearities, one usually considers numerical simulations of the stochastic differential equations describing the original system, which are time consuming. An alternative analytical approach involves the derivation of reduced deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. The study of the reduced deterministic system avoids time consuming computations associated with the need to average over many trials. We apply this technique to describe multistable phenomena. We show that increasing the noise amplitude results in a shifting of the bifurcation structure of the system.     

Potential contribution of natural enemies to patterns of local adaptation in plants

Genetic differentiation among plant populations and adaptation to local environmental conditions are well documented. However, few studies have examined the potential contribution of plant antagonists, such as insect herbivores and pathogens, to the pattern of local adaptation. Here, a reciprocal transplant experiment was set up at three sites across Europe using two common plant species, Holcus lanatus and Plantago lanceolata. The amount of damage by the main above-ground plant antagonists was measured: a rust fungus infecting Holcus and a specialist beetle feeding on Plantago, both in low-density monoculture plots and in competition with interspecific neighbours. Strong genetic differentiation among provenances in the amount of damage by antagonists in both species was found. Local provenances of Holcus had significantly higher amounts of rust infection than foreign provenances, whereas local provenances of Plantago were significantly less damaged by the specialist beetle than the foreign provenances. The presence of surrounding vegetation affected the amount of damage but had little influence on the ranking of plant provenances. The opposite pattern of population differentiation in resistance to local antagonists in the two species suggests that it will be difficult to predict the consequences of plant translocations for interactions with organisms of higher trophic levels.     

Impact of natural enemies on obligately cooperative breeders

Obligately cooperative breeders (cooperators) display a negative growth rate once they fall below a minimum density. Constraints imposed by natural enemies, such as predators or competitors, may push cooperator groups closer to this threshold, thus increasing the risk that stochastic fluctuations will drive them below it. This may indirectly drive these groups to extinction, thereby increasing the risk of population extinction. In this paper, we construct mathematical models of the dynamics of groups of cooperators and non-cooperators in the presence of two types of enemies: enemies whose dynamics do not depend on the dynamics of their victim (e.g., amensal competitor, generalist predator) and those whose dynamics do. In the latter case, we distinguish positive (e.g., specialist predator) and negative (e.g., bilateral competitor) reciprocal effects. These models correspond to the classical amensal, predation and competition models, in the presence of an Allee effect. We then develop the models to study consequences at the population level. By comparing models with or without an Allee effect, we show that enemies decrease the group size of cooperators more than that of non-cooperators, and this increases their group extinction risk. We also demonstrate how an Allee effect at a lower dynamical level can have consequences at a higher level: inverse density dependence at the group level generated lower population sizes and higher risks of population extinction. Our results also suggest that demographic compensation can be achieved by cooperators through an increased intrinsic growth rate, or by decreasing the enemy constraint. Both of these types of compensation have been observed in empirical studies of cooperators.     

The natural enemies of Bemisia argentifolii in Martinique

An eight year survey wasconducted in Martinique on vegetable crops andweeds to develop a list of the natural enemiesof the whitefly Bemisia argentifoliiBellows and Perring. More than fifteen speciesof predators and parasitoids were found as wellas one entomopathogenic fungus (Paecilomyces sp.). The primary predators wereladybirds (Delphastus pusillus and D. pallidus) and bugs (Nesidiocoris tenuis, Macrolophus cf. caliginosus, Orius insidiosus). The mostcommon parasitoids were Eretmocerustejanus, Encarsia luteola, E. nigricephala, E. transvena and Amitus bennetti. Observations on the biologyand distribution of these natural enemies are provided.