A hierarchical deductive approach for functional types in disturbed ecosystems

Abstract. We propose a hierarchical approach for plant functional classification in disturbed ecosystems to be used for vegetation modelling and global plant trait comparisons. Our framework is based on the persistence of plants at different levels of organization. We assume that the main parameters to determine persistence in chronically disturbed ecosystems are those related to: I ndividual‐persistence capacity, P ropagule‐persistence capacity (persistence at the population level), C ompetitive capacity (persistence at the community level) and D ispersal capacity (persistence at the landscape level). The IPCD approach is illustrated for fire‐prone and grazed ecosystems from the Mediterranean region and Australia and by assuming a binary classification of the four traits determining persistence which give a total 16 possible functional types. The IPCD framework provides a simple structured and synthetic view from which more elaborated schemes can be developed.     

A continuous migration model with stable demography

A probability model of a population undergoing migration, mutation, and mating in a geographic continuum R is constructed, and an integrodifferential equation is derived for the probability of genetic identity. The equation is solved in one case, and asymptotic analysis done in others. Individuals at x, y R in the model mate with probability V(x, y) dt in any time interval (t, t + dt). In two dimensions, if V(x,y) = V(x–y) where V(x) V(x/)/ ² approaches a delta function, the equilibrium probability of identity vanishes as 0. The asymptotic rate at which this occurs is discussed for mutation rates u u _o > 0 and for Cu , > 0, and u 0.Partially supported by NSF grant MCS79-03472Research was partially supported by Task Agreement No. DE-AT06-76EV71005 under Contract No. DE-AM06-76RL02225 between the U.S. Dept. Energy and the University of Washington     

A hierarchical aggregate data model with spatially correlated disease rates

The aggregate data study design (Prentice and Sheppard, 1995, Biometrika 82, 113-125) estimates individual-level exposure effects by regressing population-based disease rates on covariate data from survey samples in each population group. In this work, we further develop the aggregate data model to allow for residual spatial correlation among disease rates across populations. Geographical variation that is not explained by model predictors and has a spatial component often arises in studies of rare chronic diseases, such as breast cancer. We combine the aggregate and Bayesian disease-mapping models to provide an intuitive approach to the modeling of spatial effects while drawing correct inference regarding the exposure effect. Based on the results of simulation studies, we suggest guidelines for use of the proposed model.     

A Bayesian hierarchical model for categorical data with nonignorable nonresponse

Log-linear models have been shown to be useful for smoothing contingency tables when categorical outcomes are subject to nonignorable nonresponse. A log-linear model can be fit to an augmented data table that includes an indicator variable designating whether subjects are respondents or nonrespondents. Maximum likelihood estimates calculated from the augmented data table are known to suffer from instability due to boundary solutions. Park and Brown (1994, Journal of the American Statistical Association 89, 44-52) and Park (1998, Biometrics 54, 1579-1590) developed empirical Bayes models that tend to smooth estimates away from the boundary. In those approaches, estimates for nonrespondents were calculated using an EM algorithm by maximizing a posterior distribution. As an extension of their earlier work, we develop a Bayesian hierarchical model that incorporates a log-linear model in the prior specification. In addition, due to uncertainty in the variable selection process associated with just one log-linear model, we simultaneously consider a finite number of models using a stochastic search variable selection (SSVS) procedure due to George and McCulloch (1997, Statistica Sinica 7, 339-373). The integration of the SSVS procedure into a Markov chain Monte Carlo (MCMC) sampler is straightforward, and leads to estimates of cell frequencies for the nonrespondents that are averages resulting from several log-linear models. The methods are demonstrated with a data example involving serum creatinine levels of patients who survived renal transplants. A simulation study is conducted to investigate properties of the model.     

A model of migration modification

Two subpopulations whose different sizes are in a constant ratio interact via migration. The fitness of the diploid organisms is determined by two alleles at a single locus and by the niche the organism is in. The rates of migration depend upon two neutral modifier genes at a second locus. The second modifying allele is introduced into an equilibrium where the first modifying allele is fixed, and where the other two alleles are already polymorphic. It is shown that the new migration modifier is selected for when it reduces migration. The similarity between this result and some recombination modifier models is noted.     

A discrete model with density dependent fast migration

The aim of this work is to develop an approximate aggregation method for certain non-linear discrete models. Approximate aggregation consists in describing the dynamics of a general system involving many coupled variables by means of the dynamics of a reduced system with a few global variables. We present discrete models with two different time scales, the slow one considered to be linear and the fast one non-linear because of its transition matrix depends on the global variables. In our discrete model the time unit is chosen to be the one associated to the slow dynamics, and then we approximate the effect of fast dynamics by using a sufficiently large power of its corresponding transition matrix. In a previous work the same system is treated in the case of fast dynamics considered to be linear, conservative in the global variables and inducing a stable frequency distribution of the state variables. A similar non-linear model has also been studied which uses as time unit the one associated to the fast dynamics and has the non-linearity in the slow part of the system. In the present work we transform the system to make the global variables explicit, and we justify the quick derivation of the aggregated system. The local asymptotic behaviour of the aggregated system entails that of the general system under certain conditions, for instance, if the aggregated system has a stable hyperbolic fixed point then the general system has one too. The method is applied to aggregate a multiregional Leslie model with density dependent migration rates.     

城市生态系统灵敏度模型评述

系统复杂性是困扰城市生态系统研究和管理的因素之一,成熟的系统分析模型可以帮助研究者及管理者应对这种挑战。德国系统思想大师Vester教授开发的灵敏度模型就是致力于解决城市规划管理中的复杂性问题,并在一系列的实践应用中取得了显著成效。网状思维(Networked Thinking)与生物控制论观点是Vester教授的核心思想,也是灵敏度模型的思想基础。模型主要分为三大层次:最底层是以数据的收集与筛选过程为代表的信息组织层次;随后是系统解释层次,主要是对系统关系网进行控制论解释;最后是系统综合评价层次,采用生物控制论观点对系统结构、行为等进行检验与评价。为方便用户使用,模型被分解为9个标准步骤,每一部分都包含数个实用的数学分析工具。模型还明确提出了4个等级的系统控制论指标(或特征)体系,以帮助使用者更好地进行系统思考。灵敏度模型本身具有众多的原创性贡献,但同时也有一定的局限性。这些经验与教训为未来的城市生态系统建模工作提供了宝贵启示。     

A hierarchical model of whole assemblage island biogeography

Island systems have long played a central role in the development of ecology and evolutionary biology. However, while many empirical studies suggest species differ in vital biogeographic rates, such as dispersal abilities, quantitative methods have had difficulty incorporating such differences into analyses of whole‐assemblages. In particular, differences in dispersal abilities among species can cause variation in the spatial clustering and localization of species distributions. Here, we develop a single, hierarchical Bayes, assemblage‐wide model of 252 bird species distributions on the islands of northern Melanesia and use it to investigate a) whether dispersal limitation structures bird assemblages across the archipelago, b) whether species differ in dispersal ability, and c) test the hypothesis that wing aspect ratio, a trait linked to flight efficiency, predicts differences inferred by the model. Consistent with island biogeographic theory, we found that individual species were more likely to occur on islands with greater area, and on islands near to other islands where the species also occurred. However, species showed wide variation in the importance and spatial scale of these clustering effects. The importance of clustering in distributions was greater for species with low wing aspect ratios, and the spatial scale of clustering was also smaller for low aspect ratio species. These findings suggest that the spatial configuration of islands interacts with species dispersal ability to affect contemporary distributions, and that these species differences are detectable in occurrence patterns. More generally, our study demonstrates a quantitative, hierarchical approach that can be used to model the influence of dispersal heterogeneity in diverse assemblages and test hypotheses for how traits drive dispersal differences, providing a framework for deconstructing ecological assemblages and their drivers.     

A conceptual model of climate-related effects on lake ecosystems

Climatic variation and change affect the dynamics of organisms and ecosystem processes. Many studies in the past have analyzed and discussed various climate-driven effects on different components of the lake ecosystem. Only a few synthesis papers have been published in this field. In this overview, a conceptual model has been developed to help explain why lakes respond individually to climate. The model consists of two main components, a so-called Landscape Filter comprising the features of geographical position, catchment characteristics and lake morphology, and a so-called Internal Lake Filter, comprising the features of lake history and biotic/abiotic interactions. The application of this conceptual model on published literature findings illustrates the strength in this encompassing perspective. An assessment of current climate research methods is presented with some perspectives given.     

A hierarchical neural network model for associative memory

A hierarchical neural network model with feedback interconnections, which has the function of associative memory and the ability to recognize patterns, is proposed. The model consists of a hierarchical multi-layered network to which efferent connections are added, so as to make positive feedback loops in pairs with afferent connections. The cell-layer at the initial stage of the network is the input layer which receives the stimulus input and at the same time works as an output layer for associative recall. The deepest layer is the output layer for pattern-recognition. Pattern-recognition is performed hierarchically by integrating information by converging afferent paths in the network. For the purpose of associative recall, the integrated information is again distributed to lower-order cells by diverging efferent paths. These two operations progress simultaneously in the network. If a fragment of a training pattern is presented to the network which has completed its self-organization, the entire pattern will gradually be recalled in the initial layer. If a stimulus consisting of a number of training patterns superposed is presented, one pattern gradually becomes predominant in the recalled output after competition between the patterns, and the others disappear. At about the same time when the recalled pattern reaches a steady state in he initial layer, in the deepest layer of the network, a response is elicited from the cell corresponding to the category of the finally-recalled pattern. Once a steady state has been reached, the response of the network is automatically extinguished by inhibitory signals from a steadiness-detecting cell. If the same stimulus is still presented after inhibition, a response for another pattern, formerly suppressed, will now appear, because the cells of the network have adaptation characteristics which makes the same response unlikely to recur. Since inhibition occurs repeatedly, the superposed input patterns are recalled one by one in turn.     

A hierarchical Bayesian model for next-generation population genomics

The demography of populations and natural selection shape genetic variation across the genome and understanding the genomic consequences of these evolutionary processes is a fundamental aim of population genetics. We have developed a hierarchical Bayesian model to quantify genome-wide population structure and identify candidate genetic regions affected by selection. This model improves on existing methods by accounting for stochastic sampling of sequences inherent in next-generation sequencing (with pooled or indexed individual samples) and by incorporating genetic distances among haplotypes in measures of genetic differentiation. Using simulations we demonstrate that this model has a low false-positive rate for classifying neutral genetic regions as selected genes (i.e., Φ(ST) outliers), but can detect recent selective sweeps, particularly when genetic regions in multiple populations are affected by selection. Nonetheless, selection affecting just a single population was difficult to detect and resulted in a high false-negative rate under certain conditions. We applied the Bayesian model to two large sets of human population genetic data. We found evidence of widespread positive and balancing selection among worldwide human populations, including many genetic regions previously thought to be under selection. Additionally, we identified novel candidate genes for selection, several of which have been linked to human diseases. This model will facilitate the population genetic analysis of a wide range of organisms on the basis of next-generation sequence data.     

A biologically inspired hierarchical goal directed navigation model

We propose an extended version of our previous goal directed navigation model based on forward planning of trajectories in a network of head direction cells, persistent spiking cells, grid cells, and place cells. In our original work the animat incrementally creates a place cell map by random exploration of a novel environment. After the exploration phase, the animat decides on its next movement direction towards a goal by probing linear look-ahead trajectories in several candidate directions while stationary and picking the one activating place cells representing the goal location. In this work we present several improvements over our previous model. We improve the range of linear look-ahead probes significantly by imposing a hierarchical structure on the place cell map consistent with the experimental findings of differences in the firing field size and spacing of grid cells recorded at different positions along the dorsal to ventral axis of entorhinal cortex. The new model represents the environment at different scales by populations of simulated hippocampal place cells with different firing field sizes. Among other advantages this model allows simultaneous constant duration linear look-ahead probes at different scales while significantly extending each probe range. The extension of the linear look-ahead probe range while keeping its duration constant also limits the degrading effects of noise accumulation in the network. We show the extended model’s performance using an animat in a large open field environment.     

A hierarchical polar coordinate model for epimorphic regeneration

In the framework of polar coordinates three rules are postulated which can describe epimorphic regeneration in amphibian limbs. The rules can be seen as an extension of the polar coordinate model. When cells with different positional values are confronted, cell proliferation at the junction restores the continuity of positional values. Reestablishment of continuity is associated with the eventual congruence of the intercalating cell sequence with the host or graft, or both. The intercalating contours can be simple or twisted. The possible contours are graded within a plausible hierarchical scheme where congruent paths are favored versus non-congruent paths and simple contours are favored versus twisted contours. The model correctly predicts the multiplicity, position and different structures of supernumerary outgrowths resulting from both contralateral graftings and 180 degrees ipsilateral limb rotations. Development and regeneration of mirror-symmetric limbs are also accounted for. Several other experimental results are in agreement with the model. Many model predictions and correlations still remain to be tested.     

A hierarchical goal-seeking model of the control of breathing

A model of the overall control of the breathing pattern is presented. The model has the structure of a two-level optimization problem where the lower level criteria determine the shape of the airflow during inspiration and expiration and the higher level criterion determines the values of the other control variables. The model's general formulation makes it possible to obtain predictions of far greater accuracy than before because the previous restrictive assumptions have been avoided by increasing the number of independent control variables. In this model the control variables are the inspiratory time, expiratory time, duration of the end expiratory pause, change in the end expiratory lung volume, the dead space volume, the tidal volume, and the airflow pattern during the cycle. The model's optimization problem has clear and unique minima with respect to each control variable over a wide range of parameter values. Thus the model can be used to predict the effects of various environmental changes.     

A model of evolutionary appearance of dissipative structure in ecosystems

The interrelation between autonomous oscillations in local systems and stable dissipative structures in spatially distributed systems is analyzed. Darwinian evolution in populations comprising the ecosystem is shown to be able to cause the qualitative rearrangements of dynamic modes and smooth appearance of oscillations in local systems. The same evolutionary mechanisms analyzed within bilocal systems, may lead to appearance of dissipative structures (both smooth and sharp).     

A note on the island model with sex dependent migration

Summary A theoretical calculation is presented which extends Wright's island model of drift and migration to differential migration between the two sexes. In this circumstance, local demes no longer have Hardy-Weinberg frequencies. There may be local heterozygote excess or deficiency depending, respectively, on whether migration occurs before or after mating. The magnitude of the local departure from Hardy-Weinberg is directly proportional to the difference between the migration parameters of the two sexes. These results could have important implications for studies where genetic markers are used for inferring population structure. An example from a study of Marmot colonies is cited.     

Acceptor control in model ecosystems

The analysis of models of evolutionary games requires explicit consideration of both evolutionary game rules and mutants which infinitesimally break these rules. For example, the Scotch Auction is an evolutionary game which lacks both a rule-obeying evolutionarily stable strategy and an asymptotically stable polymorphism of rule-obeying strategies. However, an infinitesimal rule-breaking, or cheating, mutant can be found which is an evolutionarily stable strategy against rule-obeying strategies. Such cheating strategies can spread through populations initially playing the Scotch Auction, effectively changing the rules of the game. Moreover, the extent of such rule-change will then tend to increase. Thus, the Scotch Auction is a transient evolutionary game, being the initial point of a seemingly orthogenetic game evolutionary process. This sort of transience suggests that the “progressive” nature of evolution may be due in part to those game features of evolutionary processes which make the success of adaptations relative to the level of extant adaptation among competitors, predators, etc.