Regression analysis of forest inventory data with time and space dependencies

In this paper the data of a forest health inventory are analyzed. Since 1983 the degree of defoliation, together with various explanatory variables (covariates) concerning stand, site, soil and weather, are recorded by the second of the two authors, in the forest district of Rothenbuch (Spessart, Bavaria). The focus is on the space and time dependencies of the data. The mutual relationship of space-time functions and the set of covariates is evaluated. For this we use generalized linear models (GLMs) for ordinal response variables and semiparametric estimation approaches. By using goodness-of-fit measures it turns out that (i) the contribution of space-time functions is quantitatively comparable with that of the set of covariates, (ii) the contribution of space-time functions is small compared with the contribution of a set of variables describing the last-year and neighboring response values. By applying appropriate residual methods a detailed analysis of the individual sites in the area can be carried out. This analysis reveals where the predictive power of the covariates fail to explain the observed defoliation.     

Continuous-time correlated random walk model for animal telemetry data

We propose a continuous-time version of the correlated random walk model for animal telemetry data. The continuous-time formulation allows data that have been nonuniformly collected over time to be modeled without subsampling, interpolation, or aggregation to obtain a set of locations uniformly spaced in time. The model is derived from a continuous-time Ornstein-Uhlenbeck velocity process that is integrated to form a location process. The continuous-time model was placed into a state-space framework to allow parameter estimation and location predictions from observed animal locations. Two previously unpublished marine mammal telemetry data sets were analyzed to illustrate use of the model, by-products available from the analysis, and different modifications which are possible. A harbor seal data set was analyzed with a model that incorporates the proportion of each hour spent on land. Also, a northern fur seal pup data set was analyzed with a random drift component to account for directed travel and ocean currents.     

Hierarchical modeling for extreme values observed over space and time

We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values. We assume that the observations follow generalized extreme value (GEV) distributions whose locations and scales are jointly spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization. In addition, there is temporal dependence in the locations. There are various ways to provide appropriate specifications; we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for parameters and to provide spatio–temporal predictions. We fit the models to a set of gridded interpolated precipitation data collected over a 50-year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be the best choice of model.

CUSUM environmental monitoring in time and space

We consider the situation where there are n sampling sites in an area, with an environmental variable measured at some or all of the sites at m sample times. We assume that there is interest in knowing whether the environmental variable displays systematic changes over time at the sites. A cumulative sum type of analysis with associated randomization tests has been proposed before for this situation, when there is negligible correlation between the observations in different times at one site, and no correlation between the results at different sites. A modification that allows for serial correlation at the individual sites but with no correlation between sites has also been proposed before. In the present paper we discuss how the method can be modified further to allow for spatial correlation between the sites, by applying it only to a reduced set of sites that are far enough apart to give effectively independent results. Simulation results indicate that this strategy is effective providing that the level of spatial correlation is not too high.     

A nonparametric procedure for analyzing repeated measures of spatially correlated data

Many agricultural, biological, and environmental studies involve detecting temporal changes of a response variable, based on data observed at sampling sites in a spatial region and repeatedly over several time points. That is, data are repeated measures over time and are potentially correlated across space. The traditional repeated-measures analysis allows for time dependence but assumes that the observations at different sampling sites are mutually independent, which may not be suitable for field data that are correlated across space. In this paper, a nonparametric large-sample inference procedure is developed to assess the time effects while accounting for the spatial dependence using a block bootstrap. For illustration, the methodology is applied to describe the population changes of root-lesion nematodes over time in a production field in Wisconsin.     

Pastoralists' responses to variation of rangeland resources in time and space.

We explore the response of pastoralists to rangeland resource variation in time and space, focusing on regions where high variation makes it unlikely that an economically viable herd can be maintained on a single management unit. In such regions, the need to move stock to find forage in at least some years has led to the evolution of nomadism and transhumance, and reciprocal grazing agreements among the holders of common-property rangeland. The role of such informal institutions in buffering resource variation is well documented in some Asian and African rangelands, but in societies with formally established private-property regimes, where we focus, such institutions have received little attention. We examine agistment networks, which play an important role in buffering resource variation in modern-day Australia. Agistment is a commercial arrangement between pastoralists who have less forage than they believe they require and pastoralists who believe they have more. Agistment facilitates the movement of livestock via a network based largely on trust. We are concerned exclusively with the link between the characteristics of biophysical variation and human aspects of agistment networks, and we developed a model to test the hypothesis that such a link could exist. Our model builds on game theory literature, which explains cooperation between strangers based on the ability of players to learn whom they can trust. Our game is played on a highly stylized landscape that allows us to control and isolate the degree of spatial variation and spatial covariation. We found that agistment networks are more effective where spatial variation in resource availability is high, and generally more effective when spatial covariation is low. Policy design that seeks to work with existing social networks in rangelands has potential, but this potential varies depending on localized characteristics of the biophysical variability.     

Hierarchical Bayesian strategy for modeling correlated compositional data with observed zero counts

This article proposes a hierarchical multivariate conditional autoregressive model applied to a compositional response vector. We particularly focus on situations when the composition is discrete occurring when observations are based on small multinomial counts. We address drawbacks that exist in current modeling approaches for such data. Our hierarchical model will be demonstrated with data used to help manage a commercial sockeye salmon fishery in the Fraser River of British Columbia.     

Social information use is a process across time, space, and ecology, reaching heterospecifics

Decision making can be facilitated by observing other individuals faced with the same or similar problem, and recent research suggests that this social information use is a widespread phenomenon. Implications of this are diverse and profound: for example, social information use may trigger cultural evolution, affect distribution and dispersal of populations, and involve intriguing cognitive traits. We emphasize here that social information use is a process consisting of the scenes of (1) event, (2) observation, (3) decision, and (4) consequence, where the initial event is a scene in such a process of another individual. This helps to construct a sound conceptual framework for measuring and studying social information use. Importantly, the potential value of social information is affected by the distance in time, space, and ecology between the initial observation and eventual consequence of a decision. Because negative interactions between individuals (such as direct and apparent competition) also depend on the distance between individuals along these dimensions, the potential value of information and the negative interactions may form a trade-off situation. Optimal solutions to this trade-off can result in adaptively extended social information use, where using information gathered some time ago, some distance away, and from ecologically different individuals is preferred. Conceivably, using information gathered from a heterospecific individual might often be optimal. Many recent studies demonstrate that social information use does occur between species, and the first review of published cases is provided here. Such interaction between species, especially in habitat selection, has important consequences for community ecology and conservation. Adaptively extended social information use may also be an important evolutionary force in guild formation. Complex coevolutionary patterns may result depending on the effect of information use on the provider of information.     

Mouse lemurs in space and time: a test of the socioecological model

Socioecological theory predicts that the distribution of fertile females in space and time is the major determinant of male spacing behavior and mating strategies. Using a small nocturnal Malagasy primate, the gray mouse lemur (Microcebus murinus), we determined the spatiotemporal distribution of estrous females during the brief annual mating season to examine the predictive power of the socioecological model for male mating strategies. Mouse lemurs are particularly interesting in this respect because this polygynous species is characterized by seasonal reproduction, seasonally reversed sexual dimorphism, and relatively large testes. All resident animals in our 8-ha study area, a total of 30 adult males and 27 adult females, were individually marked and regularly recaptured to determine female reproductive status and to obtain home range data. We found that the mating season is limited to 4 weeks following female emergence from hibernation. Only 3-9 females could have synchronized estruses during a given week, indicating a moderately high male monopolization potential. However, receptive females were not spatially clumped and male ranges overlapped with those of many other rivals. Therefore, we suggest that individual powerful males may be unable to defend exclusive permanent access to receptive females because of prohibitive costs of range defense resulting from the strongly male-biased operational sex ratio and the corresponding intruder pressure. Our general conclusions are (1) that the socioecological model provides a useful heuristic framework for the study of mating systems, but that (2) it does not specify the degree of spatiotemporal clumping of receptive females at which male mating strategies switch among mate guarding, spatial exclusion of rivals, and roaming, and that (3) the operational sex ratio can have profound effects on male mating strategies as well.     

Ecosystem states: Creating a data-derived, ecosystem-scale ecological response model that is explicit in space and time

Increasing difficulties associated with balancing consumptive demands for water and achieving ecological benefits in aquatic ecosystems provide opportunities for new ecosystem-scale ecological response models to assist managers. Using an Australian estuary as a case study, we developed a novel approach to create a data-derived state-and-transition model. The model identifies suites of co-occurring birds, fish, benthic invertebrates and aquatic macrophytes (as ‘states’) and the changing physico-chemical conditions that are associated with each (‘transitions’). The approach first used cluster analysis to identify sets of co-occurring biota. Differences in the physico-chemical data associated with each state were identified using classification trees, with the biotic distinctness of the resultant statistical model tested using analysis of similarities. The predictive capacity of the model was tested using new cases. Two models were created using different time-steps (annual and quarterly) and then combined to capture both longer-term trends and more-recent declines in ecological condition. We identified eight ecosystem states that were differentiated by a mix of water-quantity and water-quality variables. Each ecosystem state represented a distinct biotic assemblage under well-defined physico-chemical conditions. Two ‘basins of attraction’ were identified, with four tidally-influenced states, and another four independent of tidal influence. Within each basin, states described a continuum of relative health, manifest through declining taxonomic diversity and abundances. The main threshold determining relative health was whether freshwater flows had occurred in the region during the previous 339 days. Canonical analyses of principal coordinates tested the predictive capacity of the model and demonstrated that the variance in the environmental data set was well captured (87%) with 52% of the variance in the biological data set also captured. The latter increased to >80% when long- and short-term biological data were analysed separately, indicating that the model described the available data for the Coorong well. This approach thus created a data-derived, multivariate model, where neither states nor transitions were determined a priori. The approach did not over-fit the data, was robust to patchy or missing data, the choice of initial clustering technique and random errors in the biological data set, and was well-received by local natural resource managers. However, the model did not capture causal relationships and requires additional testing, particularly during future episodes of ecological recovery. The approach shows significant promise for simplifying management definitions of ecological condition and, via scenario analyses, can be used to assist in manager decision-making of large, complex aquatic ecosystems in the future.     

The importance of space, time, and stochasticity to the demography and management of Alliaria petiolata

As population modeling is increasingly called upon to guide policy and management, it is important that we understand not only the central tendencies of our study systems, but the consequences of their variation in space and time as well. The invasive plant Alliaria petiolata (garlic mustard) is actively managed in the United States and is the focus of a developing biological control program. Two weevils (Coleoptera: Curculionidae: Ceutorhynchus) that reduce fecundity (C. alliariae) and rosette survival plus fecundity (C. scrobicollis) are under consideration for release pending host specificity testing. We used a demographic modeling approach to (1) quantify variability in A. petiolata growth and vital rates and (2) assess the potential for single- or multiple-agent biocontrol to suppress growth of 12 A. petiolata populations in Illinois and Michigan studied over three plant generations. We used perturbation analyses and simulation models with stochastic environments to estimate stochastic growth rates (lambda(S)) and predict the probability of successful management using either a single biocontrol agent or two agent species together. Not all populations exhibited invasive dynamics. Estimates of lambda(S) ranged from 0.78 to 2.21 across sites, while annual, deterministic growth (lambda) varied up to sevenfold within individual sites. Given our knowledge of the biocontrol agents, this analysis suggests that C. scrobicollis alone may control A. petiolata at up to 63% of our study sites where lambda >1, with the combination of both agents predicted to succeed at 88% of sites. Across sites and years, the elasticity rankings were dependent on lambda. Reductions of rosette survival, fecundity, or germination of new seeds are predicted to cause the greatest reduction of lambda in growing populations. In declining populations, transitions affecting seed bank survival have the greatest effect on lambda. This contrasts with past analyses that varied parameters individually in an otherwise constant matrix, which may yield unrealistic predictions by decoupling natural parameter covariances. Overall, comparisons of stochastic and deterministic growth rates illustrate how analyses of individual populations or years could misguide management or fail to characterize complex traits such as invasiveness that emerge as attributes of populations rather than species.     

The ichthyofaunal composition of the Elbe Estuary: an analysis in space and time

A stow net (90 m² opening) was used, at regular intervals between July 1989 and June 1993, to collect fish over ca. 4 h on both the flood and ebb tides at five sites distributed at regularly spaced distances throughout the Elbe Estuary. Overall, 53.4% of the species were marine, and some of these were abundant, e.g.Clupea harengus, Pleuronectes flesus, Pomatoschistus minutus, Merlangius merlangus and Sprattus sprattus. However, in terms of number of individuals, such species contributed only 9.1%, compared with 90.0% by anadromous species, which was predominantly due to exceptionally high catches of Osmerus eperlanus. The ichthyofaunal compositions on the flood and ebb tides were similar, even downstream where salinities change markedly during each tidal cycle. Although this is probably due in part to groups of fish being swept first upstream on the flood tide and then back downstream on the ebb tide, several species clearly tended to occupy particular regions of the estuary. Each year the species composition changed sequentially from the most downstream site (max. salinity=ca. 31.4‰) to the most upstream site (max. salinity=ca. 1.5‰), mainly as a result of a sequential decline in the number and abundance of marine species and a progressive increase in the contributions of both anadromous and freshwater species. However, the marine species diagnostic of differences in the compositions among regions varied between years. Thus, for example, the diagnostic species for the downstream sites were C. harengus and M. merlangus in 1990/1991 and S. sprattus in 1992/1993, reflecting differences in the recruitment strengths of these marine species in the two years. The ichthyofaunal composition exhibited pronounced annual cyclical changes in each region and thus occurred irrespective of whether or not the salinity in a region underwent pronounced changes during the year. This cyclicity was attributable to intra-annual variations in the times of recruitment of certain marine species, particularly in the downstream region, and to seasonal migrations of diadromous species into each region, as well as to the movements of freshwater species into the upstream region in winter and early spring. Received: 18 November 1999 / Accepted: 25 October 2000     

Analysis of correlated circular and extremal data with a flexible cylindrical distribution

Environmental and Ecological Statistics - In this article, we introduce a flexible cylindrical distribution for modeling and analysis of dependent extremal and directional observations. The...     

Use of time, space and food resources in the mangrove climbing crab Selatium elongatum (Grapsidae: Sesarminae)

The activity patterns and use of space of the mangrove dweller Selatium elongatum were studied in the field, in combination with gut content analyses for evaluation of the crab's natural diet. This sesarmine crab proves to be one of the most adapted to climbing and living on mangroves. Moreover, S. elongatum showed a strong preference for being active at high tide, both during the day and night, always along the trunks a few centimetres above the water level, feeding on floating algae and mangrove leaves. Larger males were always recorded within activity areas into which they allow females and smaller males but exclude males of the same size, which probably compete for females. These results confirm that, in spite of the homogeneous herbivorous diet, little niche overlap exists among the several sesarmine crabs inhabiting the East African mangroves, all being leaf consumers segregated on the basis of their horizontal and vertical zonation, and/or of their activity rhythm. Received: 28 September 1998 / Accepted: 14 June 1999     

Editorial: Special Institutional Thematic Issue: National Research Center for Statistics and the Environment,University of Washington

Environmental and Ecological Statistics -