Wise use of statistical tools in ecological field studies

The currently dominating hypothetico-deductive research paradigm for ecology has statistical hypothesis testing as a basic element. Classic statistical hypothesis testing does, however, present the ecologist with two fundamental dilemmas when field data are to be analyzed: (1) that the statistically motivated demand for a random and representative sample and the ecologically motivated demand for representation of variation in the study area cannot be fully met at the same time; and (2) that the statistically motivated demand for independence of errors calls for sampling distances that exceed the scales of relevant pattern-generating processes, so that samples with statistically desirable properties will be ecologically irrelevant. Reasons for these dilemmas are explained by consideration of the classic statistical Neyman-Pearson test procedure, properties of ecological variables, properties of sampling designs, interactions between properties of the ecological variables and properties of sampling designs, and specific assumptions of the statistical methods. Analytic solutions to problems underlying the dilemmas are briefly reviewed. I conclude that several important research objectives cannot be approached without subjective elements in sampling designs. I argue that a research strategy entirely based on rigorous statistical testing of hypotheses is insufficient for field ecological data and that inductive and deductive approaches are complementary in the process of building ecological knowledge. I recommend that great care is taken when statistical tests are applied to ecological field data. Use of less formal modelling approaches is recommended for cases when formal testing is not strictly needed. Sets of recommendations, “Guidelines for wise use of statistical tools”, are proposed both for testing and for modelling. Important elements of wise-use guidelines are parallel use of methods that preferably belong to different methodologies, selection of methods with few and less rigorous assumptions, conservative interpretation of results, and abandonment of definitive decisions based a predefined significance level.     

Statistical methods for predicting the spatial abundance of reef fish species

Understanding the spatial distribution of organism abundance is fundamental to assessing and managing ecological populations. Marine species can be difficult and logistically challenging and expensive to observe. This often results in spatial data containing low detection rates when sampling underwater, biasing spatial predictions from many modeling approaches. We propose a multistage statistical workflow that can use zero inflated sampling data to develop non-linear predictive spatial distributions of reef fish abundance. The workflow includes: (1) an individual-based discrete event simulation which generates simulated survey data under different abundance settings; (2) empirical maximum likelihood analysis to establish the relationship between survey data and abundance from the simulation; (3) a two-step random smoothing method to estimate reliable block spatial abundance around each survey station; (4) an ensemble of different machine learning models which use the estimated abundance from step three as input to compute a stable non-linear prediction of abundance across the entire study area (Gulf of Mexico). Applying our workflow greatly improved the ability to forecast abundance at small spatial scales. The ability to forecast at fine spatial scales is critical when working with species that are patchily distributed. This workflow can apply to many ecological populations to develop abundance maps even if sample data is not well distributed across the study area or is zero inflated.     

Intrinsic mode entropy based on multivariate empirical mode decomposition and its application to neural data analysis

Entropy, a measure of the regularity of a time series, has long been used to quantify the complexity of brain dynamics. Given the multiple spatiotemporal scales inherent in the brain, traditional entropy analysis based on a single scale is not adequate to accurately describe the underlying nonlinear dynamics. Intrinsic mode entropy (IMEn) is a recent development with appealing properties to estimate entropy over multiple time scales. It is a multiscale entropy measure that computes sample entropy (SampEn) over different scales of intrinsic mode functions extracted by empirical mode decomposition (EMD) method. However, it suffers from both mode-misalignment and mode-mixing problems when applied to multivariate time series data. In this paper, we address these two problems by employing the recently introduced multivariate empirical mode decomposition (MEMD). First, we extend the MEMD to multi-channel multi-trial neural data to ensure the IMEn matched at different scales. Second, for the discriminant analysis of IMEn, we propose to improve the discriminative ability by including variance that has not been used before in entropy analysis. Finally, we apply the proposed approach to the multi-electrode local field potentials (LFPs) simultaneously collected from visual cortical areas of macaque monkeys while performing a generalized flash suppression task. The results have shown that the entropy of LFP is indeed scale-dependent and is closely related to the perceptual conditions. The discriminative results of the perceptual conditions, revealed by support vector machine, show that the accuracy based on IMEn and variance reaches 83.05%, higher than that only by IMEn (76.27%). These results suggest that our approach is sensitive to capture the complex dynamics of neural data.     

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.     

Circumventing structural uncertainty: A Bayesian perspective on nonlinear forecasting for ecology

As a consequence of the complexity of ecosystems and context-dependence of species interactions, structural uncertainty is pervasive in ecological modeling. This is particularly problematic when ecological models are used to make conservation and management plans whose outcomes may depend strongly on model formulation. Nonlinear time series approaches allow us to circumvent this issue by using the observed dynamics of the system to guide policy development. However, these methods typically require long time series from stationary systems, which are rarely available in ecological settings. Here we present a Bayesian approach to nonlinear forecasting based on Gaussian processes that readily integrates information from several short time series and allows for nonstationary dynamics. We demonstrate the utility of our modeling methods on simulated from a wide range of ecological scenarios. We expect that these models will extend the range of ecological systems to which nonlinear forecasting methods can be usefully applied.     

The virtual ecologist approach: simulating data and observers

Ecologists carry a well‐stocked toolbox with a great variety of sampling methods, statistical analyses and modelling tools, and new methods are constantly appearing. Evaluation and optimisation of these methods is crucial to guide methodological choices. Simulating error‐free data or taking high‐quality data to qualify methods is common practice. Here, we emphasise the methodology of the ‘virtual ecologist’ (VE) approach where simulated data and observer models are used to mimic real species and how they are ‘virtually’ observed. This virtual data is then subjected to statistical analyses and modelling, and the results are evaluated against the ‘true’ simulated data. The VE approach is an intuitive and powerful evaluation framework that allows a quality assessment of sampling protocols, analyses and modelling tools. It works under controlled conditions as well as under consideration of confounding factors such as animal movement and biased observer behaviour. In this review, we promote the approach as a rigorous research tool, and demonstrate its capabilities and practical relevance. We explore past uses of VE in different ecological research fields, where it mainly has been used to test and improve sampling regimes as well as for testing and comparing models, for example species distribution models. We discuss its benefits as well as potential limitations, and provide some practical considerations for designing VE studies. Finally, research fields are identified for which the approach could be useful in the future. We conclude that VE could foster the integration of theoretical and empirical work and stimulate work that goes far beyond sampling methods, leading to new questions, theories, and better mechanistic understanding of ecological systems.     

Extending nonlinear analysis to short ecological time series

Nonlinearity is important and ubiquitous in ecology. Though detectable in principle, nonlinear behavior is often difficult to characterize, analyze, and incorporate mechanistically into models of ecosystem function. One obvious reason is that quantitative nonlinear analysis tools are data intensive (require long time series), and time series in ecology are generally short. Here we demonstrate a useful method that circumvents data limitation and reduces sampling error by combining ecologically similar multispecies time series into one long time series. With this technique, individual ecological time series containing as few as 20 data points can be mined for such important information as (1) significantly improved forecast ability, (2) the presence and location of nonlinearity, and (3) the effective dimensionality (the number of relevant variables) of an ecological system.     

A general framework for modeling population abundance data

Time-series data resulting from surveying wild animals are often described using state-space population dynamics models, in particular with Gompertz, Beverton-Holt, or Moran-Ricker latent processes. We show how hidden Markov model methodology provides a flexible framework for fitting a wide range of models to such data. This general approach makes it possible to model abundance on the natural or log scale, include multiple observations at each sampling occasion and compare alternative models using information criteria. It also easily accommodates unequal sampling time intervals, should that possibility occur, and allows testing for density dependence using the bootstrap. The paper is illustrated by replicated time series of red kangaroo abundances, and a univariate time series of ibex counts which are an order of magnitude larger. In the analyses carried out, we fit different latent process and observation models using the hidden Markov framework. Results are robust with regard to the necessary discretization of the state variable. We find no effective difference between the three latent models of the paper in terms of maximized likelihood value for the two applications presented, and also others analyzed. Simulations suggest that ecological time series are not sufficiently informative to distinguish between alternative latent processes for modeling population survey data when data do not indicate strong density dependence.     

Sampling in ecology and evolution – bridging the gap between theory and practice

Sampling is a key issue for answering most ecological and evolutionary questions. The importance of developing a rigorous sampling design tailored to specific questions has already been discussed in the ecological and sampling literature and has provided useful tools and recommendations to sample and analyse ecological data. However, sampling issues are often difficult to overcome in ecological studies due to apparent inconsistencies between theory and practice, often leading to the implementation of simplified sampling designs that suffer from unknown biases. Moreover, we believe that classical sampling principles which are based on estimation of means and variances are insufficient to fully address many ecological questions that rely on estimating relationships between a response and a set of predictor variables over time and space. Our objective is thus to highlight the importance of selecting an appropriate sampling space and an appropriate sampling design. We also emphasize the importance of using prior knowledge of the study system to estimate models or complex parameters and thus better understand ecological patterns and processes generating these patterns. Using a semi‐virtual simulation study as an illustration we reveal how the selection of the space (e.g. geographic, climatic), in which the sampling is designed, influences the patterns that can be ultimately detected. We also demonstrate the inefficiency of common sampling designs to reveal response curves between ecological variables and climatic gradients. Further, we show that response‐surface methodology, which has rarely been used in ecology, is much more efficient than more traditional methods. Finally, we discuss the use of prior knowledge, simulation studies and model‐based designs in defining appropriate sampling designs. We conclude by a call for development of methods to unbiasedly estimate nonlinear ecologically relevant parameters, in order to make inferences while fulfilling requirements of both sampling theory and field work logistics.     

基于不同零模型的点格局分析

在种群空间格局研究中,定量分析格局及其形成过程已成为生态学家的主要目标。在量化分析的众多方法中,点格局分析是最常用的方法,而在选择零模型时,完全空间随机模型以外的复杂零模型很少使用,实际上,这些零模型可能有助于认识格局的内在特征。为此,我们在研究实例中,选择完全空间随机模型(complete spatial randomness)、泊松聚块模型(Poisson cluster process)和嵌套双聚块模型(nested double-cluster process)对典型草原处于不同恢复演替阶段的羊草(Leymus chinensis)种群空间格局进行了分析。结果发现:完全空间随机模型仅能检测种群在不同尺度下的格局类型;而通过泊松聚块模型和嵌套双聚块模型检验表明,在恢复演替的初期阶段,羊草种群在小尺度范围内偏离泊松聚块模型,而在整个取样范围内完全符合嵌套双聚块模型;随着恢复演替时间的推移,在恢复演替的后期,在整个取样尺度上,羊草种群与泊松聚块模型相吻合。这是很有意义的生态学现象。这一实例表明在应用点格局分析种群空间格局时,仅通过完全空间随机模型的检验来分析格局特征,或许很难论证复杂的生态过程,而选择一些完全空间随机模型以外的较复杂的零模型,可能发现一些有价值的生态学现象,对揭示格局掩盖下的内在机制有所裨益。     

Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study

MOTIVATION: In this study, we address the problem of estimating the parameters of regulatory networks and provide the first application of Markov chain Monte Carlo (MCMC) methods to experimental data. As a case study, we consider a stochastic model of the Hes1 system expressed in terms of stochastic differential equations (SDEs) to which rigorous likelihood methods of inference can be applied. When fitting continuous-time stochastic models to discretely observed time series the lengths of the sampling intervals are important, and much of our study addresses the problem when the data are sparse. RESULTS: We estimate the parameters of an autoregulatory network providing results both for simulated and real experimental data from the Hes1 system. We develop an estimation algorithm using MCMC techniques which are flexible enough to allow for the imputation of latent data on a finer time scale and the presence of prior information about parameters which may be informed from other experiments as well as additional measurement error.     

辐射传输模型多尺度反演植被理化参数研究进展

植被是生态系统最重要的组成成分之一,许多与植被有关的物质能量交换过程都与植被的理化参数密切相关,因此定量估算植被的理化参数含量对监测植被生长状况、森林火灾预警以及研究全球碳氮循环过程等都具有重要意义.在众多定量反演植被理化参数的方法中,基于数学、物理学以及生物学的基本理论建立起来的辐射传输模型受到越来越多的关注.辐射传输模型描述了植被与入射辐射之间的相互作用过程和特征,相对于传统的经验/半经验方法,辐射传输模型物理意义明确,具有稳定性和可移植性强的特点.在分析国内外最新相关研究的基础上,首先从植被叶片、冠层和像元3个不同的尺度阐述反演植被理化参数的辐射传输模型.叶片尺度上主要介绍PROSPECT模型和LIBERTY模型;冠层尺度上主要介绍SAIL冠层辐射传输模型以及PROSPECT与SAIL耦合的PROSAIL叶片-冠层辐射传输模型;像元尺度的植被理化参数反演目前主要采用冠层尺度的辐射传输模型.其次,分析尺度变化下植被理化参数遥感反演所面临的主要问题,如不同尺度下模型参数敏感性的变化、辐射传输模型的选取以及混合像元的影响等.最后,总结展望植被理化参数反演多模型与多种数据源相互结合的研究趋势,以及将来具有高空间分辨率的高光谱遥感卫星升空后所带来的发展前景.     

Systematic error is of minor importance to feedback structure estimates derived from time series of nonlinear population indices

Most modern population dynamics analyses of time series use simple population indices for ecological inference. These indices, collected for many years for various agricultural pests or game animals, are generally believed not to distort systematically feedback estimates because the assumption of linearity to population size roughly holds. To assess the relative importance of this assumption, we examined the effect of nonlinearity in a burrow index for voles on feedback estimates obtained through autoregressive modeling. We show that the issue of linearity is of less importance to ecological inference because the feedback estimates are routinely obtained on a logarithmic scale. Transforming data to logs has a strong linearization effect, removing most of the nonlinearity observed on the original scale. We conclude that the statistical tools for ecological inference, such as autoregressive log-linear models, are sufficiently robust to the systematic error imposed by index nonlinearity and that indices are valuable sources of ecological information even in situations when the assumed linear functional forms to population size were not exactly validated. We suggest that for time series modelers, the issue of a large sampling variation in small “noisy” populations is by far a more burning one than the systematic error due to index nonlinearity.     

Modeling baseline conditions of ecological indicators: Marine renewable energy environmental monitoring

Ecological indicators are often collected to detect and monitor environmental change. Statistical models are used to estimate natural variability, pre-existing trends, and environmental predictors of baseline indicator conditions. Establishing standard models for baseline characterization is critical to the effective design and implementation of environmental monitoring programs. An anthropogenic activity that requires monitoring is the development of Marine Renewable Energy sites. Currently, there are no standards for the analysis of environmental monitoring data for these development sites. Marine Renewable Energy monitoring data are used as a case study to develop and apply a model evaluation to establish best practices for characterizing baseline ecological indicator data. We examined a range of models, including six generalized regression models, four time series models, and three nonparametric models. Because monitoring data are not always normally distributed, we evaluated model ability to characterize normal and non-normal data using hydroacoustic metrics that serve as proxies for ecological indicator data. The nonparametric support vector regression and random forest models, and parametric state-space time series models generally were the most accurate in interpolating the normal metric data. Support vector regression and state-space models best interpolated the non-normally distributed data. If parametric results are preferred, then state-space models are the most robust for baseline characterization. Evaluation of a wide range of models provides a comprehensive characterization of the case study data, and highlights advantages of models rarely used in Marine Renewable Energy environmental monitoring. Our model findings are relevant for any ecological indicator data with similar properties, and the evaluation approach is applicable to any monitoring program.     

Upscaling leaf area index in an Arctic landscape through multiscale observations

Monitoring and understanding global change requires a detailed focus on upscaling, the process for extrapolating from the site‐specific scale to the smallest scale resolved in regional or global models or earth observing systems. Leaf area index (LAI) is one of the most sensitive determinants of plant production and can vary by an order of magnitude over short distances. The landscape distribution of LAI is generally determined by remote sensing of surface reflectance (e.g. normalized difference vegetation index, NDVI) but the mismatch in scales between ground and satellite measurements complicates LAI upscaling. Here, we describe a series of measurements to quantify the spatial distribution of LAI in a sub‐Arctic landscape and then describe the upscaling process and its associated errors. Working from a fine‐scale harvest LAI–NDVI relationship, we collected NDVI data over a 500 m × 500 m catchment in the Swedish Arctic, at resolutions from 0.2 to 9.0 m in a nested sampling design. NDVI scaled linearly, so that NDVI at any scale was a simple average of multiple NDVI measurements taken at finer scales. The LAI–NDVI relationship was scale invariant from 1.5 to 9.0 m resolution. Thus, a single exponential LAI–NDVI relationship was valid at all these scales, with similar prediction errors. Vegetation patches were of a scale of ～0.5 m and at measurement scales coarser than this, there was a sharp drop in LAI variance. Landsat NDVI data for the study catchment correlated significantly, but poorly, with ground‐based measurements. A variety of techniques were used to construct LAI maps, including interpolation by inverse distance weighting, ordinary Kriging, External Drift Kriging using Landsat data, and direct estimation from a Landsat NDVI–LAI calibration. All methods produced similar LAI estimates and overall errors. However, Kriging approaches also generated maps of LAI estimation error based on semivariograms. The spatial variability of this Arctic landscape was such that local measurements assimilated by Kriging approaches had a limited spatial influence. Over scales >50 m, interpolation error was of similar magnitude to the error in the Landsat NDVI calibration. The characterisation of LAI spatial error in this study is a key step towards developing spatio‐temporal data assimilation systems for assessing C cycling in terrestrial ecosystems by combining models with field and remotely sensed data.     

Two-phase species–time relationships in North American land birds

The species–time relationship (STR) is a macroecological pattern describing the increase in the observed species richness with the length of time censused. Understanding STRs is important for understanding the ecological processes underlying temporal turnover and species richness. However, accurate characterization of the STR has been hampered by the influence of sampling. I analysed STRs for 521 breeding bird survey communities. I used a model of sampling effects to demonstrate that the increase in richness was not due exclusively to sampling. I estimated the time scale at which ecological processes became dominant over sampling effects using a two‐phase model combining a sampling phase and either a power function or logarithmic ecological phase. These two‐phase models performed significantly better than sampling alone and better than simple power and logarithmic functions. Most community dynamics were dominated by ecological processes over scales <5 years. This technique provides an example of a rigorous, quantitative approach to separating sampling from ecological processes.     

Monitoring program design for data‐limited marine biogenic habitats: A structured approach

Marine biogenic habitats—habitats created by living organisms—provide essential ecosystem functions and services, such as physical structuring, nutrient cycling, biodiversity support, and increases in primary, secondary, and tertiary production. With the growing trend toward ecosystem approaches to marine conservation and fisheries management, there is greater emphasis on rigorously designed habitat monitoring programs. However, such programs are challenging to design for data‐limited habitats for which underlying ecosystem processes are poorly understood. To provide guidance in this area, we reviewed approaches to benthic assessments across well‐studied marine biogenic habitats and identified common themes related to indicator selection, sampling methods, and survey design. Biogenic habitat monitoring efforts largely focus on the characteristics, distribution, and ecological function of foundation species, but may target other habitat‐forming organisms, especially when community shifts are observed or expected, as well as proxies of habitat status, such as indicator species. Broad‐scale methods cover large spatial areas and are typically used to examine the spatial configuration of habitats, whereas fine‐scale methods tend to be laborious and thus restricted to small survey areas, but provide high‐resolution data. Recent, emerging methods enhance the capabilities of surveying large areas at high spatial resolution and improve data processing efficiency, bridging the gap between broad‐ and fine‐scale methods. Although sampling design selection may be limited by habitat characteristics and available resources, it is critically important to ensure appropriate matching of ecological, observational, and analytical scales. Drawing on these common themes, we propose a structured, iterative approach to designing monitoring programs for marine biogenic habitats that allows for rigorous data collection to inform management strategies, even when data and resource limitations are present. A practical application of this approach is illustrated using glass sponge reefs—a recently discovered and data‐limited habitat type—as a case study.     

Estimating species – area relationships by modeling abundance and frequency subject to incomplete sampling

Models and data used to describe species–area relationships confound sampling with ecological process as they fail to acknowledge that estimates of species richness arise due to sampling. This compromises our ability to make ecological inferences from and about species–area relationships. We develop and illustrate hierarchical community models of abundance and frequency to estimate species richness. The models we propose separate sampling from ecological processes by explicitly accounting for the fact that sampled patches are seldom completely covered by sampling plots and that individuals present in the sampling plots are imperfectly detected. We propose a multispecies abundance model in which community assembly is treated as the summation of an ensemble of species‐level Poisson processes and estimate patch‐level species richness as a derived parameter. We use sampling process models appropriate for specific survey methods. We propose a multispecies frequency model that treats the number of plots in which a species occurs as a binomial process. We illustrate these models using data collected in surveys of early‐successional bird species and plants in young forest plantation patches. Results indicate that only mature forest plant species deviated from the constant density hypothesis, but the null model suggested that the deviations were too small to alter the form of species–area relationships. Nevertheless, results from simulations clearly show that the aggregate pattern of individual species density–area relationships and occurrence probability–area relationships can alter the form of species–area relationships. The plant community model estimated that only half of the species present in the regional species pool were encountered during the survey. The modeling framework we propose explicitly accounts for sampling processes so that ecological processes can be examined free of sampling artefacts. Our modeling approach is extensible and could be applied to a variety of study designs and allows the inclusion of additional environmental covariates.     

Variation Thresholds for Extinction and Their Implications for Conservation Strategies

We examine the degree to which fitting simple dynamic models to time series of population counts can predict extinction probabilities. This is both an active branch of ecological theory and an important practical topic for resource managers. We introduce an approach that is complementary to recently developed techniques for estimating extinction risks (e.g., diffusion approximations) and, like them, requires only count data rather than the detailed ecological information available for traditional population viability analyses. Assuming process error, we use four different models of population growth to generate snapshots of population dynamics via time series of the lengths commonly available to ecologists. We then ask to what extent we can identify which of several broad classes of population dynamics is evident in the time series snapshot. Along the way, we introduce the idea of "variation thresholds," which are the maximum amount of process error that a population may withstand and still have a specified probability of surviving for a given length of time. We then show how these thresholds may be useful to both ecologists and resource managers, particularly when dealing with large numbers of poorly understood species, a common problem faced by those designing biodiversity reserves.     

Confidence in ecological indicators: A framework for quantifying uncertainty components from monitoring data

The value of an ecological indicator is no better than the uncertainty associated with its estimate. Nevertheless, indicator uncertainty is seldom estimated, even though legislative frameworks such as the European Water Framework Directive stress that the confidence of an assessment should be quantified. We introduce a general framework for quantifying uncertainties associated with indicators employed to assess ecological status in waterbodies. The framework is illustrated with two examples: eelgrass shoot density and chlorophyll a in coastal ecosystems. Aquatic monitoring data vary over time and space; variations that can only partially be described using fixed parameters, and remaining variations are deemed random. These spatial and temporal variations can be partitioned into uncertainty components operating at different scales. Furthermore, different methods of sampling and analysis as well as people involved in the monitoring introduce additional uncertainty. We have outlined 18 different sources of variation that affect monitoring data to a varying degree and are relevant to consider when quantifying the uncertainty of an indicator calculated from monitoring data. However, in most cases it is not possible to estimate all relevant sources of uncertainty from monitoring data from a single ecosystem, and those uncertainty components that can be quantified will not be well determined due to the lack of replication at different levels of the random variations (e.g. number of stations, number of years, and number of people). For example, spatial variations cannot be determined from datasets with just one station. Therefore, we recommend that random variations are estimated from a larger dataset, by pooling observations from multiple ecosystems with similar characteristics. We also recommend accounting for predictable patterns in time and space using parametric approaches in order to reduce the magnitude of the unpredictable random components and reduce potential bias introduced by heterogeneous monitoring across time. We propose to use robust parameter estimates for both fixed and random variations, determined from a large pooled dataset and assumed common across the range of ecosystems, and estimate a limited subset of parameters from ecosystem-specific data. Partitioning the random variation onto multiple uncertainty components is important to obtain correct estimates of the ecological indicator variance, and the magnitude of the different components provide useful information for improving methods applied and design of monitoring programs. The proposed framework allows comparing different indicators based on their precision relative to the cost of monitoring.