New insights into global patterns of ocean temperature anomalies: implications for coral reef health and management

Aim Coral reefs are widely considered to be particularly vulnerable to changes in ocean temperatures, yet we understand little about the broad‐scale spatio‐temporal patterns that may cause coral mortality from bleaching and disease. Our study aimed to characterize these ocean temperature patterns at biologically relevant scales. Location Global, with a focus on coral reefs. Methods We created a 4‐km resolution, 21‐year global ocean temperature anomaly (deviations from long‐term means) database to quantify the spatial and temporal characteristics of temperature anomalies related to both coral bleaching and disease. Then we tested how patterns varied in several key metrics of disturbance severity, including anomaly frequency, magnitude, duration and size. Results Our analyses found both global variation in temperature anomalies and fine‐grained spatial variability in the frequency, duration and magnitude of temperature anomalies. However, we discovered that even during major climatic events with strong spatial signatures, like the El Niño–Southern Oscillation, areas that had high numbers of anomalies varied between years. In addition, we found that 48% of bleaching‐related anomalies and 44% of disease‐related anomalies were less than 50 km², much smaller than the resolution of most models used to forecast climate changes. Main conclusions The fine‐scale variability in temperature anomalies has several key implications for understanding spatial patterns in coral bleaching‐ and disease‐related anomalies as well as for designing protected areas to conserve coral reefs in a changing climate. Spatial heterogeneity in temperature anomalies suggests that certain reefs could be targeted for protection because they exhibit differences in thermal stress. However, temporal variability in anomalies could complicate efforts to protect reefs, because high anomalies in one year are not necessarily predictive of future patterns of stress. Together, our results suggest that temperature anomalies related to coral bleaching and disease are likely to be highly heterogeneous and could produce more localized impacts of climate change.     

Analysis of seasonal variation of birth defects in Atlanta

BACKGROUND: Compared with analyses of temporal trends, analyses of seasonal variations in the prevalence of birth defects have been more limited and have provided less consistent information. Possible reasons for this lack of consistency in findings include differences in populations, underlying factors, seasons or climates, and methods of ascertainment and analysis between studies. This study examines possible seasonal variation in the prevalence of selected birth defects in a defined study population using graphical displays and three statistical methods. METHODS: Cases were infants and fetal deaths in nine birth defect groups born to residents of mothers in five counties of metropolitan Atlanta during the period of 1978-2001 and ascertained by the Metropolitan Atlanta Congenital Defects Program. These birth defect groups were anencephaly, spina bifida, total neural tube defects, cleft palate, cleft lip with or without cleft palate, anomalies of the pulmonary valve, anomalies of the aortic valve, hypoplastic left heart syndrome, and congenital dislocation of the hip. We pooled monthly case counts and calculated monthly rates for each of these birth defect groups for five different birth periods: 1978-2001, 1978-1989, 1990-2001, 1990-1994, and 1995-2001. We applied the Cochran-Armitage test for trend to rule out homogeneity in pooled monthly rates. Data for each defect group were examined for possible seasonal (i.e., cyclical) variation overall and within the cited birth periods using the Hewitt-Rogerson test and the Walter-Elwood test. RESULTS: Graphical analyses of the pooled monthly rates showed no apparent seasonal patterns for any of the nine defect groups examined. Statistical tests for seasonality suggested possible seasonality for three defect groups: the Hewitt-Rogerson test was statistically significant for anencephaly (peak March-August, p = 0.048),while the Walter-Elwood test was significant for anomalies of the pulmonary valve (peak September, p = 0.02), and anomalies of the aortic valve (peak July, p = 0.039). With both methods, the results appeared to be influenced by the choice of time (i.e., birth) period. Results for anomalies of the pulmonary valve were statistically significant and more consistent with all tests in most of the time periods examined. CONCLUSIONS: Graphical analyses and basic statistical tests for seasonality showed no consistent evidence of seasonality for any of the nine defect groups examined, except for anomalies of the pulmonary valve. The two basic statistical methods coupled by a trend test for exploring seasonal patterns of the prevalence of birth defects can be useful for preliminary analyses of possible seasonal patterns. However, these methods have some limitations: (1) an assumption of no strong temporal trend over the study years, and (2) the results can vary by time period chosen. For specific hypotheses regarding seasonality, a more robust analytical approach such as time-series analysis might be more appropriate.     

Controlling false discoveries in genome scans for selection

Population differentiation (PD) and ecological association (EA) tests have recently emerged as prominent statistical methods to investigate signatures of local adaptation using population genomic data. Based on statistical models, these genomewide testing procedures have attracted considerable attention as tools to identify loci potentially targeted by natural selection. An important issue with PD and EA tests is that incorrect model specification can generate large numbers of false‐positive associations. Spurious association may indeed arise when shared demographic history, patterns of isolation by distance, cryptic relatedness or genetic background are ignored. Recent works on PD and EA tests have widely focused on improvements of test corrections for those confounding effects. Despite significant algorithmic improvements, there is still a number of open questions on how to check that false discoveries are under control and implement test corrections, or how to combine statistical tests from multiple genome scan methods. This tutorial study provides a detailed answer to these questions. It clarifies the relationships between traditional methods based on allele frequency differentiation and EA methods and provides a unified framework for their underlying statistical tests. We demonstrate how techniques developed in the area of genomewide association studies, such as inflation factors and linear mixed models, benefit genome scan methods and provide guidelines for good practice while conducting statistical tests in landscape and population genomic applications. Finally, we highlight how the combination of several well‐calibrated statistical tests can increase the power to reject neutrality, improving our ability to infer patterns of local adaptation in large population genomic data sets.     

On temporal partitioning of a community of ectomycorrhizal fungi

Several mechanisms may contribute to the high species richness often reported in ectomycorrhizal (ECM) fungal communities, including spatial and temporal partitioning. Here, we focus on temporal partitioning. Using molecular methods, we determined the frequencies of occurrence of ECM fungal species detected as hyphae and ECM roots in the forest floor of a Pinus resinosa plantation during a 13-month period. We then used a novel statistical procedure to place the most frequently occurring ECM fungal species into groups distinguished by their patterns of relative frequency over time. Three groups with contrasting temporal patterns were distinguishable for fungal species detected as hyphae. Two groups were distinguishable for species detected as ECM roots. Our results support the hypothesis that temporal partitioning occurs among the species of ECM fungi in this community, but we did not address its causes, which may have involved interactions among species' physiological tolerances, temporal environmental variability, temporal patterns of root production, and variation in fungal genet lifespan. These interactions should be the subjects of future research.     

Test for a population expansion after a drastic reduction in population size using DNA sequence data

Populations may, during their evolutionary history, go through drastic changes in population size due to bottlenecks or founder events upon colonization of new areas. This involves a subsample of haplotypes, causing the allele frequencies to be different from the original population. In addition, the period of recovery after a bottleneck can be of considerable length. If reproduction is unequal among individuals but random with regard to haplotype, large deviations from the patterns expected in a stable population may result. By means of computer simulation, I have analysed the patterns arising when populations undergo bottlenecks and then slowly recover, and used two new statistical tests for the detection of the bottleneck. A test based on the variance of the relative frequency of haplotypes had generally high power even at low sample size (n=25). This statistic was most powerful after very strong bottlenecks and lost power with increasing propagule size. A test based on the variance of the pairwise differences shows slightly less power. As expected, power was reduced when migration into the founder population was allowed from the source population. This suggests that the test is particularly suited for detecting relatively recent and strong bottlenecks, and thus may be a valuable tool for identifying population events on a fine temporal scale, such as colonisations after the last glaciation.     

A new testing strategy to identify rare variants with either risk or protective effect on disease

Rapid advances in sequencing technologies set the stage for the large-scale medical sequencing efforts to be performed in the near future, with the goal of assessing the importance of rare variants in complex diseases. The discovery of new disease susceptibility genes requires powerful statistical methods for rare variant analysis. The low frequency and the expected large number of such variants pose great difficulties for the analysis of these data. We propose here a robust and powerful testing strategy to study the role rare variants may play in affecting susceptibility to complex traits. The strategy is based on assessing whether rare variants in a genetic region collectively occur at significantly higher frequencies in cases compared with controls (or vice versa). A main feature of the proposed methodology is that, although it is an overall test assessing a possibly large number of rare variants simultaneously, the disease variants can be both protective and risk variants, with moderate decreases in statistical power when both types of variants are present. Using simulations, we show that this approach can be powerful under complex and general disease models, as well as in larger genetic regions where the proportion of disease susceptibility variants may be small. Comparisons with previously published tests on simulated data show that the proposed approach can have better power than the existing methods. An application to a recently published study on Type-1 Diabetes finds rare variants in gene IFIH1 to be protective against Type-1 Diabetes.     

New Statistical Tests of Neutrality for DNA Samples from a Population

The purpose of this paper is to develop statistical tests of the neutral model of evolution against a class of alternative models with the common characteristic of having an excess of mutations that occurred a long time ago or a reduction of recent mutations compared to the neutral model. This class of population genetics models include models for structured populations, models with decreasing effective population size and models of selection and mutation balance. Four statistical tests were proposed in this paper for DNA samples from a population. Two of these tests, one new and another a modification of an existing test, are based on EWENS'' sampling formula, and the other two new tests make use of the frequencies of mutations of various classes. Using simulated samples and regression analyses, the critical values of these tests can be computed from regression equations. This approach for computing the critical values of a test was found to be appropriate and quite effective. We examined the powers of these four tests using simulated samples from structured populations, populations with linearly decreasing sizes and models of selection and mutation balance and found that they are more powerful than existing statistical tests of the neutral model of evolution.     

Using Combined Diagnostic Test Results to Hindcast Trends of Infection from Cross-Sectional Data

Infectious disease surveillance is key to limiting the consequences from infectious pathogens and maintaining animal and public health. Following the detection of a disease outbreak, a response in proportion to the severity of the outbreak is required. It is thus critical to obtain accurate information concerning the origin of the outbreak and its forward trajectory. However, there is often a lack of situational awareness that may lead to over- or under-reaction. There is a widening range of tests available for detecting pathogens, with typically different temporal characteristics, e.g. in terms of when peak test response occurs relative to time of exposure. We have developed a statistical framework that combines response level data from multiple diagnostic tests and is able to ‘hindcast’ (infer the historical trend of) an infectious disease epidemic. Assuming diagnostic test data from a cross-sectional sample of individuals infected with a pathogen during an outbreak, we use a Bayesian Markov Chain Monte Carlo (MCMC) approach to estimate time of exposure, and the overall epidemic trend in the population prior to the time of sampling. We evaluate the performance of this statistical framework on simulated data from epidemic trend curves and show that we can recover the parameter values of those trends. We also apply the framework to epidemic trend curves taken from two historical outbreaks: a bluetongue outbreak in cattle, and a whooping cough outbreak in humans. Together, these results show that hindcasting can estimate the time since infection for individuals and provide accurate estimates of epidemic trends, and can be used to distinguish whether an outbreak is increasing or past its peak. We conclude that if temporal characteristics of diagnostics are known, it is possible to recover epidemic trends of both human and animal pathogens from cross-sectional data collected at a single point in time.     

Temporal population code of concurrent vocal signals in the auditory midbrain

Unique patterns of spike activity across neuron populations have been implicated in the coding of complex sensory stimuli. Delineating the patterns of neural activity in response to varying stimulus parameters and their relationships to the tuning characteristics of individual neurons is essential to ascertaining the nature of population coding within the brain. Here, we address these points in the midbrain coding of concurrent vocal signals of a sound-producing fish, the plainfin midshipman. Midshipman produce multiharmonic vocalizations which frequently overlap to produce beats. We used multivariate statistical analysis from single-unit recordings across multiple animals to assess the presence of a temporal population code. Our results show that distinct patterns of temporal activity emerge among midbrain neurons in response to concurrent signals that vary in their difference frequency. These patterns can serve to code beat difference frequencies. The patterns directly result from the differential temporal coding of difference frequency by individual neurons. Difference frequency encoding, based on temporal patterns of activity, could permit the segregation of concurrent vocal signals on time scales shorter than codes requiring averaging. Given the ubiquity across vertebrates of auditory midbrain tuning to the temporal structure of acoustic signals, a similar temporal population code is likely present in other species.     

A New Test for Selection Applied to Codon Usage in Drosophila simulans and D. mauritiana

In many organisms, synonymous codon usage is biased by a history of natural selection. However, codon bias, itself, does not indicate that selection is ongoing; it may be a vestige of past selection. Simple statistical tests have been devised to infer ongoing selection on codon usage by comparing the derived state frequency spectra at polymorphic sites segregating either derived preferred codons or derived unpreferred codons; if selection is effective, the frequency of derived states should be higher in the former. We propose a new test that uses the inferred degree of preference, essentially calculating the correlation of derived state frequency and the difference in preference between the derived and the ancestral states; the correlation should be positive if selection is effective. When implementing the test, derived and ancestral states can be assigned by parsimony or on the basis of relative probability. In either case, statistical significance is estimated by a simple permutation test. We explored the statistical power of the test by sampling polymorphism data from 14 loci in 16 strains of D. simulans, finding that the test retains 80% power even when quite a few of the data are discarded. The power of the test likely reflects better use of multiple features of the data, combining population frequencies of polymorphic variants and quantitative estimates of codon preferences. We also applied this novel test to 14 newly sequenced loci in five strains of D. mauritiana, showing for the first time ongoing selection on codon usage in this species.     

An exact test for the association between the disease and alleles at highly polymorphic loci with particular interest in the haplotype analysis

The association analysis between the disease and genetic alleles is one of the simple methods for localizing the susceptibility locus in the genes. For revealing the association, several statistical tests have been proposed without discussing explicitly the alternative hypotheses. We therefore specify two types of alternative hypotheses (i.e., there is only one susceptibility allele in the locus, and there is an extension or shortening of alleles associated with the disease) and derive exact tests for the respective hypotheses. We also propose to combine these two tests when the prior knowledge is not sufficient enough to specify one of these two hypotheses. In particular, these ideas are extended to the haplotype analysis of three-way association between the disease and bivariate allele frequencies at two closely linked loci. As a by-product, a factorization of the probability distribution of the three-way cell frequencies under the null hypothesis of no three-way interaction is obtained.     

Genetic association mapping based on discordant sib pairs: the discordant-alleles test.

Family-based tests of association provide the opportunity to test for an association between a disease and a genetic marker. Such tests avoid false-positive results produced by population stratification, so that evidence for association may be interpreted as evidence for linkage or causation. Several methods that use family-based controls have been proposed, including the haplotype relative risk, the transmission-disequilibrium test, and affected family-based controls. However, because these methods require genotypes on affected individuals and their parents, they are not ideally suited to the study of late-onset diseases. In this paper, we develop several family-based tests of association that use discordant sib pairs (DSPs) in which one sib is affected with a disease and the other sib is not. These tests are based on statistics that compare counts of alleles or genotypes or that test for symmetry in tables of alleles or genotypes. We describe the use of a permutation framework to assess the significance of these statistics. These DSP-based tests provide the same general advantages as parent-offspring trio-based tests, while being applicable to essentially any disease; they may also be tailored to particular hypotheses regarding the genetic model. We compare the statistical properties of our DSP-based tests by computer simulation and illustrate their use with an application to Alzheimer disease and the apolipoprotein E polymorphism. Our results suggest that the discordant-alleles test, which compares the numbers of nonmatching alleles in DSPs, is the most powerful of the tests we considered, for a wide class of disease models and marker types. Finally, we discuss advantages and disadvantages of the DSP design for genetic association mapping.     

Inference of Functional Divergence Among Proteins When the Evolutionary Process is Non-stationary

Functional shifts during protein evolution are expected to yield shifts in substitution rate, and statistical methods can test for this at both codon and amino acid levels. Although methods based on models of sequence evolution serve as powerful tools for studying evolutionary processes, violating underlying assumptions can lead to false biological conclusions. It is not unusual for functional shifts to be accompanied by changes in other aspects of the evolutionary process, such as codon or amino acid frequencies. However, models used to test for functional divergence assume these frequencies remain constant over time. We employed simulation to investigate the impact of non-stationary evolution on functional divergence inference. We investigated three likelihood ratio tests based on codon models and found varying degrees of sensitivity. Joint effects of shifts in frequencies and selection pressures can be large, leading to false signals for positive selection. Amino acid-based tests (FunDi and Bivar) were also compromised when several aspects of the substitution process were not adequately modeled. We applied the same tests to a core genome “scan” for functional divergence between light-adapted ecotypes of the cyanobacteria Prochlorococcus, and carried out gene-specific simulations for ten genes. Results of those simulations illustrated how the inference of functional divergence at the genomic level can be seriously impacted by model misspecification. Although computationally costly, simulations motivated by data in hand are warranted when several aspects of the substitution process are either misspecified or not included in the models upon which the statistical tests were built.     

Trapline foraging by bumble bees: II. Definition and detection from sequence data

Trapline foraging—repeated sequential visits to a seriesof feeding locations—presents interesting problems seldomtreated in foraging models. Work on traplining is hampered bythe lack of statistical, operational approaches for detectingits existence and measuring its strength. We propose severalstatistical procedures, illustrating them with records of interplantflight sequences by bumble bees visiting penstemon flowers.An asymmetry test detects deviations from binomial expectationin the directionality of visits between pairs of plants. Severaltests compare data from one bee to another frequencies of visitsto plants and frequencies of departures to particular destinationsare compared using contingency tables; similarities of repeatedsequences within bees are compared to those between bees bymeans of sequence alignment and Mantel tests. We also comparedobserved movement patterns to those generated by null modelsdesigned to represent realistic foraging by non-traplining bees,examining: temporal patterns of the bee's spatial displacementfrom its starting point using spectral analysis; the varianceof return times to particular plants; and the sequence alignmentof repeated cycles within sequences. We discuss the differentindications and the relative strengths of these approaches     

Detecting balancing selection in genomes: limits and prospects

In spite of the long‐term interest in the process of balancing selection, its frequency in genomes and evolutionary significance remain unclear due to challenges related to its detection. Current statistical approaches based on patterns of variation observed in molecular data suffer from low power and a high incidence of false positives. This raises the question whether balancing selection is rare or is simply difficult to detect. We discuss genetic signatures produced by this mode of selection and review the current approaches used for their identification in genomes. Advantages and disadvantages of the available methods are presented, and areas where improvement is possible are identified. Increased specificity and reduced rate of false positives may be achieved by using a demographic model, applying combinations of tests, appropriate sampling scheme and taking into account intralocus variation in selection pressures. We emphasize novel solutions, recently developed model‐based approaches and good practices that should be implemented in future studies looking for signals of balancing selection. We also draw attention of the readers to the results of recent theoretical studies, which suggest that balancing selection may be ubiquitous but transient, leaving few signatures detectable by existing methods. Testing this new theory may require the development of novel high‐throughput methods extending beyond genomic scans.     

Improved statistical inference from DNA microarray data using analysis of variance and a Bayesian statistical framework. Analysis of global gene expression in Escherichia coli K12

We describe statistical methods based on the t test that can be conveniently used on high density array data to test for statistically significant differences between treatments. These t tests employ either the observed variance among replicates within treatments or a Bayesian estimate of the variance among replicates within treatments based on a prior estimate obtained from a local estimate of the standard deviation. The Bayesian prior allows statistical inference to be made from microarray data even when experiments are only replicated at nominal levels. We apply these new statistical tests to a data set that examined differential gene expression patterns in IHF(+) and IHF(-) Escherichia coli cells (Arfin, S. M., Long, A. D., Ito, E. T., Tolleri, L., Riehle, M. M., Paegle, E. S., and Hatfield, G. W. (2000) J. Biol. Chem. 275, 29672-29684). These analyses identify a more biologically reasonable set of candidate genes than those identified using statistical tests not incorporating a Bayesian prior. We also show that statistical tests based on analysis of variance and a Bayesian prior identify genes that are up- or down-regulated following an experimental manipulation more reliably than approaches based only on a t test or fold change. All the described tests are implemented in a simple-to-use web interface called Cyber-T that is located on the University of California at Irvine genomics web site.     

Inter-Network Interactions: Impact of Connections between Oscillatory Neuronal Networks on Oscillation Frequency and Pattern

Oscillations in electrical activity are a characteristic feature of many brain networks and display a wide variety of temporal patterns. A network may express a single oscillation frequency, alternate between two or more distinct frequencies, or continually express multiple frequencies. In addition, oscillation amplitude may fluctuate over time. The origin of this complex repertoire of activity remains unclear. Different cortical layers often produce distinct oscillation frequencies. To investigate whether interactions between different networks could contribute to the variety of oscillation patterns, we created two model networks, one generating on its own a relatively slow frequency (20 Hz; slow network) and one generating a fast frequency (32 Hz; fast network). Taking either the slow or the fast network as source network projecting connections to the other, or target, network, we systematically investigated how type and strength of inter-network connections affected target network activity. For high inter-network connection strengths, we found that the slow network was more effective at completely imposing its rhythm on the fast network than the other way around. The strongest entrainment occurred when excitatory cells of the slow network projected to excitatory or inhibitory cells of the fast network. The fast network most strongly imposed its rhythm on the slow network when its excitatory cells projected to excitatory cells of the slow network. Interestingly, for lower inter-network connection strengths, multiple frequencies coexisted in the target network. Just as observed in rat prefrontal cortex, the target network could express multiple frequencies at the same time, alternate between two distinct oscillation frequencies, or express a single frequency with alternating episodes of high and low amplitude. Together, our results suggest that input from other oscillating networks may markedly alter a network''s frequency spectrum and may partly be responsible for the rich repertoire of temporal oscillation patterns observed in the brain.     

Development and Application of Genomic Control Methods for Genome-Wide Association Studies Using Non-Additive Models

Genome-wide association studies (GWAS) comprise a powerful tool for mapping genes of complex traits. However, an inflation of the test statistic can occur because of population substructure or cryptic relatedness, which could cause spurious associations. If information on a large number of genetic markers is available, adjusting the analysis results by using the method of genomic control (GC) is possible. GC was originally proposed to correct the Cochran-Armitage additive trend test. For non-additive models, correction has been shown to depend on allele frequencies. Therefore, usage of GC is limited to situations where allele frequencies of null markers and candidate markers are matched. In this work, we extended the capabilities of the GC method for non-additive models, which allows us to use null markers with arbitrary allele frequencies for GC. Analytical expressions for the inflation of a test statistic describing its dependency on allele frequency and several population parameters were obtained for recessive, dominant, and over-dominant models of inheritance. We proposed a method to estimate these required population parameters. Furthermore, we suggested a GC method based on approximation of the correction coefficient by a polynomial of allele frequency and described procedures to correct the genotypic (two degrees of freedom) test for cases when the model of inheritance is unknown. Statistical properties of the described methods were investigated using simulated and real data. We demonstrated that all considered methods were effective in controlling type 1 error in the presence of genetic substructure. The proposed GC methods can be applied to statistical tests for GWAS with various models of inheritance. All methods developed and tested in this work were implemented using R language as a part of the GenABEL package.     

Compound tests for the detection of hitchhiking under positive selection

Many statistical tests have been developed for detecting positive selection. Most of these tests draw conclusions based on significant deviations from the patterns of polymorphism predicted by the neutral model. However, many non-equilibrium forces may cause similar deviations, and thus the tests usually have low statistical specificity to positive selection. The main challenge is hence to construct test statistics that are reasonably powerful in detecting positive selection, but are relatively insensitive to other forces. Recently, Zeng et al. (2006) proposed a new test, DH, which is a compound of Tajima's D and Fay and Wu's H, and showed that DH has reasonably high statistical specificity to positive selection. In this report, we expand the idea of a compound test by combining Fay and Wu's H or DH with the Ewens-Watterson (EW) test. We refer to these 2 new tests as HEW and DHEW, respectively. Compared to the DH test, HEW and DHEW are more robust against the presence of recombination, and are also more powerful in detecting positive selection. Furthermore, the DHEW test, similar to DH, is also relatively insensitive to background selection and demography. The HEW test, on the other hand, tends to be somewhat less conservative than DH and DHEW in some cases.     

Addressing the complexity in non-linear evolution of vegetation phenological change with time-series of remote sensing images

Earth observation based monitoring of change in vegetation phenology and productivity is an important and widely used approach to quantify degradation of ecosystems due to climatic or human influences. Most satellite based studies apply linear or polynomial regression methods for trend detections. In this paper it is argued that natural systems hardly react to human or natural influences in a linear or a polynomial manner. At shorter time-scales of few decades natural systems fluctuate to a certain extent in a non-systematic manner without necessarily changing equilibrium. Finding a systematic model that describes this behavior on large spatial scales is certainly a difficult challenge. Furthermore, the manner vegetation phenology reacts to climate and to socio-economic changes is also dependent on the land cover type and on the bioclimatic region. In addition to this, traditional parametric methods require the fulfillment of several statistical criteria. In case these criteria are violated confidence intervals and significance tests of the models may be biased, even misleading. This paper proposes an alternative approach termed the Steadiness to traditional trend analysis methods. Steadiness combines the direction or tendency of the change and the net change of the time-series over a selected time period. It is a non-parametric approach which can be used without violation of statistical criteria, it can be applied on short time-series as well and results are not dependent on the significance test or on thresholds. To demonstrate differences, a time-series of satellite derived Season Length images for 24 years is analyzed for the entire European continent using linear regression and the Steadiness approach. Spatial and temporal change patterns and sensitivity to pre-processing algorithms are compared between the two methods. We show that linear regression limits the possibilities of assessing fluctuating ecosystem changes whereas the non-parametric Steadiness index more consistently confirms the fluctuating phenological change patterns.