In the deep end: pooling data and other statistical challenges of zoo and aquarium research

Zoo and aquarium research presents many logistic challenges, including extremely small sample sizes and lack of independent data points, which lend themselves to the misuse of statistics. Pseudoreplication and pooling of data are two statistical problems common in research in the biological sciences. Although the prevalence of these and other statistical miscues have been documented in other fields, little attention has been paid to the practice of statistics in the field of zoo biology. A review of articles published in the journal Zoo Biology between 1999–2004 showed that approximately 40% of the 146 articles utilizing inferential statistics during that span contained some evidence of pseudoreplication or pooling of data. Nearly 75% of studies did not provide degrees of freedom for all statistics and approximately 20% did not report test statistic values. Although the level of pseudoreplication in this dataset is not outside the levels found in other branches of biology, it does indicate the challenges of dealing with appropriate data analysis in zoo and aquarium studies. The standardization of statistical techniques to deal with the methodological challenges of zoo and aquarium populations can help advance zoo research by guiding the production and analysis of applied studies. This study recommends techniques for dealing with these issues, including complete disclosure of data manipulation and reporting of statistical values, checking and control for institutional effects in statistical models, and avoidance of pseudoreplicated observations. Additionally, zoo biologists should seek out other models such as hierarchical or factorial models or randomization tests to supplement their repertoire of t‐tests and ANOVA. These suggestions are intended to stimulate conversation and examination of the current use of statistics in zoo biology in an effort to develop more consistent requirements for publication. Zoo Biol 0:1–14, 2006. © 2006 Wiley‐Liss, Inc.     

Pseudoreplication in experimental designs for the manipulation of seed germination treatments

In the published reports concerning the design of laboratory experiments examining signals that might trigger seed germination, there is currently a misunderstanding of what might constitute correct replication of the experimental treatment. This is particularly true for the study of dry heat, smoke and charcoal, where either an individual seed or a batch of seeds in a Petri dish or tray is being treated as the unit of replication of the experimental treatment, irrespective of whether or not those seeds were all subjected to the experimental manipulation simultaneously. Under these circumstances, the application of the treatment is unreplicated, while samples nested within that single application have been replicated, and the Petri dishes/trays are functioning solely as independent replicates of the variability in germination response within the seed batch used and variation within the pretreatment and post‐treatment environments. Thus any observed difference in germination may be due to the germination treatment but, potentially, it could also be due to any chance event affecting the treated sample. There are a number of alternative experimental designs that avoid this problem. The essential point with these designs is that the application of the experimental manipulation to each replicate should be separated in space by the use of separate experimental equipment and/or in time by the repeated use of the same experimental apparatus.     

Pseudofactorialism,response structures and collective responsibility

Pseudofactorialism is defined as ‘the invalid statistical analysis that results from the misidentification of two or more response variables as representing different levels of an experimental variable or treatment factor. Most often the invalid analysis consists of use of an (n + 1)‐way anova in a situation where two or more n‐way anova s would be the appropriate approach’. I and my students examined a total of 1362 papers published from the 1960s to 2009 reporting manipulative experiments, primarily in the field of ecology. The error was present in 7% of these, including 9% of 80 experimental papers examined in 2009 issues of Ecology and the Journal of Animal Ecology. Key features of 60 cases of pseudofactorialism are tabulated as a basis for discussion of the varied ways and circumstances in which the error can occur. As co‐authors, colleagues, editors and anonymous referees and editors who approved them for publication, a total of 459 persons other than the senior authors shared responsibility for these 60 papers. Pseudofactorialism may sometimes be motivated by a desire to test whether different response variables respond in the same way to treatment factors. Proper procedures for doing that are briefly reviewed. A major cause of pseudofactorialism is the widespread failure in statistics texts, primary literature and documentation for statistics software packages to distinguish the three major components of experimental design – treatment structure, design structure, response structure – and clearly define key terms such as experimental unit, evaluation unit, split unit, factorial and repeated measures. A quick way to check for the possible presence of the pseudofactorialism is to determine whether the number of valid experimental units in a study is smaller than (i) the error degrees of freedom in a multi‐way anova ; or (ii) the total number of tallies (N) in a multi‐way contingency table. Such situations also can indicate the commission of pseudoreplication, however.     

Anonymous fecal sampling and NIRS studies of diet quality: Problem or opportunity?

Investigating the drivers of diet quality is a key issue in wildlife ecology and conservation. Fecal near infrared reflectance spectroscopy (f‐NIRS) is widely used to assess dietary quality since it allows for noninvasive, rapid, and low‐cost analysis of nutrients. Samples for f‐NIRS can be collected and analyzed with or without knowledge of animal identities. While anonymous sampling allows to reduce the costs of individual identification, as it neither requires physical captures nor DNA genotyping, it neglects the potential effects of individual variation. As a consequence, regression models fitted to investigate the drivers of dietary quality may suffer severe issues of pseudoreplication. I investigated the relationship between crude protein and ecological predictors at different time periods to assess the level of individual heterogeneity in diet quality of 22 marked chamois Rupicapra rupicapra monitored over 2 years. Models with and without individual grouping effect were fitted to simulate identifiable and anonymous fecal sampling, and model estimates were compared to evaluate the consequences of anonymizing data collection and analysis. The variance explained by the individual random effect and the value of diet repeatability varied with seasons and peaked in winter. Despite the occurrence of individual variation in dietary quality, ecological parameter estimates under identifiable or anonymous sampling were consistently similar. This study suggests that anonymous fecal sampling may provide robust estimates of the relationship between dietary quality and ecological correlates. However, since the level of individual heterogeneity in dietary quality may vary with species‐ or study‐specific features, inconsequential pseudoreplication should not be assumed in other taxa. When individual differences are known to be inconsequential, anonymous sampling allows to optimize the trade‐off between sampling intensity and representativeness. When pseudoreplication is consequential, however, no conclusive remedy exists to effectively resolve nonindependence.     

Experimental separation of effects of consumers on sessile prey in the low zone of a rocky shore in the Bay of Panama: direct and indirect consequences of food web complexity

The effects of predation by a diverse assemblage of consumers on community structure of sessile prey was evaluated in the low rocky intertidal zone at Taboguilla Island in the Bay of Panama. Four functional groups of consumers were defined: (1) large fishes, (2) small fishes and crabs, (3) herbivorous molluscs, and (4) predaceous gastropods, (l) and (2) included fast-moving consumers and (3) and (4) included slow-moving consumers. Experimental treatments were: no consumers deleted (all groups present), most combinations of deletions of single groups (i.e., one group absent, three present), pairs of groups deleted (two absent, two present), trios of groups deleted (three absent, one present), and the entire consumer assemblage deleted (all groups absent). Changes in abundance (percent cover) of crustose algae, solitary sessile invertebrates, foliose algae, and colonial sessile invertebrates were quantified periodically in 2–4 plots of each treatment from February 1977 to January 1980 after the initiation of the experiment in January 1977.

Space on this shore is normally dominated by crustose algae; foliose algae, solitary sessile invertebrates, and colonial sessile invertebrates are all rare. After deletion of all consumers, ephemeral green algae increased from 0 to nearly 70% cover. Thereafter, a succession of spatial dominants occurred, with peak abundances as follows: the foliose coralline alga Jania spp. by July 1977, the barnacle Balanus inexpectatus by April 1978, and the rock oyster Chama echinata by January 1980. Although no longer occupying primary rock space, Jania persisted as a dominant or co-dominant turf species (with the brown alga Giffordia mitchelliae and/or the hydrozoan Abietinaria sp.) by colonizing shells of sessile animals as they became abundant instead of the rock surface.

Multivariate analysis variance (MANOVA) indicated that the effect of each group was as follows. Molluscan herbivores grazed foliose algae down to the grazer-resistant, but competitively inferior algal crusts, altered the relative abundances of the crusts, and inhibited recruitment of sessile invertebrates. Predaceous gastropods reduced the abundance of solitary sessile animals. Small fishes and crabs, and large fishes reduced the cover of solitary and colonial sessile animals and foliose algae, although they were incapable of grazing the foliose algae down to the rock surface. Many of the effects of each consumer group on prey groups or species were indirect; some effects were positive and some were negative. The variety of these indirect effects was due to both consumer-prey interactions among the consumers, and competitive or commensalistic interactions among the sessile prey. Comparison of the sum of the effects of each of the single consumer groups (i.e., the sum of the effect observed in treatments with one group absent, three present) with the total effects of all consumers (i.e., the effect observed in the treatment with all groups absent) indicates that a “keystone” consumer was not present in this community. Rather, the impacts of the consumer groups were similar but, due to dietary overlap and compensatory changes among the consumers, not readily detected in deletions of single consumer groups. The normally observed dominance of space by crustose algae is thus maintained by persistent, intense predation by a diverse assemblage of consumers on potentially dominant sessile animals and foliose algae. The large difference in structure between this and temperate intertidal communities seems due to differences in degree, not kind of ecological processes which produce the structure.     

生态学试验设计与解释中的常见问题

一个"好"的试验,统计检验的显著差异可证明处理效应存在;而一个"坏"的试验,统计检验的显著差异本身并不能证明处理效应的真实存在.试验单位的不独立就可能使干扰因素偏倚地影响试验结果,是多种形式的伪重复的根本原因.如果不统筹地考虑试验方法和数据分析方法,环境要素的时空格局就可能被错误地当成处理效应.以案例分析的形式探讨了中国生态学试验设计与解释中常见的3个问题:(1)简单伪重复问题,这是Hurlbert[2]早已指出的伪重复情形中的一种,通常是把取样的重复当成了处理的重复;(2)把反复测量结果当成重复的问题,即对同一个对象的反应变量前后进行多次观测,却把这些观测值视为重复而进行统计检验所造成的问题;(3)混淆时空效应与处理效应的问题,由于取样方法(破坏性取样)或者研究对象(例如流动的水体)性质的特殊性等原因,数据中所体现出来的格局有可能由于时空效应而并非处理效应所造成.在这3种情况下,数据的产生方式与所用统计方法的前提相违背.     

Diel variation in feeding rate and prey composition of herring and mackerel in the southern Gulf of St Lawrence

Diel feeding patterns of herring Clupea harengus and mackerel Scomber scombrus in the southern Gulf of St Lawrence were examined based on samples obtained by midwater trawling between 19 and 26 June 2001. Within 3 h time periods, stomach contents tended to be more similar between fish from the same tow than between fish from different tows. Thus, in contrast to previous diet studies, which have used individual fish stomachs as independent observations, tow was used as the experimental unit in statistical analyses in this study. Diel patterns in stomach fullness were identified using generalized additive models. Two peaks in stomach fullness occurred for herring, one in the morning and the other in the evening. Mackerel showed an increase in feeding intensity throughout the day with a peak in mid‐afternoon. The diel changes in stomach contents suggested rapid gastric evacuation rates for both species, especially for herring. The estimate of the instantaneous evacuation rate for herring was twice that for mackerel. Calanus copepods (mainly C. hyperboreus ), fishes (mainly capelin Mallotus villosus ) and euphausiids were the main prey found in the stomachs of both species. Calanus copepods dominated the diet of herring regardless of time period. They also dominated the diet of mackerel during the late afternoon, evening and night while fishes and euphausiids were dominant during the morning and early afternoon. These diel patterns emphasize the need for sampling throughout the day and night in order to estimate ration and diet composition for bioenergetic and ecosystem models.