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Methods for Assessing the Effects of Mixtures of ChemicalsEdited by V. B. Vouk, G. C. Butler, A. C. Upton, D. V. Parke and S. C. Asher@ 1987 SCOPE

Statistical and Mathematical Aspects:Distinction between Natural and InducedVariation

Roger H. Green

ABSTRACT

Any good scientific study should test hypotheses which flow logically from thepurpose of the study. When the purpose is detection of biological response tomixtures of chemicals in the environment, there is a hierarchy of hypotheses:Ho = no biological response, Hi = an additive biological response to one ormore chemicals, and Hz = a biological response to interaction effects among thechemicals. Formulation of a statistical model which reflects such a hierarchy ofhypotheses is essential, as is the correct choice of the error term to be used in testsof the various hypotheses.

There are good reasons for the use of standard 'end-points', but we must alsoconsider new biological response variables for use both in the field and in thelaboratory. Attributes of a good response variable include relevance andsensitivity to impact, intrinsic value, low spatial and temporal variability, andease of estimation from field sampling. Biological responses are hierarchical, withbehavioural followed by physiological, then growth rate or other morphologicalchange, fecundity or mortality rate, and finally population genetic change. Foreach of these, response variables which have been used are reviewed andappropriate statistical models, univariate and multivariate, are discussed. Mosttests of response to interaction effects of chemicals in the environment arelaboratory studies. Organisms are integrated response systems; therefore apriority should be development of multivariate models for integrated biologicalresponses to effectsof chemical mixtures superimposed on natural environmentalvariation.

Random allocation of treatments to true replicates is rarely possible inobservational 'impact studies'. Use of sampling or analytical error as the error fortests of hypotheses is common practice but inappropriate. The alternatives areexperimental studies in the field, or observational studies conducted over enoughyears that natural, among-year variation can be estimated and used as the errorterm.

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336 Methods for Assessing the Effects of Mixtures of Chemicals

Need for true controls and balanced designs is emphasized. Tests for effects ofmixtures should be based on factorial analysis of variance designs with equalreplication at each combination of concentrations of different chemicals. Thismodel easily extends to the multivariate case (more than one biological responsevariable). Effective description of effects can be done by use of the multivariatelinear model to produce a response surface.

1 INTRODUCTION

In any scientific study there should be a logical flow of purpose from a question tohypotheses and thence to a model. This is the necessary basis for goodexperimental/sampling design, statistical analyses, tests of hypotheses, andinterpretation and presentation of results (Green, 1979, 1984).

The subtitle of this paper suggests a question such as, 'Does some man-produced environmental impact result in a biological response which isdetectable against a background of biological responses produced by naturalvariation?' In the context of this Workshop and of the section in which this paperappears, the biological response is assumed to be at the population, community,or ecosystem level.The impact is assumed to be directly or indirectly related to thepresence of a mixture of chemicals in the environment.

We now proceed from the question to hypotheses. There is a logical hierarchyof hypotheses:

(I) The null hypothesis Ho is that there is no biological response to the impact,i.e. that any biological response iscaused by natural environmental variation('baseline variation').

(2) The hypothesis H 1 is that there are biological responses attributable partiallyto one, or to the additive effectsof more than one, of the chemicals introduced(or subsequently created as by-products of those introduced) into theenvironment.

(3) The hypothesis H2 is that there are biological responses attributable partiallyto interaction effects among the introduced chemicals, or between them andtheir by-products.

These hypotheses must be expressed in terms of a statistical model, which willnecessarily be an abstraction and simplification of the typically complex, noisyreality (Green, 1979; Levins, 1966). The model must explicitly relate biologicalresponse variables to predictor variables. The predictor variables must includemeasures of the hypothesized causal factors represented by Hl and H2, and theymay also include measures of the causal factors subsumed under 'naturalvariation' (part of the Ho). The final predictor variable in any statistical model is'error', which in the real world is always greater than zero. In the realms oftheology, political ideology, and 'Creationist Science', models with no error (i.e.models associated with unfalsifiable hypotheses) are often put forward. However,

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Statistical and Mathematical Aspects 337

it is the essence of statistics, statistical models, and of science itself, that there isuncertainty. We do statistical tests to quantify our uncertainty about the truth ofalternative hypotheses. Estimation of the error term in any statistical model isessential to that process. Usually some assumption is made about the nature ofthe distribution of the errors, most often that they are normal, uncorrelated witheach other, and independent of the other predictor variables in the model.

In this paper I will first consider the question of choice of the biologicalresponse variable(s). The process of formulation of explicit null and alternativehypotheses will then be discussed, followed by a review of principles ofexperimental/sampling design. Finally I will consider the incorporation ofinteraction effects (i.e. among chemicals) into the design as an alternativehypothesis. All discussion will maintain relevance to tests of hypotheses whichconcern biological responses to mixtures of chemicals in the environment.

2 CHOICE OF BIOLOGICAL RESPONSE VARIABLES:RESPONSES AT DIFFERENT LEVELS OF BIOLOGICAL

ORGANIZA nON

Biological responses to environmental stress, or 'end-points' as they are oftencalled by toxicologists, are hierarchical in nature (Slobodkin, 1968). The firstresponse of an organism is typically behavioural (e.g. moving away from thesource of the stress), then if necessary physiological (e.g. increased respirationrate), and, as a last resort, death or failure to reproduce which carry the biologicalresponse to the population genetics and community levels. Biologists tend toadopt standard response systems; for cross-comparison of results from differentstudies this has great value. However, we should not close our eyes to promisingnew end-points for use in monitoring and baseline and impact studies which arerelated to the biological effects of mixtures of chemicals in the environment.

What are the attributes of a good biological response variable? I suggest thatthey should include: (1) relevance to the impact effectsand sensitivity of responseto them; (2) some intrinsic economic or aesthetic value if possible; (3) stability inspace and time; and (4) the possibility of being estimated from sampling-quickly, precisely, and at reasonable cost. A general review of types of responsevariables is in Green (1979, section 3.7).

Below I discuss biological response variables at different hierarchical levels,give examples of their use in studies of biological response to chemicals in theenvironment, and in some cases suggest new possibilities. It will be obvious thatrelatively few examples relate explicitly to effects of mixtures of chemicals in thesense that the biological response is demonstrably produced by an interaction ofchemicals in the mixture (the hypothesis Hz-see section I). It may be that mysearch for such examples has been inadequate, but I suspect that there arerelatively few and that those few relate, at least in part, to controlled laboratoryexperimentation.Somereasons for this are discussedin section 5.

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2.1 Changes in Community Composition

Why should we go to the expense and trouble to use a community jecosystem levelresponse as a dependent variable? As noted by Cairns (1983), interactions ofbiotic and abiotic materials at the ecosystem level 'are so complex that they couldnot be predicted from a detailed examination of the isolated component parts',but 'in the field of toxicity testing an assumption is made that responses at levelsabove singlespeciescan be reliably predicted with single speciestoxicity tests. Themost pressing need is not further perfection of single species tests, but rather thedevelopment of parallel tests at higher levels of organization.' For a generalreview of 'indices for measuring responses of aquatic ecological systems tovarious human influences', see FAa (1976).

Traditional approaches include the use of diversity indices or indicator speciesas measures of community composition under environmental stress. These twoapproaches represent, respectively, each of the two philosophical approaches: (1)find a generalizable, 'objective' measure of community change that is an indicatorof environmental stress, or (2) forget generality, and from experience graduallyaccumulate a list of species that are known to respond in certain ways toparticular kinds of impact occurring in specific environments. In theory theformer approach is preferred but many workers, including myself, have decidedthat a general objective measure does not exist. There are two problems: it is notcertain what it is about communities that the fancier diversity indices (e.g.Shannon-Weaver, Brillouin) are actually measuring (Poole, 1974: theyare 'answers to which questions have not yet been found '), and the indices do notseem to be a reliable indicator of man-caused environmental stress or deteriora-tion (Rosenberg, 1976).An extensive treatment of this subject is found in Green(1979, 1980). The enthusiasm for diversity indices seems to have waxed andwaned. On the one hand it has been realized that 'information theory' and'entropy' -based diversity indices do not really measure anything fundamentalabout communities (Goodman, 1975;Hurlbert, 1971;Pielou, 1969).On the otherhand, for those who do want to measure diversity there is a return to simplermeasures such as the number of species present (Green, 1977; Heltshe andForrester, 1983;Poole, 1974;Southward and Southward, 1978).The result of arecent attempt to define an objective and generalizable measure of communityresponse to stress is the log-normal distribution of species abundance, said byGray and co-workers (Gray, 1979, 1981;Ugland and Gray, 1982)to respond in acharacteristic way to environmental stress. The value of this method has not yetbeen determined.

Indicator species can be used successfully and have been described for manyhabitats [e.g. in freshwater (Cairns and Dickson, 1971; Hart and Fuller, 1974;Keup et al., 1966;Rosenberg and Wiens, 1976;Travis, 1978);in estuarine habitats(Hart and Fuller, 1979)]. One can choose 'best indicator species' from


preliminary sampling data by using variable subset selection techniques (e.g.lancey, 1979;Orloci, 1973),cluster analysis (Green and Vascotto, 1978;Williamsand Lambert, 1959, 1960), or by application of classical multivariate linearmodels (Green 1977, 1979, sections 4.1 and 4.2). Cairns (1984) emphasizes theneed for multispecies response systems in monitoring for environmental impact,but in many communities-including stressed ones-there is high redundancyand a few species may be sufficient to convey most of the information about thecommunity structure (Kaesler et aI., 1974).

Multivariate statistical approaches (clustering, ordination, canonical discrimin-ant analysis, multivariate linear model, response surfaces, etc.) are taking hold inapplied ecology (Green, 1980) and are preferred to the old approaches becausethey tend to retain more information about the community structure whilereducing it to an ecologically meaningful form which leads directly to standardtests of hypotheses. Also, correlation structure among the variables in a set can bedescribed. A comparison between a cluster analysis and a diversity indexapproach to an impact study of a pulp mill effiuent is presented in Green (1979,pp. 102-103) and examples of other multivariate approaches to impact ormonitoring studies are presented in section 4 of the same reference. Clusteranalysis is also used by Sanders (1978) and Sanders et al. (1980) to describe theresponse of a marine community to an oil spill, and by Crossman et al. (1974) todescribe the response of a river community to a fly-ash spill. Eilers et al. (1983)use cluster and discriminant analyses to model the susceptibility of lakes toacidification as a function of environmental variables. Multivariate approachesare of course not limited to cases where the biological response variables measurechange in community composition. For example (see section 2.2 below), changein reproductive success can be displayed by response surfaces (Alderdice, 1972),and change in morphology can be analysed by a multivariate linear model calledcanonical correlation analysis (see sections 2.3, 2.6 and 5). Change in numericalcommunity composition is not the only class of biological response variablessuitable for measuring community/ecosystem change. Biomass, productivity,caloric content, and other variables can also be used (seeGreen, 1979,section 3.7,for a brief review). Again, these and numerical abundance tend to be fairlyredundant measures in practice (e.g. Macdonald and Green, 1983), despite pastsemitheological controversies about which variables supposedly measure themost fundamental properties of communities (Hurlbert, 1971).

Following are some examples of studies which use some measure of change incommunity composition as a response to a chemical mixture in the environment.Most relate, explicitly or implicitly, to the test ofH1 and not to H2 (see section Iabove). Rosenberg (1971,1972, 1973, 1976)takes a largely graphical and tabular,rather than statistical, approach to the assessment of the impact of a pulp milleffiuent and the subsequent recovery of a fjord benthic community. It is effectiveand successful nonetheless. Kelso's (1977)study of a pulp mill effiuent found that

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chemical interaction and dilution of the effluent with the lake water producedaboundary region where the numbers of fish increased, probably because ofincreased macroinvertebrate production. Papers that relate to the effects of oil onmarine benthic communities (taken from J. Fish. Res. Board Can., 35(5), 1978)are by Thomas (rocky and soft substrate intertidal), Sanders (see also Sanders etal., 1980) (soft substrate intertidal and subtidal), Atlas et al. (soft substratesubtidal including microbial), Southward and Southward (rocky intertidal) andHampson and Moul (salt marsh). For a summary of the results of studies on theimpact of the Amoco Cadiz oil spill on the coast of Brittany see Laubier (1980)and other papers in that issue of Ambio. Long-term studies of naturalcommunities are badly needed (Green, 1984) to establish the magnitude of theirnatural 'baseline' variation which is necessarily part of the null hypothesis (Ho) inany impact study (see sections 1, 3, and 5). Experiments conducted in the fieldover several years must also be done (see Keating, 1982, for a newspaper reporton an experimental arctic marine oil spill which is still in progress).

2.2 Change in Fecundity or Mortality Rate

The standard laboratory LCso determination by toxicologists is of course anexample of studies using mortality as a biological response variable. Here I aminterested more in 'natural', longer-term studies. Extrapolation of laboratoryLCso estimates to an indefinitely long period of exposure (as in the naturalenvironment) can be done using a hyperbolic regression approach (Green, 1965,1979,section 4.2; Sprague, 1969).However, there is no substitute for field studies.Change in fecundity or recruitment rates is a particularly sensitive indicatorbecause eggs, larvae, and juveniles are often more vulnerable to impacts than areadults. Also, it is the ability of the species to produce a new generation to replaceitself that is being measured. Artificial substrate sample data are often goodmeasures of this ability (see section 2.4).

Oil spill related effects on mortality, fecundity, and recruitment of marineorganisms are described by Linden (1976), Busdosh and Atlas (1977), Andersonet af. (1978), Krebs and Burns (1978), and Bayne et al. (1979). Effects of residuesof chlorinated hydrocarbon pesticides on shell thickness associated withpopulation declines of raptorial bird species are described by Hickey andAnderson (1968). Embryo deaths in estuarine fishes caused by methyl mercuryare reported by Weis (1981), and de March (1979) describes results of alaboratory study of mortality in freshwater amphipods caused by interactingeffects of differing copper concentrations and different pH levels. Studies byMcLeese (1956) and Alderdice (1972) also deal with interaction effects amongmore than one chemical or physical factor, using laboratory simulations of theenvironment. None of their manipulated factors are 'pollutants', but the responsesurface displays that are used would be equally effective with toxic chemicalconcentrations as variables (see section 5).

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2.3 Change in Individual Growth Rate or Morphology

These categories of biological response can be considered at the individual or thepopulation level. The statistical methodology which can be used is diverse andinadequately exploited by researchers. Response surface displays, as describedabove, can be used effectively. Many multivariate analyses are applicable, forexample principal components analysis and other ordination techniques, clusteranalysis, canonical discriminant analysis, and canonical correlation analysis(Blackith and Reyment, 1971; Bookstein, 1978; Pimentel, 1978; Siegel andBenson, 1982).Green (1972) applies canonical correlation analysis to relate a setof morphological response variables (shells of freshwater clams) to a set ofenvironmental predictor variables, the majority of which are chemical variables.No interaction terms were used to represent Hz effects (see section I) but there isno reason why this could not be done, given a balanced design (see sections 2.6and 5). Another statistical approach that can be used is analysis of covariance forcomparison of regression lines. Shape or 'condition' can be described by log-logrelationships between various morphological measurements, and those relation-ships can be contrasted between control and impacted environments (e.g.Thomas, 1978).Growth curves can be described and their parameters estimatedby using Walford plots of'size this year' versus 'size last year'; the commonly usedvon Bertalanffy growth curve (Green, 1979, section 2.7; Ricker, 1958) isrepresented by a straight line on such a plot, and standard linear regression oranalysis of covariance can be applied to contrast growth curves between controland impacted environments. Such data can arise either from mark-recapturestudies or from the use of annual markers such as winter growth rings in bivalves.McCuaig and Green (1983)provide an example of analysis of covariance appliedto data of the latter type. More flexiblegrowth functions can also be used (Ebert,1980; Richards, 1959).

Studies using growth rate or morphological criteria as measures of response tochemicals are as follows. Bayne et al. (1979)describe effects of oil on the growthrate of the mussel Mytilus. Other papers describing effects of oil on marineorganisms (all from J. Fish. Res. Board Can., 35(5), 1978)are by Gilfillan andVandermeulen (growth of the clam Mya), Cole (shape in snails), Percy (growthand molting in an isopod), McCain et al. (abnormalities in fish), and Payne et al.(abnormalities in fish). Frazier (1976) describes change in shell thickness ofoysters caused by heavy metals. For effects of water chemistry on shellmicrostructure and chemistry see Laporte (1968), Lee and Wilson (1969),Sturesson and Reyment (1971), Rhoads and Lutz (1980), and Imlay (1982).Fisher (1977)presents evidence that the effecton growth rate (of a marine diatom)by exotic chemicals is less if the population comes from a harsh natural chemicalenvironment (estuarine) than if it comes from a benign one (open ocean). Thissuggests that some populations of a species can be phenotypically (and perhapsgenotypically-see section 2.5) pre-adapted for exposure to a new chemical. This


can be viewed as an interaction between a chemical stressor and the pre-existingchemical environment.

2.4 Change in Physiology or Behaviour

Many of the previously described or cited statistical methods are applicable hereas well.

In the marine environment, effects of oil on carbon flux rate and assimilationrate in Mya are described by Gilfillan and Vandermeulen (1978). Effects onrespiration rate of Mya are described by Stainken (1978). Bayne et al. (1979)describe effects on respiration rate of Mytilus. In freshwater, Salanki andVaranka (1976)found that the rhythmic movement of the valves of unionid clamswas affected by copper sulphate whereas lead compounds had no such effect.They describe a 'mussel actograph' (Salanki and Balla, 1964) for automaticrecording of the rhythms. Uptake of chemical compounds by an organism is auseful response which is discussed, with examples, by Green (1979, section 3.7).High zinc concentrations in oyster tissue caused by pulp mill effluent, andsubsequent loss of zinc after the discharge ceased, are described by Ellis et al.(1981). Uptake of various heavy metals into the tissue and shell of oysters isdescribed by Frazier (1976).

When an organism detects a deteriorating environment its first response isoften behavioural (Slobodkin, 1968),and behavioural responses have importanteffects at the population level, for example aggregation (swarming, flocking, etc.)or dispersal which may increase or decrease effectiveness of feeding, reproduc-tion, or defence against predation. As mentioned in section 2.2 above, simplepassive devices such as artificial substrates and gill nets in aquatic environments,and pitfall and snap traps in terrestrial environments, can record mobility oforganisms. Flannagan (1973) found that many stream benthic species left thebottom and entered the drift after the drainage was sprayed with fenitrothion.The standing crop did not change, presumably because of replacement frompopulations upstream. Percy (1976, 1977) and Percy and Mullin (1977) describethe behavioural responses of marine invertebrates to oil in food, sediment andwater.

2.5 Change at the Genetic Level

Genetic response by a population is in a sense the last resort (Slobodkin, 1968)because it implies that the repertoire represented by the distribution of individualphenotypes and underlying genotypes in the population has failed to deal withthe environment of the recent past. As a consequence, increased mortality orlowered fecundity has acted, inevitably differentially, on the geneticallyheterogeneous population.

Regarding the genetic response to chemicals in the environment, Cole (1978)


describes genetic changes in an oyster drill (Urosalpinx) population caused bymass mortality following an oil spill. The possible genetic basis of the greaterresistance to polychlorinated biphenyls by estuarine diatoms compared with openocean diatoms has already been mentioned (section 2.3). The susceptibility ofestuarine killifish to methyl mercury (craniofacial defects and deaths in embryos)described by Weis (1981) probably has some genetic basis. Gradients in allozymefrequencies corresponding to salinity gradients are well documented (e.g. Koehnet aI., 1976, 1980).McNair (1979)describes a genetic basis for copper tolerance ina terrestrial plant. Nevo and co-workers have done interesting work on thegenetic basis of response to pollution in marine invertebrates (Nevo et al., 1978,1980).

2.6 Choice of Biological Response Variables: Summary

The list of chemical contaminants in the environment is long and frightening(Moore and Moore, 1976,Table 16.1)and certainly some of them can cause andhave caused damage to organisms. The potential for chemical interactionsinfluencing biological response is great. Whether the reality is 'The Monster WeCreated' as described by Schanberg (1983) is not yet determined. Since thenumber of potential interactions increases very rapidly with the number ofpotentially interacting chemicals in the 'soup', it is of critical importance todetermine the biological relevance of interactions in general (see section 5).

The separate categories above (sections 2.1-2.5) are somewhat misleading.Organisms are highly integrated response systems and they rarely respond in onlyone response 'compartment'. For example, in studies cited above it should benoted that Bayne et al. (1979) describe both growth and respiration responses tooil in the marine mussel Mytilus, as do Gilfillan and Vandermeulen (1978) for theclam Mya. Perhaps the best approach for the future is to seek multivariatedescriptions of coupled biological responses, and the genetic bases of thoseresponses, based on a combination offield and laboratory studies. For example,Green et al. (1983) describe a growth and temperature tolerance response in theestuarine clam Macoma which appears to have some genetic basis. Koehn andShumway (1982) report results of a laboratory experiment which clarify anapparent three-way relationship observed in the field among growth rate,metabolism, and genotype, in Mytilus and other marine bivalves.

Finally, it should be remembered that the direction of causality is oftenambiguous, and that an apparent biological response is often an integratedreciprocal relationship between organisms and environment as well as amongand within organisms. Path analysis models (Li, 1975), which at first glanceappear to be very useful models for our problem, often founder on theirassumption that 'paths' are one-way causal links. For example, the microbialresponse to an oil spill is also an effect which leads to the degradation of the soil(Colwell et aI., 1978).Similarly,Rhoads et al. (1978)and Gordon et al. (1978)


describe how community succession and the feeding behaviour of macrofauna,especially polychaete worms, hasten-and indeed are part of-the process ofrecovery of chemically fouled marine benthic environments.

Obviously we need to develop general models which can predict a multivariateresponse of correlated biological variables predicted by environmental variableswhich both act on and are acted upon by the biological variables. The canonicalcorrelation model (see Harris, 1975, or Pimentel, 1978, for an introduction;Gittins, 1979, for a biologically oriented monograph; and Green, 1972, for anexample) is the standard method that is perhaps closest to this ideal. However,interpretation of results can be difficult when interset causality is reciprocal.Also, it is a linear model and therefore the non-linear responses typical ofecological systems must be incorporated by using appropriate a priori trans-formations of variables. Further development of models in this area is a highpriority. See further discussion in section 5.

3 FORMULATION OF EXPLICIT NULL AND ALTERNATIVEHYPOTHESES

Given that the biological response of variable(s) has been chosen, and thenature of chemical impact is known, we must explicitly state the relevanthypotheses Ho, HI, and H2 (section 1).The null hypothesis, Ho, should be thesimplest possible explanation that is consistent with the evidence. The Ho couldbe that any observed relationships between biological responses and chemicalconcentrations in the environment are attributable to chance sampling orexperimental error. However, this is unrealistic when studies are done in the fieldbecause in most cases there will be substantial biological response to un-controlled variation in natural environmental factors, even in the absence ofman-caused impacts (e.g. Hinckley, 1969,described by Green, 1979,section 2.1).Therefore, the Ho should be formulated as described in section 1, i.e. includingresponse to natural environmental variation.

This leads to two important considerations: (1) that each hypothesis should betested against its hierarchically next most complicated alternative, and (2) thatthe choice of error term to be used in any test of a hypothesis influences thevalidity of the conclusions. These points are considered further in sections 4 and5, and also in Green (1984). When the alternative hypothesis is 'impact causesbiological response', the valid error term for tests is not the estimate of samplingerror, particularly when there is added variation caused by non-impact naturalenvironmental variation. However, most computer statistical packages, whenpresented with an array of data in an analysis of variance design, will by defaultcalculate all tests of hypotheses using the pooled within-cell error for the cellsthat are lowest in the hierarchical design. This means that in a design of the form'(a) control versus impact areas, (b) different stations sampled in different yearswithin each such area, (c) replicated field samples taken at each station in each


year, (d) replicate subsamples of the biological material and replicate analyticaldeterminations within the field samples', the default analysis would use the last ofthese (counting error and analytical error) as the implicit null hypothesis in alltests including the test of impact effects. This would be inappropriate. In mostcomputer packages it is possible to choose your desired error term, but with mostpackages this is not emphasized.

To formalize this concern, I will in this paper refer to any 'analytical orcounting error' null hypothesis as H -2' It could be validly used as an error termto test a hypothesis which I will call H - I' that there are no differences amongreplicate field samples within stations and years. The hypothesis H_I could inturn be used as the error term to test Ho, that there is biological responsevariation that is 'natural' (i.e. unrelated to impact) among stations or years. Thedesignation Ho is here reserved for that null hypothesis which is the mostmeaningful and realistic expression of 'no biological responses related to impact',against the alternative HI that there is. A hypothesis related to chemicalinteractions producing a biological response would be designated H2 (as insection I).

4 PRINCIPLES OF EXPERIMENT ALjSAMPLING DESIGN

Principles of sampling design for environmental studies are outlined by Green(1979, section 2.3) and discussed with examples. Here I would emphasize thefollowing: the need for true replication, controls, balanced designs (especiallywhen testing for interactions between main effects-see section 5), and the needfor preliminary sampling.

That there must be replication to test hypotheses is obvious to all but the mostnaive. However, true replication for testing hypotheses about impact is notreplication of analyses or counts in the laboratory, nor is it field samplingreplication. These two levelsof replication lead, respectively, to hypotheses H - 2

and H_I, neither of which is appropriate to use as an error term for testingwhether introduced chemicals have caused biological responses. The term'pseudoreplication' is applied to the use of such error terms in tests related toimpact (Green, 1984; Hurlbert, 1984). Many have done this, including myself(Green, 1979, section 4.1, as noted by Hurlbert), and the problem is that withenvironmental studies done in the field it is difficult to find an alternative. Oftenenvironmental biologists are presented with a de facto impact situation, say apoint-source chemical effluent on a river. With luck there may be a pre-impactperiod of time for assessment of the baseline situation, but even so the result willbe an observational study (see Anderson et aI., 1980) instead of a properinferential hypothesis-testing design in which replicates are chosen a priori andthen the treatments (e.g. control versus impact) are randomly assigned to thereplicates. If we could randomly select sites on the river from a universe ofpotential sites, and then randomly select from those sites a subset where identical


effluent-producing industrial plants would be used as controls, only then wouldwe have a design with true replication. It is unlikely that environmental biologistswould ever have this opportunity.

With what, then, are we left? Less formal statistical assessments or graphicaldescriptions of impact effects are still of value, but the best alternative is probablyexperiments done in the field, thus combining the ability to experimentallymanipulate with the realism of the natural environment. No doubt we willcontinue to take advantage of 'natural experiments' such as the Buzzards Bay,Chedabucto Bay, and Brittany oil spills, but this is less than satisfactory. In suchcases the researcher has not manipulated the treatment effects and randomlyassigned them to replicates, and therefore it is possible that effects will beconfounded. For example, tankers may tend to have accidents near certain kindsof coastlines in certain parts of the world with certain kinds of climate. Thenatural communities in those habitats may be characteristic of those environ-mental regimes and as a consequence may be more or less sensitive to impact.Fisher's (1977) results (see section 2.3) suggest that populations in estuaries-where tanker traffic tends to be heaviest-may be more resistant to impact byexotic chemicals than populations in the open ocean. Therefore it is essential thatscientific research include planned and controlled field experiments involvingchemical impacts. When possible, they should be designed (see section 5) so thattests of H2-type hypotheses (chemical interactions causing biological response)can be made.

When conducting the usual suboptimal observational impact studies, whatshould be used as the null hypothesis error term, Ho, for tests about impacteffects? As indicated, nothing is truly satisfactory because there is no truereplication. Green (1984)argues for long-term studies in tests of impact, with theamong-year variation in the baseline situation (pre-impact time or control area)used as the error term. Such studies will be costly if they are of long enoughduration to provide adequate among-year degrees of freedom. However, triviallysignificant results (judged against pseudo replication error) would be eliminated,and the word 'significant' would become much more meaningful in human terms.

The need for controls in environmental studies is obvious, especially in fieldstudies. It is important to remember that for our purposes a control must be asituation in which the chemical impact does not occur but all else is the same. Forexample, if administration of a chemical requires a 'carrier' to dissolve or mix thechemical with the water, then the control must receive the same amount of thecarrier without the test chemical. In field studies the natural environment shouldbe the same in all respects in the control and impact areas.

In any study the assumptions of the statistical methods should always beunderstood, and the extent to which those assumptions have been satisfiedevaluated. This is now easy to do by descriptive graphical methods, rather thanformal tests, using standard statistical packages. The MINIT AB package (Ryanet aI., 1981), for example, easily produces scatter plots of model residual errors.

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Assessment of the normality of those errors and their independence from modeleffects is also easily done. One should not become too concerned about failure tosatisfy assumptions. If error degrees of freedom are adequate, sampling/experi-mental designs are balanced, and among-replicate errors are not wildlyheterogeneous, most overall F-tests of hypotheses will be valid (Harris, 1975). Itis rarely necessary to flee to non-parametric statistics because of failure ofassumptions of the classical tests. Usually standard transformations will sufficeto correct any problems.

A concern that is specific to tests of hypotheses about biological responses tochemicals is that responses may be non-monotonic. For example, diversityindices often peak at some 'moderately polluted' level (e.g. Rosenberg, 1976),and productivity is often highest in a slightly eutrophied ecosystem. Ecologistsoften generate data which contain such non-monotonic relationships, and theyunthinkingly enter those data into computer package programs for analysis bymodels which assume linearity, not to mention monotonicity. Again, the simpleprecaution of examining scatter plots-in this case all possible bivariate plots-should be a sufficient precaution.

5 TESTING INTERACTION AMONG CHEMICALS INPRODUCING BIOLOGICAL RESPONSE

Whether interactions among chemicals are important in producing biologicalresponse is a question that continues to leave many researchers uneasy, and onethat many researchers ignore or avoid. For example, Brasfield (1972) uses linearregression analysis to predict bacterial population size in a river from observa-tions on seven chemical concentration variables (one of them detergents) plustemperature. No attempt to assess interaction among the environmentalvariables is made (i.e. to test the hypothesis H2), but the unbalanced design wasunsuitable for the purpose in any case (see discussion below). There is somejustification not to be concerned with significance of chemical interactions. Thenumber of possible interactions rises rapidly with the number of potentiallyinteracting chemicals: 1 for two chemicals, 4 for three chemicals, 11 for fourchemicals, and so on. As Vandermeer (1981) says, 'To ask if there are higherorder interactions is a meaningless question if taken in isolation. We all knowthat they are there and it is only a question of enough grant money. . . todemonstrate them statistically. What we want to know is whether they areimportant biologically. . . ' Furthermore, the difficulty and expense of conduct-ing field studies for testing interactions among chemicals are almost prohibitive.Many designs which suffice for testing the effects of individual chemicals onorganisms cannot be used. It could be argued that for the present such studiesshould be conducted in the laboratory except for chemicals which have beendemonstrated to have obvious and important interactions in their effects onorganisms.


However, there are such chemicals, ones whose puzzling behaviour in naturehas made the existence of interactions obvious, and for which laboratory studieshave verified and quantified the interactions. The best example is probably theinteraction of heavy metals in freshwater environments with the pH of the water[e.g. de March, 1979; Rudd et al., 1983;and companion papers in Can. J. Fish.Aquat. Sci., 40(12)]. Experiments should now be conducted in the field, and thishas already been done in a few cases (e.g. Nero and Schindler, 1983). I use theword 'experiments' intentionally because it is highly improbable that anyobservational study, such as that of Brasfield, would result in a balanced designof observations on different chemicals at different concentrations. The twoobvious and minimal requirements are (1) that two or more chemicals be presentover a range of concentrations, and (2) that observations evenly cover the rangeof possible combinations oflevels of all chemicals that vary in concentration (i.e.a balanced design).

Statistically, the problem with unbalanced designs is that any apparentinteraction between two chemicals is likely to be confounded with the samplingeffort. With two potentially interacting chemicals (say copper and the hydrogenion as measured by pH) and a hypothesized biological response (say decreasedreproduction in an amphipod), the hypothesis H2 is that the effect of copperconcentration on rate of reproduction is dependent on the pH of the medium. (Itwould also be correct to say that the effect of pH on reproduction is dependent onthe copper concentration.) If the null hypothesis Ho (variation in reproductiverate is only by chance or is a function of natural environmental variation) isrejected where H2 is the alternative hypothesis, and a balanced experimentaldesign allows unambiguous interpretation of this result, then a test ofHo againstHl (that copper and/or pH separately or additively influence reproductive rate) isno longer meaningful. It is easy to seewhy, given this realistic example. If there isinteraction, then it follows that the answer to the question 'Does copperconcentration or pH influence reproduction?' is 'It depends on what theconcentration of the other is at the time.' Thus any test with H 1 as an alternativeceases to be of interest, although the Hl-related main effects of copper and pHremain in the ANOV A model. The above reasoning implies that we should testagainst H2 as an alternative first, and only if Ho is accepted with H2 as thealternative should we proceed to test Ho against H 1 .

In the tests of these hypotheses the experimental design should be appropriatefor a factorial ANOV A (of dimension equal to the. number of potentiallyinteracting chemicals) and for the tests of hypotheses associated with thatanalysis (Snedecor and Cochran, 1980, chapter 16). The requirements of thefactorial ANOV A design will ensure that the allocation of experimentalobservations be balanced. For effective graphical description of the results,response surface analysis is appropriate (previously mentioned in sections 2.1-2.3) and is a logical extension of the ANOV A. See Snedecor and Cochran (1980)for details of calculations and worked examples. Lee (1971) provides a computer


program but response surface analysis can also be done with standard statisticalcomputer packages.

If there is more than one biological response variable then a multivariatestatistical approach is appropriate (see sections 2.1 and 2.6). Here the multi-variate factorial ANOV A model would obviously be appropriate (see Green,1979, section 4.1). For example, we could be interested in the effect of copperinteracting with pH on both reproduction and mortality rates in an amphipod.The multivariate linear model could then be used to produce response surfacesassociated with the corresponding multivariate ANOV A (Lee, 1971).

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