The conservation biologist s toolbox principles for the design and … · 2015-09-04 · The conservation biologist’s toolbox – principles for the design ... (Chapter 14). Because

CHAP T E R 1 6

The conservation biologist’stoolbox – principles for the designand analysis of conservation studiesCorey J. A. Bradshaw and Barry W. Brook

“Conservation biology” is an integrative branch ofbiological science in its own right (Chapter 1); yet,it borrows from most disciplines in ecology andEarth systems science; it also embraces genetics,dabbles in physiology and links to veterinary sci-ence and human medicine. It is also a mathemati-cal science because nearly all measures arequantified and must be analyzed mathematicallyto tease out pattern from chaos; probability theoryis one of the dominant mathematical disciplinesconservation biologists regularly use. As rapidhuman-induced global climate change (Chapter8) becomes one of the principal concerns for allbiologists charged with securing and restoringbiodiversity, climatology is now playing a greaterrole. Conservation biology is also a social science,touching on everything from anthropology, psy-chology, sociology, environmental policy, geogra-phy, political science, and resource management(Chapter 14). Because conservation biology dealsprimarilywith conserving life in the face of anthro-pogenically induced changes to the biosphere, italso contains an element of economic decisionmaking (Chapter 14). This is a big toolbox indeed,so we cannot possibly present all aspects here. Wetherefore focus primarily in this chapter on theecological components of conservation biology(i.e. we concentrate on the biology per se).

Conservation biology, and the natural sciencesin particular, require simplified abstractions, ormodels, of the real world to make inferencesregarding the implications of environmentalchange. This is because ecosystems are inherentlycomplex networks of species interactions, physical

constraints and random variation due to stochastic(random) environmental processes. The conserva-tion biologist’s analytical toolbox therefore com-prises methods that mainly serve to simplify thecomplexity of the real world such that it is under-standable and (partially) predictable. The quantifi-cation of these relationships – from the effects ofhabitat loss on biodiversity (Chapter 4) to the im-plications of small population size for extinctionrisk (Chapter 10) – is the backbone of analyticalconservation biology and evidence-based decisionmaking. Without quantified relationships androbust measures of associated uncertainty, recom-mendations to improve biodiversity’s plight viamanagement intervention or policy change aredoomed to fail.

Even though we have chosen to focus on thetechniques dealing with the biological data in theconservation realm, we can by no means be com-prehensive; there are simply too many ideas, me-trics, tests, paradigms, philosophies and nuancesto present within a single chapter of this book.However, we have striven to compile a compendi-um of the major approaches employed along witha list of the best textbook guides andpeer-reviewedscientific papers providing the detail necessary fortheir implementation.We first presentmeasures ofbiodiversity patterns followed by a general discus-sion of experimental design and associated statisti-cal paradigms. We then introduce the analysis ofabundance time series followed by assessments ofspecies’ fate risks. The final section is a brief intro-duction to genetic tools used to assess a species’conservation status. Although issues of reserve

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design and their associated algorithms are an es-sential part of the conservation biologist’s toolbox,they have beendiscussed in detail elsewhere in thisbook (Chapter 11) and so do not feature in thischapter.

16.1 Measuring and comparing‘biodiversity’

Chapter 2 provides an excellent overview of thesomewhat nebulous concept of ‘biodiversity’ anda brief mention of how it can be measured, andChapter 11 introduces the concept of ‘surrogacy’(simplified measures of biodiversity patterns) inconservation planning. Here we develop theseconcepts further with particular emphasis onpractical ways to obtain comparable and mean-ingful metrics over space and time. It should benoted that regardless of the logistic constraints,biological consideration and statistical minutiaedriving the choice of a particular set of metricsfor biodiversity, one must not forget to considerthe cost-benefit ratio of any selected method(Box 16.1) or the difficulties and challenges ofworking across cultures (Box 16.2).

16.1.1 Biodiversity indices

It is simply impossible tomeasure every formof life(Chapter 2), regardless of the chosenmetric or focaltaxon, due to the sheer number of species and thedifficulty of sampling many of the Earth’s habitats(e.g. ocean depths and tropical forest canopies).Weare therefore required to simplify our measure-ments into tractable, quantifiable units thatcan be compared across time and space. The sim-plest and perhaps easiest way to do this has tradi-tionally been to use organism-based metrics thatcount, in one way or another, the number of ‘dis-tinct’ species in a defined area. Species richnessis therefore the base currency used for most biodi-versity assessments, but it can be complicatedby adjusting for relative abundance, uniqueness,representativeness, spatial scale or evolutionaryhistory.

Asmentioned above, a direct count of the num-ber of species within a defined area is known asspecies richness (S). Species richness can be cor-rected for total abundance (number of indivi-duals) to produce the diversity index betterknown as Simpson’s Diversity Index ð1� DÞ(Simpson 1949):

Box 16.1 Cost effectiveness of biodiversity monitoringToby A. Gardner

There is a shortage of biological datawith whichto meet some of the primary challenges facingconservation, including the design of effectiveprotected area systems and the development ofresponsible approaches to managingagricultural and forestry landscapes. This datashortage is caused by chronic under‐funding ofconservation science, especially in the species‐rich tropics (Balmford and Whitten 2003), andthe high financial cost and logistical difficultiesofmulti‐taxafield studies.Wemust therefore bejudicious in identifying the most appropriatespecies groups for addressing a particularobjective. Such focal groups are varyinglytermed ‘surrogates’ or ‘indicators’. However,indicators are often chosen subjectively on thebasis of anecdotal evidence, ‘expert’ opinion,and ease of sampling. This common approachhas resulted in finite resources being wasted on

the collection of superficial (including the‘record everything’mantra) andunrepresentative biodiversity data that may beof only limited value. This failing threatens toerode the credibility of conservation science tofunding bodies and policy makers.To maximize the utility of biodiversity

monitoring, it should adhere to the concepts ofreturn on investment, and value for money. Inessence this means that field‐workers need toplan around two main criteria in selecting whichspecies to sample: (i) what types of data areneeded to tackle the objective in hand; and(ii) feasibility of sampling different candidatespecies groups. Practical considerations shouldinclude the financial cost of surveying, butalso the time and expertise needed to conducta satisfactory job. Species groups that satisfy

continues

314 CONSERVATION BIOLOGY FOR ALL

Sodhi and Ehrlich: Conservation Biology for All. http://ukcatalogue.oup.com/product/9780199554249.do


1� D∧ ¼ SS

i¼1niðni � 1ÞNðN � 1Þ

where S ¼ the number of species, N ¼ the totalnumber of individual organisms, and ni ¼ thenumber of individuals of species i. The unique-

ness of species in a sample can be incorporatedby using indices of evenness (also known as equi-tability), of which Shannon’s Index (H; also knownmistakenly as the Shannon-Weaver index, or cor-rectly as the Shannon-Weiner index) is the mostcommon:

Box 16.1 (Continued)

both demands can be thought of as having a‘high performance’.Using a large database from work in the

Brazilian Amazon, Gardner et al. (2008) recentlypresented a framework and analytical approachfor selecting such high performance indicatortaxa. The objective of that study was to providerepresentative and reliable information on theecological consequences of converting tropicalrainforest to Eucalyptus plantations or fallowsecondary regeneration. An audit wasconducted of the cost (in money and time) ofsampling 14 groups of animals (vertebrates andinvertebrates) across a large, managed, lowlandforest landscape. Notably, survey costs varied bythree orders of magnitude and comparingstandardised costs with the indicator value ofeach taxonomicgroup clearly demonstrated thatbirds and dung beetles (Coleoptera:Scarabaeinae) are high‐performance groups –they provide the most amount of valuableinformation for the least cost. By contrast, othergroups like small mammals and large mothsrequired a large investment for little return (seeBox 16.1 Figure). The fact that both birds anddung beetles are well‐studied and performimportant ecological functions gives furthersupport to their value for biodiversitymonitoring and evaluation. This importantfinding will help conservation biologists inprioritising the study of the effects ofdeforestation on land‐use change in theAmazon, allowing them to design cost‐effectivefield expeditions thatwill deliver themost usefulinformation for the money available.Finally when planning biodiversity surveys it is

also important to consider how the data may beused to address ancillary objectives that mayensure an even greater return on investment.

One example is the opportunity to synthesiseinformation frommany small‐scale monitoringprograms to provide robust nation‐wideassessments of the status of biodiversity withoutneeding to implement independent studies. Abetter understanding of the distribution ofspecies in threatenedecosystemswill improveourability to safeguard the future of biodiversity.Wecannot afford to waste the limited resources wehave available to achieve this fundamental task.

Birds

Dung beetles

Small mammalsMoths

Standardised sampling cost ($)0

0

5

10

15

Ind

icat

or p

erfo

rman

ce (%

ind

icat

or s

peci

es o

f tot

al)

20

25

30

35

40

2000 4000 6000 8000

Box 16.1 Figure Cost effectiveness of different species groups forindicating habitat change in a multi‐purpose forest landscape inBrazilian Amazonia.

REFERENCES

Balmford, A. and Whitten, T. (2003). Who should pay fortropical conservation, and how could the costs be met?Oryx, 37, 238–250.

Gardner, T. A., Barlow, J., Araujo, I. S., et al. (2008). Thecost‐effectiveness of biodiversity surveys in tropical for-ests. Ecology Letters, 11, 139–150.

THE CONSERVATION BIOLOGIST TOOLBOX – PRINCIPLES FOR THE DESIGN AND ANALYSIS OF CONSERVATION STUDIES 315

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Box 16.2 Working across culturesDavid Bickford

Establishing conservation projects in countrieswith cultures and languages that are differentfrom your own can be both daunting andchallenging. Without proper thoughtfulness,openness, flexibility, and (most importantly)humour, these projects fail for reasons that areoften difficult to distil. All conservation projectsinvolve a mix of stakeholders (local people,scientists, conservation practitioners,governmental and public administrators,educators, community leaders, etc.) that mayhave widely different expectations andresponsibilities for the project. Having workedon both successful and failed projects with adiversity of people in nine countries and sixlanguages, much of what I have learned can besummed up in two simple yet powerful ideasfor all stakeholders: clear communication andequity. The two are intricately linked.Clear communication is an ideal often sought

after, yet rarely achieved. No matter the socio‐cultural context, a common denominator oftransparency is necessary for a successfulconservation project. Having stakeholdersexplicitly state their intentions, desires andgoals is a good start. It also helps elicittraditional or anecdotal knowledge that can beuseful in formal analysis (e.g. as Bayesian priors,see Box 16.4). Methods, benefits, andresponsibilities should be outlined and agreedupon, as well as limits of what objective(s) eachstakeholder perceives as ‘bare minimum’. Acommon pitfall is an inability for leaders tocommunicate effectively (for many and sundryreasons), re‐enforcing top‐down stereotypes.Lateral communication (peer‐to‐peer) can bemore effective and avoids many constraintsimposed by translating among differentlanguages or cultures, effectively levelling theplaying field and enabling everyone toparticipate (at least for heuristic purposes).Activities that enhance transparentcommunication include small group discussions,workshops, regular and frequentmeetings, project site visits and even informalgatherings such as shared meals orrecreational activities.Almost all social hierarchies involve some

component of conflict based around inequity.

People want to balance their personal costs andbenefits relative to others’. Conservationprojects should, wherever possible, bridge gapsand narrow divides by developing equitablyamong stakeholders. By alleviating largedisparities in cost:benefit ratios, responsibilities,and expectations between differentstakeholders, the project will become moreefficient because there will be less conflictbased on inequity. Equity will evolve andchange, with stakeholders adapting to behavefairly in a transparent system. In general, teamswill reward members who treat othersunselfishly and promote the overall goals of thegroup.To achieve such a framework of open

communication and equity, impartialleadership and long periods of interpersonalrelationship building are often required. Ashackneyed as they seem, capacity‐buildingexercises, when done correctly, are excellentmechanisms of sharing information andbuilding the competency to use it. Engagingand training local or regional counterparts is anoutstanding method for ensuring clearercommunication and promoting fairness,instead of forcing information from the top‐down and expecting results to emerge from thebottom‐up. Further links between transparencyand equity can be realised through ‘hands‐on’applications instead of just talking aboutconcepts. Leaders should participate at alllevels, learning the most menial tasksassociated with the project (e.g. anadministrator should go and catch frogs for amonitoring project).In the broadest terms, working across

cultures is a high risk‐high rewardsystem. Although there are complex obstacles,the ultimate litmus for biodiversityconservation might be our ability to learn andwork together across cultures to preservenature.

SUGGESTED READING

Reed, M.S. (2008). Stakeholder participation for environ-mental management: a literature review. BiologicalConservation, 141, 2417–2431.




H 0 ¼Xs

i¼1

ni

Nlog e

ni

N

� �

The index provides a measure of the amount ofdisorder in a system, such that communities withmore unique species have higher H (a systemwith S = 1, by this definition, is perfectly orderedbut has no diversity). Most of these measuresassume a random sampling of species within acommunity, but this assumption is often violated(Pielou 1966). When sampling is done withoutreplacement, then indices such as Brillouin’s Hare recommended:

H ¼ 1

Nlog

N !

n1!n2!n3. . .

� �

However, where representativeness is un-known, then rarefaction or resampling can beused to standardize samples from different areasor periods to a comparable metric (Krebs 1999).This includes inferring the total diversity of acommunity by using a statistical model to predictunobserved data (unsampled species). Of course,the measures presented here are the basic foun-dations of species diversity indices, but there aremyriad variants thereof, many assumptions thatcan be tested and adjusted for, and different dis-tributions that may be more or less importantunder particular circumstances. For an excellentoverview of these issues, we recommend thereader refers to Krebs (1999).

16.1.2 Scale

Interpretation of the indices and their variantsdescribed above depend on the scale of measure-ment. Whittaker (1972) introduced the conceptsof alpha (a), beta (b), and gamma (g) diversity tomeasure and compare biodiversity patterns overvarious spatial scales. a (local) diversity refers tothe quantification of species richness, etc. within aparticular area or ecosystem, whereas b diversity(differentiation) is the difference in the metricbetween ecosystems. In other words, b diversityis a measure of species uniqueness between areas,so as b diversity increases, locations differ morefrom one another and sample a smaller propor-

tion of the total species richness occurring in thewider region (Koleff et al. 2003).

Whittaker (1972) sensibly recommended that bdiversity (Whittaker’s bw) should be measured asthe proportion by which the species richness of aregion exceeds the average richness of a singlelocality within that region:

bw ¼ S

�a¼ ða þ b þ cÞ

ð2aþbþcÞ2

where S = the total number of species recordedfor all sites (regional richness) and the averagenumber of species found within sites (local rich-ness), a ¼ the number of species in common inboth sites (e.g. for a simple two-site comparison),b ¼ the number of species in site 1, and c ¼ thenumber of species in site 2. Since then, however,many other variants of the metric have been pro-posed. These include comparisons along spatialor environmental gradients, between patches ofsimilar habitats, and the degree of similarity be-tween sites (see references in Koleff et al. 2003).Indeed, Koleff et al. (2003) reviewed 24 differentmeasures of b diversity and categorized theminto four main groups: measures of (i) continuity(similarity in species composition among sites)and loss (fewer species relative to focal sites);(ii) species richness gradients; (iii) continuityonly; and (iv) gain and loss. Not only is therelack of agreement on the most appropriate mea-sure to use, there is also variation in the pattern ofscaling applied. As such, Koleff et al. (2003) sug-gested that one should use measures that exhibitthe homogeneity property (i.e. the measure isindependent of the total number of species aslong as the proportions comprising the differentcomponents are constant) and that when mea-sures reveal different patterns of variation whenbased on absolute and proportional species num-bers, both types should be examined.

g diversity is otherwise known as “geographic-scale species diversity” (Hunter 2002), whichmeans it is used as a measure of overall diversityfor the different constituent ecosystems of a re-gion. This metric becomes particularly valuableto explain broad-scale (regional or continental)patterns of species relative to local (site-specific)indices. Indeed, there are two theoretical types of


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relationships hypothesized for local versus re-gional species richness (Figure 16.1). Most data-sets support the existence of a proportionalrelationship between local and regional richness(Type I), albeit local richness always tends to beless than regional (Gaston 2000). It appears thatType II relationships (local richness reachingan asymptote) are rare because local assemblagesdo not seem to become saturated as one mightexpect from ecological mechanisms such asdensity dependence, parasitism and predation(Gaston 2000).

16.1.3 Surrogacy

An important goal of conservation biology,which deals with a world of limited resourcesand options, is to protect areas that have relative-ly higher biodiversity than surrounding areas.Prioritizing areas for conservation, however,does not always require a complete descriptionof a site’s biodiversity, but merely relative mea-sures of differences among them (Margules et al.2002) described using a representative taxonomicsubset. The quest for a simple estimator, a surro-gate (i.e. the number, distribution or pattern ofspecies in a particular taxon in a particular areathought to indicate a much wider array of taxa)that is sufficiently related to the biodiversity pa-

rameter of interest is an essential tool in conser-vation planning (see Chapter 11).

Unfortunately, there is no consensus regardingwhich surrogates are best for what purposesamong ecosystems –many problems with currentsurrogate approaches remain. For instance, focus-ing only on a set of species-rich sites may selectonly a single habitat type with similar species inall areas, thus many rare species may be excludedfrom protection (Margules and Pressey 2000).Many methods to overcome these problemshave been developed based on multivariatemeasures of biodiversity (e.g. multi-taxa inci-dence matrices) or reserve-selection algorithms(e.g. Sarkar and Margules. 2002). Advances havebeen made with recent work (Mellin et al. Inreview) examining surrogate effectiveness in themarine realm. It was shown that higher-taxa sur-rogates (taxonomic levels such as order, family orgenus acting as a surrogate for some lower taxo-nomic level such as species) outperform cross-taxa (one taxon is used as a surrogate for anotherat the same taxonomic resolution) and subset-taxa (diversity in one taxonomic group is takenas representative of the entire community) surro-gates. Likewise, surrogacy was least effective atbroad (> 100 km) spatial scales.

16.1.4 Similarity, dissimilarity, and clustering

Although indices of biodiversity take on differentaspects of species richness, abundance, evennessand scale, there are many relatively simple tech-niques available for comparing samples of spe-cies and individuals among sites. Most indices ofsimilarity (> 25 types exist – Krebs 1999) aresimple descriptors that do not lend themselveseasily to measures of uncertainty (e.g. confidenceintervals; although resampling methods can pro-vide an index of parameter uncertainty), so theirapplication is generally exploratory. There aretwo broad classes of similarity: (i) binary; and(ii) quantitative. Binary measures are applied topresence-absence data (i.e. does a species exist ina defined area?) and can be compared amongsites using contingency tables using metrics suchas Jaccard’s similarity, Sorren’s similarity, simplematching, or Baroni-Urbani and Buser

Regional species richness

Loc

al s

peci

es r

ichn

ess

Type II

Type I

Local richness =regional richness

Figure 16.1 Hypothesized relationship between local and regionalspecies richness (number of species). Type I occurs where local richnessis proportional to, but less than, regional richness; Type II demonstratessituations where local richness asymptotes regardless of how muchregional richness increases. Reprinted from Gaston (2000).




coefficients (see Krebs 1999). Of course, somemethod to assess the probability of missing spe-cies in presence-absence surveys should also beapplied to account for insufficient sampling effort(e.g. MacKenzie et al. 2002).

Quantitative indices require some aspect of in-dividual abundance to be assessed such as thenumber of individuals, biomass, cover or produc-tivity. Distance dissimilarity indices using abun-dance data instead of species richness can beapplied to the same binary indices listed above.Alternatively Euclidean, Manhattan, Canberra orBray-Curtis distances between samples can becalculated using relative abundance measures be-tween sites (see Krebs 1999). Simple correlationcoefficients such as Pearson product-moment,Spearman’s rank and Kendall’s t can also beused in certain situations to compare sites, butthese tend to be insensitive to additive or propor-tional differences between community samples(Romesburg 1984) and they depend strongly onsample size (generally, n > 30 is sufficient for areliable characterization of the relationship).

When many focal communities are sampled,some form of cluster analysis may be warranted.Cluster analysis refers to any technique thatbuilds classifications, but there is no preferredmethod given that the choice depends on thetype of data being compared. Some considera-tions for choice include whether the data are:(i) hierarchical (e.g. taxonomic classifications) orreticulate (overlapping classifications); (ii) divi-sive (sample divided into classes) or agglomera-tive (fine to coarse resolution); (iii) monothetic(groups distinguished by a single attribute) orpolythetic (many attribute-based); or (iv) qualita-tive (binary) or quantitative (distance measures)(see Krebs 1999 for an overview).

16.1.5 Multivariate approaches

When the principal aim of a conservation study isto quantify the relationships between a largenumber ofmeasurements, whether they be of spe-cies, individuals or abiotic predictors of ecologicalpatterns, some form of multivariate analysis isusually required. Over thirty different multivari-ate techniques have been designed for various

applications (Pérez et al. 2008), each with theirown particular strengths and weaknesses. Ordi-nation describes those methods that summarizemultivariate information in a low-dimensionalscatter diagram where points represent samplesand distances among them are proportional totheir similarity measured, for example, by Euclid-ean distance, Bray-Curtis or other indices. Com-mon techniques include eigen-based principalcomponents analysis (PCA) or correspondenceanalysis (CA) and distance-based multidimen-sional scaling (MDS), cluster analysis or polarordination that provide coefficients quantifyingthe relative contribution of component variablesto the reduced-dimension principal axes.

Such multivariate approaches are useful forvisualizing patterns that would otherwise be dif-ficult or impossible to discern in multidimension-al space, such as ecologically related speciesassemblages or trophic guilds. They can alsosummarize the principal gradients of variationwithin and among communities and condenseabiotic and other potential explanatory variables(e.g. climate, soil conditions, vegetation structure,chemistry, etc.) into simple gradients themselvesthat may be used as correlates to explain varia-tion in species or community patterns. Their dis-advantage is that they cannot be used to test therelative likelihood of alternative hypotheses, maynot appropriately reflect statistical power andeffect size, and if applied incautiously, can bemisused to mine data for phantom ‘patterns’that on closer examination turn out to be randomnoise or system-specific peculiarities.

16.2 Mensurative and manipulativeexperimental design

Conservation biology typically deals with assess-ments of previous environmental degradationand the quantification of its effects on biodiversi-ty patterns. Another major aim is to design waysof preserving existing, relatively intact commu-nities through management intervention (e.g. re-serve design, control of harvest). Conservationbiologists also devote a large proportion of theirefforts to quantifying the most efficient and


1


effective methods for restoring degraded habitatsto some semblance of previous ecological func-tion. These three principal aims, and the logisticalconstraints on large-scale system manipulations,generally preclude the use of strict experimentaldesign and control – there are simply too manyextenuating variables modifying species patternsto control, and the systems of interest are gener-ally too expensive to apply meaningful manipu-lations such as those which typify medicalexperimentation.

There are some notable exceptions to this rule,such as replicated microcosm experiments exam-ining the processes of extinction in rapidly repro-ducing invertebrate populations. For example,the frequency of extinction times under condi-tions of low and high environmental variability(Drake 2006), the persistence probability of popu-lations exposed to various spatial configurationsof refugia and intensities of harvest (Fryxell et al.2006) and the implications for extinction risk ofchaotic and oscillatory behavior in populations(Belovsky et al. 1999; Hilker and Westerhoff2007), have all been successfully examined incontrolled laboratory settings. Other well-known manipulations at broader spatial scales(albeit with far less experimental control) includeexamining the effects of forest fragmentationon species diversity (Laurance et al. 2002),controlling the size and configuration of agricul-tural plots to test bee pollination success (Brosiet al. 2008), examining the effects of landscapecomposition on the initial dispersal success ofjuvenile amphibians (Rothermel and Semlitsch2002), determining the effects of inbreeding de-pression on individual survival (Jimenez et al.1994), measuring arthropod responses in tropicalsavannas exposed to repeated catchment-scale prescribed burning (Andersen and Müller2000) and the many applications of Before-After-Control-Impact (BACI) experimental designs todetect point-source changes to systems (Under-wood 1994).

The above notwithstanding, most conservationstudies rely mainly on quantifying existing pat-terns (observational studies) or take advantage ofexisting gradients or measurable differences inhabitat quality or type to infer mechanisms. This

latter category is sometimes referred to as men-surative experimentation because it does not ex-plicitly control for confounding variables(Hurlbert 1984). There has been plenty of discus-sion on this topic over the past twenty or soyears (Hurlbert 1984; Krebs 1991; Hargroveand Pickering 1992; Oksanen 2001; Hurlbert2004; Oksanen 2004), but it is now acceptedamong most conservation biologists that tomake strong inferences on biological patternsand mechanisms, multiple lines of evidence,from observational, mensurative and manipula-tive experiments, are all required at various spa-tial and temporal scales (Brook et al. 2008).

16.2.1 Hypothesis testing

The classic scientific approach adopts the conceptof falsifiability (Popper 1959) – that is, demonstrat-ing that a mechanism or phenomenon is not true(null hypothesis) by controlling all other plausi-ble determinants except the one of interest andreplicating the experiment sufficiently to avoidspurious patterns that may arise simply bychance (see section below). This is still a coreaspect of science because it reduces the chanceof making subjective interpretations of the datacollected. This is the philosophical basis for themajority of the statistical techniques used by nat-ural scientists; we attempt to discern pattern fromthe ‘noise’ in natural systems using theory toestimate the probability that our observationscould have been derived merely by chance.

Neyman-Pearson null hypothesis testing(NHT) begins with the assertion that no differ-ences exist between experimental units (null hy-pothesis), with the implicit view that if the null isunsupported by the data, then one or more ‘alter-native’ hypotheses must therefore be plausible(although these are not explicitly evaluated).Classic statistical theory that has been developedaround the NHT approach provides methods toestimate the chance of making an error whenrejecting the null hypothesis (Type I or a error);in other words, this is the probability of conclud-ing that there is a difference (or effect) when infact, there is none. The flip side to this is thatclassic NHT tests do not provide an estimate of




the probability of making an error when failing toreject the null hypothesis (known as Type II or berror) – this is essentially the chance one con-cludes there is no difference (or effect) when infact, there is. Various a priori and a posteriorimeth-ods exist to estimate Type II errors (more precise-ly, the power of a statistical test taken as 1 – Type IIerror), with the latter depending on three princi-pal elements: sample size (see below), magnitudeof the difference one is attempting to detect (effectsize) and the total variance associated with themeasure used (see Gerrodette 1987; Osenberget al. 1994; Steidl et al. 1997; Thomas 1997; Thomas& Krebs 1997; Thompson et al. 2000 for moredetail on power analyses).

The disconnect between these two estimates ofhypothesis-conclusion error, the implicit confla-tion of effect size and sample size, as well as theambiguity related to just how much chance ofmaking an error is acceptable (i.e. the moribundand bankrupt concept of statistical ‘significance’beyond some arbitrary threshold), have formedfor decades some of the main arguments against

using NHT (reviewed in Elliott and Brook 2007,see also Burnham and Anderson 2002; Lukacset al. 2007). This is especially true in the ecologicaland psychological sciences, which are typicallyrestricted to observational studies and subject toextensive variability. The alternative approachescan be classed into the general category of multi-ple working hypotheses (MWH), including best-model selection and multimodal inference(Box 16.3). MWH approaches are now becomingrecognized as providing the most logical andobjective approaches to assess conservation is-sues because they explicitly consider uncertaintyin the underlying models used to abstract the realworld, rather than relying on simple and arbi-trarily assessed ‘yes-or-no’ conclusions typical ofthe NHT paradigm.

16.2.2 Sample size

Regardless of the statistical paradigm invoked oranalysis method applied, perhaps the least con-troversial requirement of good scientific inference

Box 16.3 Multiple working hypothesesCorey J. A. Bradshaw and Barry W. Brook

Science is, at its core, all about evaluating thesupport for different ideas – workinghypotheses – about how the world works.Because they never reflect the totality of real‐world effects, any such hypothesis can beconsidered a model. But how to decide whatideas have support and which ones should bediscarded?A traditional approach has been to set up

some null model (which states that there is nochange or measureable effect in a variable ofinterest), and then proceed to evaluatewhether the data conform to this model. Thisusually involves the arbitrary selection of athreshold probability of making Type I errors(i.e. failing to reject a null hypothesis when it istrue) to conclude so‐called ‘significance’ ofeffect. This line of reasoning still pervades mostprobabilitistic sciences today. Yet many havecalled for the abandonment of such subjectivestatistical practices (Burnham and Anderson

2004; Lukacs et al. 2007) in favour of a conceptoriginally forwarded in 1890 by Thomas C.Chamberlin known as multiple workinghypotheses (Elliott and Brook 2007). The idea isrelatively simple – instead of considering asingle (null) hypothesis and testing whether thedata can falsify it in favour of some alternative(which is not directly tested), the use of multipleworking hypotheses does not restrict thenumber of models considered to abstract thesystem under investigation. In fact, theapproach can specifically accommodate thesimultaneous comparison of hypotheses insystems where it is common to find multiplefactors influencing the observations made (suchas complex ecological systems). This is alsoparticularly applicable to conservation biologybecause experimental manipulation is oftentechnically difficult or ethically unreasonable.The basic approach is to construct models

(abstractions of complex systems) that

continues


1



represent combinations of hypothesesconstructed to explain variation in the metric ofinterest. Models (plausible hypotheses) thencan be ranked or compared on the basis ofrelative evidential support, using methods thattend to reinforce the principle of parsimony(the simplest combination of factors providingthe strongest explanatory power) via their biascorrection terms. Model comparison basedon information theory (usually assessedusing Aikaike’s information criterion– AIC – when conforming to maximumlikelihood approaches – Box 16.4) immediatelysupposes that all models are false because theyrepresent incomplete approximations of thetruth (Elliott and Brook 2007). Weighting AICsthen can be used as a means to assess therelative distance to ‘truth’ by approximatingKullback‐Leibler information loss (i.e.measuring the relative distance betweenconceptual reality and the abstraction underconsideration). The Bayesian informationcriterion (BIC) is a dimension‐consistent form ofmodel comparison that provides a measure ofthe weight of evidence relative to other models(the Bayes factor – see Box 16.4), assuminguninformative prior information. As samplesizes increase, BIC approaches the estimation ofthe dimension of a ‘true’model (not necessarilyembedded in the model set) with a probability= 1 (Burnham and Anderson 2004). Here thetrue model is one which captures main effectsbut ignores minor (tapering) influences.It is generally accepted that AIC performs

well when sample sizes are small (and AIC itselfcan be corrected to account for small samples),but it is a priori weighted to favour morecomplex models when tapering effects(biologically important signals that characterisefull truth but defy reductionism) are present(Link and Barker 2006). When the aim is todetermine the most important variablesexplaining variation in some measured‘response’, BIC is recommended, especiallywhen sample sizes are large (Link and Barker2006). When prediction is the goal, AIC‐basedrankings are preferred.

Multimodel inference is gaining increasingpopularity in conservation biology because itembraces the concept of multiple workinghypotheses to describe complex systems.Rather than choose a single ‘best’ model (ornot even test alternative models, as per nullhypothesis testing), multimodel inference ismade on the basis of all models in the a prioricandidate set; here, each model’s prediction isweighted by its relative support from the data(e.g. AIC weights or Bayesian posteriorprobabilities – see Box 16.4) (Burnham andAnderson 2002; Burnham and Anderson 2004;Elliott and Brook 2007). Thus, multimodelinference is advantageous because it accountsfor uncertainty in the underlying choice ofmodels used to describe the system ofinterest, it permits inference from differentmodels simultaneously, and it allows forunconditional ranking of the relativecontribution of variables tested (Elliott andBrook 2007). Of course, no inference is madeon models/variables not included in the apriori model set.The cases where null hypothesis testing can

be justified (see Johnson and Omland 2004;Stephens et al. 2005; Stephens et al. 2007) arerare in conservation biology for the reasonsdescribed above (system complexity, lack ofexperimentation potential). It is our opinionthat the multiple working hypothesesapproach, even for relatively simpleassessments of effect, should embrace thephilosophy of estimating the strength ofevidence and avoid the pitfalls associatedwith arbitrary Type I error probabilitythresholds. This can be usefully done even fora comparison of a null model to a singlealternative, using evidence factors (the ratioof AIC or BIC weights of the two models – aconcept akin to Bayesian odds ratios) and ispreferable to a classic null hypothesis testbecause the likelihood of the alternativemodel is explicitly evaluated.The basic formulae for the most common

model‐ranking criteria (AIC, AICc, QAIC and BIC)are provided below:

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in conservation biology is obtaining measure-ments from as many representative and unbiasedunits (individuals, plots, habitats, ecosystems,etc.) as possible. The main reason for obtaininglarge sample sizes is that when one measuresonly a few units, the chance of obtaining a goodestimate of the central tendency (e.g. mean ormedian), variance (i.e. the spread of true values),or distribution (i.e. shape of the frequency distri-bution of units such as Normal, binomial,

log-Normal, etc. and extreme values which char-acterize the tails of distributions) of a parameter islow. Without good estimates of such parameters,the ability to tease pattern and noise apart be-comes increasingly intractable.

There are no rules of thumb for ‘adequate’sample sizes because they depend on the hypoth-esis being tested, the inherent variability of themeasures chosen and the temporal or spatialscales examined. The most useful generalization


AIC ¼ � 2L þ 2k

where AIC ¼ Akaike’s information criterion,k ¼ number of model parameters and L ¼ themaximised log-likelihood function for theestimated model (MLE). Note that the varianceterm of a statistical model, when estimated(e.g. in a Gaussian model), is a parameter.

AICc ¼ AIC þ 2kðk þ 1Þn� k � 1

where AICc ¼ AIC corrected for small samplesize and n ¼ sample size.

QAIC ¼ 1

c2L þ 2k

where QAIC ¼ quasi-AIC and c ¼ the varianceinflation factor (when data are over-dispersed).This is commonly used in capture-mark-recapture model assessments (see White andBurnham 1999). The small-sample version ofQAIC (QAICc) is calculated the sameway as AICc.The Bayesian information criterion (BIC) iscalculated as:

�2logepðxjkÞ � BIC ¼ � 2L þ klogen

where x ¼ observed data and P(xjk) ¼ thelikelihood of x given k which is the same as theMLE used in AIC.

REFERENCES

Burnham, K. P. and D. R. Anderson. (2002). Modelselection and multimodel inference: a practical

information-theoretical approach. 2nd edn. Springer-Verlag, New York, NY.

Burnham, K. P. and Anderson, D. R. (2004). UnderstandingAIC and BIC in model selection. Sociological Methodsand Research, 33, 261–304.

Elliott, L. P. and Brook, B. W. (2007). Revisiting Chamber-lain: multiple working hypotheses for the 21st Century.Bioscience, 57, 608–614.

Johnson, J. and Omland, K. (2004). Model selection inecology and evolution. Trends in Ecology and Evolution,19, 101–108.

Link, W. A. and Barker, R. J. (2006). Model weights and thefoundations of multimodel inference. Ecology, 87,2626–2635.

Lukacs, P. M., Thompson, W. L., Kendall, W. L., Gould,W. R., Doherty, P. F., Burnham, K. P., and Anderson,D. R. (2007). Concerns regarding a call forpluralism of information theory and hypothesistesting. Journal of Applied Ecology,44, 456–460.

Stephens, P. A., Buskirk, S. W., Hayward, G. D., and DelRio, C. M. (2005). Information theory and hypothesistesting: a call for pluralism. Journal of Applied Ecology,42, 4–12.

Stephens, P. A., Buskirk, S. W., Hayward, G. D., anddel Rio, C. M. (2007). A call for statisticalpluralism answered. Journal of Applied Ecology,44, 461–463.

White, G. C. and Burnham, K. P. (1999). Program MARK:survival estimation from populations of marked animals.Bird Study, 46 (Supplement), 120–138.


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is that there is no substitute for adequate sam-pling – more representative samples will inevita-bly provide more power to discern patterns(Caughley and Gunn 1996). While we generallyrecommend against using classic power tests(see Krebs 1999 for examples) because of theirreliance on the NHT paradigm, there are techni-ques that can be applied to estimate adequateminimum sample size, and the sensitivity of in-formation-theoretic and Bayesian methods(Boxes 16.3 and 16.4) to power can be evaluated

in various ways. First, resampling can be used toassess to what extent sampling should continue,but this generally requires a moderately largeinitial sample. The basic approach is to resample(with replacement) observations from a distribu-tion at incrementing subsample sizes (Manly1997). The sample size at which the desired mag-nitude of effect can be detected then becomes theminimum target for future studies applying thesame metric. These are typically known as satura-tion or rarefaction curves (Heck et al. 1975). Other

Box 16.4 Bayesian inferenceCorey J. A. Bradshaw and Barry W. Brook

The most common statistical theoryunderpinning conservation (indeed, mostecological) research today is still likelihood‐based; i.e. the likelihood of observing the dataat hand based on the expected frequency (froma probability density function) that such datawould be observed if the same procedure ofdata collection was repeated many times(McCarthy 2007). Maximum likelihood istherefore the optimisation process that choosesthe model parameters that make the data themost likely relative to other parameter values.The process implicitly assumes no priorinformation on the relevant parameters, withthe maximum likelihood estimate coincidingwith the most probable values of thatdistribution. The approach essentially askswhatis the probability of observing the data giventhat the assumed model structure (hypothesis)is correct?An alternative approach is the Bayesian

paradigm, which instead asks: what is theprobability the model/hypothesis is true giventhe data? Bayes’ theorem states that theprobability of A occurring given that B hasoccurred is equal to the probability that both Aand B occur divided by the probability of Boccurring. Reframing A as a (or set of)parameter estimate y and B as the datacollected (x), then

PðθjxÞ ¼ PðxjθÞPðθÞPðxÞ

where P(y|x) = the posterior probability ofobtaining y given x, and P(y) = the prior

probability of y and P(x) is the probabilityof the data – a scaling constant (usuallyderived numerically). Thus, P(y) quantifiesthe available knowledge about y prior tocollecting x. This can often take the formof information collected during otherstudies that quantify the distribution (e.g.mean and standard deviation) of y. Notonly does the incorporation of priorinformation follow the spirit of scientificreasoning and logic (i.e. if A and B, then C)(McCarthy 2007), it generally provideshigher certainty in parameter estimatesbecause the model is not starting fromscratch (no information). Other advantagesof Bayesian approaches include: (i) errorsare not assumed to follow any particulardistribution, so departures from assumeddata distributions are less problematic thanin maximum likelihood‐based models; (ii)Markov Chain Monte Carlo (MCMC)numerical optimisation (a computer‐intensive method) is more flexible thanmaximum likelihood approaches becausethere is less of a tendency to become miredin local minima; and (iii) model parametersare assumed to be variable (i.e. adistribution), not fixed (a point value).The most commonly used software to

implement Bayesian models is the freelyavailable WinBUGS (Windows Bayesianinference Using Gibbs Sampling – www.mrc‐bsu.cam.ac.uk/bugs), which includes afriendly graphical user interface (GUI).While exceedingly popular, certain aspectsof the software make it somewhat

continues




rules of thumb on sufficient sample sizes haveemerged from the statistical literature based onassumptions regarding the underlying distribu-tion of the observations (Krebs 1999), the width ofBayesian posterior credibility intervals comparedto the prior distributions, or on experience fromprevious studies.

16.2.3 Replication and controls

One of the most common errors made whendesigning conservation studies is insufficientor biased replication. Replication essentiallymeans repetition of the experiment (Krebs1999) and is another type of sample size. In-sufficient replication will inflate the estimatesof error associated with any metric, so thestatistical power to detect differences (or ef-fects) even when present declines with reducedreplication. Biased sampling will distort ourability to make inferences about population-level differences on the basis of finite samples.Replication is also essential to avoid the intru-sion of chance events; for example, the com-parison of only two sites experiencing differentintensities of modification may be invalidatedbecause some variable other than the onebeing tested (e.g. soil type instead of habitatquality) may drive the differences observed in,say, species richness. Only by replicating thesampling unit sufficiently will the chance ofspurious events occurring be reduced.

It is important though to ensure that the appro-priate statistical unit is replicated. In the aboveexample, increasing the number of sub-samplesin each of the two sites does not solve the problemof insufficient replication – the basic unit of com-parison is still the ‘site’. This is known as pseudo-replication because it may appear that increasedeffort leads to greater replication of the sampledunit, when in reality it is simply the reproductionof non-independent samples (see Hurlbert 1984;Underwood 1994; Krebs 1999).Without true inde-pendence among sampling units, estimates of var-iance, and hence, the power to detect differences(or effects), are downwardly biased, leading tohigher probabilities of making Type II errors. An-other form of pseudoreplication can occur whendesigns do not account for temporal autocorrela-tion among samples or repeat sampling of thesame unit (e.g. multiple measures from the sameanimal that has been recaptured repeatedly). Ifsequential samples within plots are taken overtime, there is a high probability that measurestherein will be correlated. There are many experi-mental designs and statistical tests that can taketemporal autocorrelation into account (e.g.Mulleret al. 1992; Cnaan et al. 1997; Krebs 1999; Gueor-guieva and Krystal 2004; Ryan 2007).

Another rule often broken by conservation biol-ogists is the failure to incorporate some kind ofcontrol in their experimental (manipulative ormen-surative) design. A control is an experimental unitthat receives no direct treatment. In conservationterms, these could be, for example, sites that have


cumbersome to implement, such as therequirement to re‐initialise parametersettings whenever models are re‐run. Analternative interface that is based on thesame basic language is the BRugs library(R interface to R2WinBUGS) in the Rprogramming language (R DevelopmentCore Team 2008 – also free, open sourcesoftware). BRugs is a command‐based,object‐orientated implementationthat can be re‐run repeatedly without

having to reset parameter valueseach time.

REFERENCES

McCarthy, M.A. (2007). Bayesian methods forecology. Cambridge University Press,Cambridge, UK.

R Development Core Team (2008). R: A language andenvironment for statistical computing. R Foundation forStatistical Computing, Vienna, Austria.


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not been changed (degraded) in a particular way,areas without invasive species (i.e. the ‘treatment’being the presence of the invasive species), or siteswhere no re-introductions of native species haveoccurred.While gradient studies looking for corre-lations between well-known predictors of biodi-versity patterns (e.g. forest fragment areaexplaining variation in species richness; Lauranceet al. 2002) do not necessarily require ‘controls’ (e.g.contiguous forest patches of equivalent size) be-cause the relationships are so well-established,any study attempting some form of manipulativeormensurative experimental inferenceMUSThavecontrols (note that controlsmust also be replicated)(Krebs 1999). This applies particularly to the Be-fore-After-Control-Impact (BACI) design – con-temporaneous ‘controls’ are essential to be able todetect any differences (or effects) (Underwood1994; Krebs 1999).

16.2.4 Random sampling

The complexities of experimental design cannotbe treated sufficiently in this chapter; however,one last element that applies to all forms of exper-imental design is the concept of randomization.Randomization refers to the process of placing arandom spatial or temporal order on the samplingdesign such that each unit measures statisticallyindependent values. While complete randomiza-tion is not always possible (nor entirely desirablein cases of stratified random sampling – e.g. Krebs1999) for many conservation studies, one shouldalways strive to maximize sample randomizationwherever andwhenever possible. The key point isto ensure that your sample is representative of thepopulation parameters about which you aretrying to make inference – this is the fundamentaltheoretical tenet of statistical sampling theory.

16.3 Abundance Time Series

if species are the currency of biodiversity assess-ments, then counts of individuals represent theprincipal unit for population dynamics modelsused to assess conservation risk (see followingsection). The restrictions imposed on comprehen-

sive biodiversity assessment by the sheer numberof species on Earth (Chapter 2) also apply to thequantification of population dynamics for singlespecies – there are simply too many species to beable to obtain detailed demographic data (e.g.survival, fertility, dispersal, etc. ) for the majorityof them to build population models (see follow-ing section). Therefore, many types of phenomeno-logical model have been developed to dealwith sequential censuses (time series) of absoluteor relative population size. Phenomenological sim-ply means that the dynamical properties thesemodels emulate represent the end-point phenome-non of total population size (number of indivi-duals at any given point in time), that is, theemergent property of various mechanisms suchas birth, death, reproduction and dispersal.Therefore, phenomenological models applied toabundance time series are restricted in their ca-pacity to explain ecological mechanisms, but theycertainly provide fertile ground for testing broadhypotheses, describing gross population behav-ior, and making predictions about populationchange (provided mechanisms remain constant).

One of the commonest and simplest questionsconservation biologists ask is whether a popula-tion is trending or stationary. Indeed, one of themain criteria used by the World ConservationUnion (IUCN) to define a population or speciesas threatened (i.e. either Vulnerable, Endangeredor Critically Endangered) on its Red List (www.iucnredlist.org) is its rate of decline. As such,reliably determining both the direction of thetrend (i.e. if declining, to highlight conservationconcern, or if increasing, to indicate successful re-covery) and quantifying the rate of change, are cen-tral goals of conservation biology. While it mayseem superficially straightforward to determineat least the direction of population’s abundancetrend, factors such as the difficulty in censusingthe population (counting all individuals),measure-ment (observation) error, and the presence ofhigh seasonal variance in abundancedue tonormalenvironmental stochasticity (variation), are com-mon real-world challenges that can make conclu-sions of population trajectory uncertain.

Many statistical tools have been developed todeal with these problems, including traditional




NHT power analyses to detect trends (e.g. Gerrod-ette 1987; see also Gerrodette 1993 for associatedsoftware), nonlinear models (e.g. Fewster et al.2000) and the simultaneous application ofmultipletime series models (Box 16.3) applied to relativeabundance counts to determine the direction oftrend and strength of feedbacks (e.g. McMahonet al. 2009). We certainly recommend the multipleworking hypotheses approach (Box 16.3) whenquerying abundance time series, but argue thatmuch more mathematical development and em-pirical testing is required on this topic.

Trending, or nonstationary populations maybe driven by exogenous influences (“changes inthe environment that affect population change,but are not themselves influenced by popula-tion numbers” – Turchin 2003) and/or by en-dogenous influences (“dynamical feedbacksaffecting population numbers, possibly involv-ing time lags” – Turchin 2003). It is of courseimportant to determine the interplay betweensuch drivers (Bradshaw 2008) because eithermay dominate at certain times or on certainstages of the population, or short-term trendsmay simply represent periods of re-equilibra-tion of longer-term cycles that are not readilyapparent when sampling over too few timeintervals relative to the scale of disturbance orthe species’ generation length.

The development of population dynamicsmodels in ecology dates back to the early 19th

century (Pearl 1828; Verhulst 1838) and has de-veloped in the intervening 180 years into an ex-pansive discipline in its own right, dealing withthe many and complex ways in which organismsinteract within and among populations and spe-cies. We cannot possibly provide a summary ofall the relevant components of time series analy-sis here (for an excellent overview with workedexamples, see Turchin 2003), but we do highlightsome of the essential basics.

An important component of extinction models isthe presence of density feedback, because thestrength and form of such endogenous influencescan strongly affect predictions of extinction risk (seebelow) (Philippi et al. 1987; Ginzburg et al. 1990). Insituations where detailed measurements of theways in which population density modifies demo-

graphic processes are unavailable, phenomenologi-calmodels applied to abundance time series can stillprovide some direction. The idea that populationstend tofluctuate around an equilibrium abundance,encapsulated by the general logistic (S-shapedcurve) model (Turchin 2003), was generalized fortime series by Ricker’s model (Ricker 1954) wherethe rate of population change (r):

r ¼ log eNtþ1

Nt

� �

(N is the discrete population size estimate at timet), can be expressed as a simple linear function ofNt declining from an intrinsic (maximum) growthrate (rm):

r ¼ rm 1� Nt

K

� ��

When r is positive, the population is growing;above carrying capacity (K), the population de-clines. Here, the environment’s K is assumed toimpose some upper limit to total abundance.There are many variants and complications ofthis basic model, and even more debates regard-ing its role in explaining complex populationdynamics; however, we argue this basic modelhas been instrumental in defining some of themore important theoretical elements of popula-tion dynamics applied to questions of sustain-able harvest and extinction risk. Indeed, Turchin(2003) goes as far as to call it a fundamental‘law’ of population ecology.

In real-world situations, the negative influence ofdensity on population rate of change is likely toapplymainly to the regionaroundcarryingcapacityand be of less importance for small populationsbelow their minimum viable population size (seebelow). For instance, as populations decline, indivi-duals may lose average fitness due to phenomenasuch as inbreeding depression (see Genetic Toolssection below), reduced cooperative anti-predatorbehavior (e.g. flocking or herding), reduced mateavailability, and the loss or degradation of coopera-tive breeding effort (Courchamp et al. 2008). Thus,density feedback at these small population sizes canbe positive, and this is generally known as an Alleeeffect (Allee 1931). Although the phenomenologicalevidence for Allee effects using abundance time


1


series is sparse –mainly because obtaining observa-tions at low densities is logistically challenging andobservation error tends to be inflated when detec-tion probabilities are low – there are somemodels that can be applied, such as the Ricker-Alleemodel:

r ¼ rm 1� Nt

K

� �Nt � A

K

� �

whereA represents the critical lower Allee thresh-old abundance below which positive feedbackbegins. For a comprehensive discussion of Alleeeffects, see Courchamp et al. (2008) and Berec et al.(2007).

16.4 Predicting Risk

A longstanding goal in conservation biology ispredicting the risk a species, community or eco-system faces when humans change the environ-ment. Questions such as: How many individualsare required for a population to have a high chanceof persisting in the future? What species are mostsusceptible to human-induced changes to the environ-ment? Are some species more likely to become invasivethan others? and What types of species are requiredto maintain ecosystem function? pervade the con-servation literature from purely theoretical tohighly applied perspectives. Not only do thesequestions require substantial data to provide re-alistic direction, the often arbitrary choice of thedegree of risk (defined as a probability of, forexample, becoming threatened, invasive, or fall-ing below a predefined population size), can addsubjectivity to the assessment.

16.4.1 Cross-taxa approaches

The ranking of species’ life history traits (e.g.evolved characteristics such as generation time,mean body mass, reproductive potential; ecolog-ical attributes such as dispersal capacity, nicheconstraints) and environmental contexts, whichtogether predict a species’ response to environ-mental change, has received considerable atten-tion in recent years (e.g. Bennett and Owens 1997;Owens and Bennett 2000; Purvis et al. 2000; Kolar

and Lodge 2001; Heger and Trepl 2003; Brooket al. 2006; Pimm et al. 2006; Bielby et al. 2008;Bradshaw et al. 2008; Sodhi et al. 2008a, b, 2009).Determining which traits lead to higher extinc-tion or invasion risk, for instance, is importantfor prioritizing management to eradicate harm-ful invasive species or recover threatened taxa(Bradshaw et al. 2008). Developing simple predic-tive generalizations (‘rules’) for categorizingpoorly studied species into categories of relativerisk (proneness) thus becomes a tool to assistin the efficient allocation of finite conservationresources.

There is now good correlative evidence thatparticular combinations of life history and eco-logical characteristics (e.g. organism size, dispers-al capacity, geographic range, and otherreproductive, dispersal, morphological and phys-iological attributes) influence a species’ risk ofbecoming extinct or invasive, with the strengthof effect depending on the spatial scale of mea-surement, environmental context, and rate ofchange of the forcing factor (e.g. deforestation orclimate change) (Bradshaw et al. 2008). Much ofthis evidence is derived from three main types ofmodels: generalized linear mixed-effects models(e.g. Brook et al. 2006; Bradshaw et al. 2008; Sodhiet al. 2008a, c), generalized estimating equations(Bielby et al. 2008) and phylogenetically indepen-dent contrasts (e.g. Bennett and Owens 1997;Owens and Bennett 2000; Purvis et al. 2000). Theprincipal reason why these complex models mustbe used instead of simple correlations is becauseof the confounding effects of shared evolutionarytraits when making cross-species comparisons(Felsenstein 1985). In other words, because spe-cies are related hierarchically according to theirphylogeny (evolutionary relationships and com-mon ancestry), they are not strictly independentstatistical units, and so their relationships shouldbe taken into account.

Linear mixed-effects models (Pinheiro and Bates2000) take phylogeny inferred from Linnaean tax-onomy into account by using a nested structure inthe random effect component of the model (Black-burn and Duncan 2001); once the variance compo-nent due to correlated relationships is taken(partially) into account, the residual variation can




be attributed to fixed effects (e.g. life history traits)of hypothetical interest. Generalized estimatingequations are similar to mixed-effects models, butthe parameters are estimated by taking correla-tions among observations into account (Paradisand Claude 2002). Phylogenetically independentcontrasts (PIC) compute the differences in scoresbetween sister clades and rescale the variance as afunction of evolutionary branch length (Purvis2008). The PIC approach (and its many variants –see Purvis et al. 2005; Purvis 2008) is useful, but hasbeen criticized because of: (i) its sensitivity to errorsin estimated phylogenetic distance (Ramon andTheodore 1998); (ii) incorrect treatment of extinc-tion risk as an evolved trait (Putland 2005); (iii)overestimation of differences between closelyrelated species (Ricklefs and Starck 1996); (iv) re-quirement of a complete phylogeny; (v) inability todeal with categorical variables; and (vi) its restric-tion of using the NHT framework (Blackburn andDuncan 2001; Bradshaw et al. 2008). Despite thesecriticisms, no onemodeling approach is superior inall situations, sowe recommend several techniquesbe applied where possible.

16.4.2 Population viability analyses

When the goal is to estimate risk to a single spe-cies or population instead of evolved life historiesthat may expose species to some undesirablestate, then the more traditional approach is todo a population viability analysis (PVA). PVAbroadly describes the use of quantitative methodsto predict a population’s extinction risk (Morrisand Doak 2002). Its application is wide andvaried, tackling everything from assessment ofrelative risk for alternative management options(e.g. Allendorf et al. 1997; Otway et al. 2004; Brad-shaw et al. 2007), estimating minimum viablepopulation sizes required for long-term persis-tence (e.g. Traill et al. 2007 and see sectionbelow), identifying the most important life stagesor demographic processes to conserve or manip-ulate (e.g. Mollet and Cailliet 2002), setting ade-quate reserve sizes (e.g. Armbruster and Lande1993), estimating the number of individualsrequired to establish viable re-introduced popu-lations (e.g. South et al. 2000), setting harvest

limits (e.g. Bradshaw et al. 2006), ranking poten-tial management interventions (e.g. Bradshawet al. in press), to determining the number andgeographical structure of subpopulations re-quired for a high probability of persistence (e.g.Lindenmayer and Possingham 1996).

The approaches available to do PVAs are asvaried as their applications, but we define herethe main categories and their most common uses:(i) count-based; (ii) demographic; (iii) metapopu-lation; and (iv) genetic. A previous section out-lined the general approaches for the analysis ofpopulation dynamics and the uses of abundancetime series in conservation biology; count-basedPVAs are yet another application of basic abun-dance (either total or relative) surveys. Briefly, thedistribution of population growth rates on thelogarithmic scale, constructed from a (ideally)long time series (or multiple populations) ofabundance estimates, provides an objectivemeans of projecting long-term population trajec-tories (either declining, increasing, or stable) andtheir variances. The basic premise is that, given aparticular current population size and a mini-mum acceptable value below which the popula-tion is deemed to have gone quasi-extinct (i.e. notcompletely extinct, but where generally too fewindividuals remain for the population to be con-sidered viable in the long term), the mean long-term population growth rate and its associatedvariance enables the calculation of the probabilityof falling below the minimum threshold. Whilethere are many complications to this basic ap-proach (e.g. accounting for substantial measure-ment error, catastrophic die-offs, environmentalautocorrelation, density feedback and demo-graphic fluctuations (e.g. uneven sex ratio – foran overview, see Morris and Doak 2002), themethod is a good first approximation if the onlydata available are abundance time series. A recentextension to the approach, based on the multipleworking hypotheses paradigm (Box 16.3), hasbeen applied to questions of sustainable harvest(Bradshaw et al. 2006).

A more biologically realistic, yet data-intensiveapproach, is the demographic PVA. Count-basedPVAs essentially treat all individuals as equals –that is, equal probabilities of dying, reproducing


1


and dispersing. In reality, because populationsare usually structured into discernable and differ-entiated age, sex, reproductive and developmentstages (amongst others), demographic PVAscombine different measured (or assumed) vitalrates that describe the probability of performingsome demographic action (e.g. surviving, breed-ing, dispersing, growing, etc.). Vital rates are ide-ally estimated using capture-mark-recapture(CMR) models implemented in, for example, pro-gram MARK (White and Burnham 1999), butsurrogate information from related species orallometry (body mass relationships) may also beused. The most common method of combiningthese different life stages’ vital rates into a singlemodel is the population projection matrix. Whilethere are many complicated aspects to these,they allow for individuals in a population to ad-vance through sequential life stages and performtheir demographic actions at specified rates.Using matrix algebra (often via computer simula-tion), static, stochastic and/or density-modifiedmatrices are multiplied by population vectors(stage-divided population abundance) to projectthe population into the future. The reader is re-ferred to the comprehensive texts by Caswell(2001) and Morris and Doak (2002) for all thegory details. Freely or commercially availablesoftware packages such as VORTEX (www.vor-tex9.org) or RAMAS (www.ramas.com) can dosuch analyses.

Metapopulations are networks of spatially sepa-rated sub-populations of the same species that areconnected by dispersal (see Chapter 5). A meta-population can be thought of as a “population ofpopulations” (Levins 1969) or a way of realistical-ly representing patches of high habitat suitabilitywithin a continuous landscape. In ways thatare analogous to the structuring of individualswithin a single population, metapopulations‘structure’ sub-populations according to habitatquality, patch size, isolation and various othermeasures. The mathematical and empirical devel-opment of metapopulation theory has burgeonedsince the late 1990s (see Hanski 1999) and hasbeen applied to assessments of regional extinc-tion risk for many species (e.g. Carlson and Eden-hamn 2000; Molofsky and Ferdy 2005; Bull et al.

2007). For a recent review of the application ofmetapopulation theory in large landscapes, seeAkçakaya and Brook (2008).

Although genetic considerations are not nearlyas common in PVAs as they perhaps should be(see more in the following section, and the bookby Frankham et al. 2002 for a detailed overview),there is a growing body of evidence to suggestthat the subtle determinants of extinction arestrongly influenced by genetic deteriorationonce populations become small (Spielman et al.2004; Courchamp et al. 2008). The most commonapplication of genetics in risk assessment hasbeen to estimate a minimum viable population size– the smallest number of individuals required fora demographically closed population to persist(at some predefined ‘large’ probability) for some(mainly arbitrary) time into the future (Shaffer1981). In this context, genetic considerations aregrowing in perceived importance. Genetically vi-able populations are considered to be those largeenough to avoid inbreeding depression (reducedfitness due to inheritance of deleterious allelesby descent), prevent the random accumulationor fixation of deleterious mutations (genetic driftand mutational meltdown), and maintain evolu-tionary potential (i.e. the ability to evolve whenpresented with changing environmental condi-tions; see following section). The MVP size re-quired to retain evolutionary potential is theequilibrium population size where the loss ofquantitative genetic variation due to small popu-lation size (genetic drift) is matched by increasingvariation due to mutation (Franklin 1980). Ex-panded detail on the methods for calculating ge-netically effective population sizes and a reviewof the broad concepts involved in genetic stochas-ticity can be found in Frankham et al. (2002) andTraill et al. (2009). The next section gives moredetails.

16.5 Genetic Principles and Tools

The previous sections of this chapter have fo-cused primarily on the organismic or higher tax-onomic units of biodiversity, but ignored the sub-organism (molecular) processes on which




Box 16.5 Functional genetics and genomicsNoah K. Whiteman

Conservation genetics has influenced the fieldof conservation biology primarily by yieldinginsight into the provenance of individuals andthe ecological and evolutionary relationshipsamong populations of threatened species. Asilluminated in the section on genetic diversity,conservation genetics studies rely primarily ongenomic data obtained from regions of thegenome that are neutral with respect to theforce of natural selection (neutral markers).Conservation biologists are also interested inobtaining information on functional (adaptive)differences between individuals andpopulations, typically to ask whether there isevidence of local adaptation (Kohn et al. 2006).Adaptive differences are context‐dependentfitness differences between individuals and areultimately due to differences betweenindividuals in gene variants (alleles) at one ormultiple loci, resulting in differences inphenotype. These phenotypic differences arealways the result of gene‐environmentinteractions and can only be understood in thatlight. However, unraveling the associationbetween particular nucleotide substitutionsand phenotype is challenging even for scientistswho study genetic model systems.Adaptive differences between individuals

and populations are difficult to identify at themolecular genetic level (see also Chapter 2).This is typically because genomic resources arenot available for most species. However, with aset of unlinked molecular markers scatteredthroughout the genome, such asmicrosatellites, it is possible to identifycandidate loci of adaptive significance that arephysically linked to these markers. If thefrequency of alleles at these loci is significantlygreater or less than the expectation based onan equilibrium between migration and geneticdrift, one can infer that this locus might haveexperienced the effects of natural selection.These analyses are often referred to as outlieranalyses and aim to find genes linked to neutralmarkers that are more (or less) divergedbetween individuals and populations than thebackground (neutral) divergence (Beaumont

2005). Despite the immediate appeal of thesestudies, moving from identification of outlierloci to identification of the function of thatlocus and the individual nucleotide differencesunderlying that trait is a difficult task.The genomics revolution is now enabling

unprecedented insight into the molecular basisof fitness differences between individuals.Completed genome sequences of hundreds ofplants and animals are available or in progressand next generation sequencing technology israpidly increasing the number of species thatwillbecome genomically characterized. Massivelyparallel sequencing technology is enabling therapid characterization of entire genomes andtranscriptomes (all of the expressed genes in agenome) at relatively low cost. Currently,sequence reads from these technologies are, onaverage, <500 base pairs in length and sotraditional Sanger sequencing still outperformsmassively parallel technology at the level of theindividual read. Digital gene expression (whereall of the expressed genes are sequenced andcounted; Torres et al. 2008) and microarrayanalysis allows one to study differences in globalgene expression without a priori information onthe identity of genes used in the analysis. Singlenucleotide polymorphism (SNP) analysis is likelyto be an effective tool in identifying loci andindividual substitutions that are associated withdifferences in trait values between individuals,even when pedigree information andheritabilities of traits are not available, as is thecase for most threatened species.Although there is considerable debate over

the relative importance of cis regulatorymutations (in non-coding sequences flankingprotein-coding genes) versus structuralmutations (in protein coding genes) in themolecular basis of phenotypic evolution acrossspecies, methods are best developed fordetecting a signature of selection at codonswithin protein-coding genes. In this case, aconservation biologist may be interested inknowingwhat loci andwhat codons within thatgene have experienced positive, adaptiveselection. The redundancy of the DNA code

continues


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evolution itself operates. As such, no review ofthe conservation biologist’s toolbox would becomplete without some reference to the hugearray of molecular techniques now at our dispos-able used in “conservation genetics” (Box 16.5).Below is a brief primer of the major concepts.

Conservation genetics is the discipline dealingwith the genetic factors that affect extinction riskand the methods one can employ to minimizethese risks (Frankham et al. 2002). Frankham etal. (2002) outlined 11 major genetic issues that thediscipline addresses: (i) inbreeding depression’snegative effects on reducing reproduction andsurvival; (ii) loss of genetic diversity; (iii) reduction

in gene flow among populations; (iv) genetic drift;(v) accumulation and purging of deleterious muta-tions; (vi) genetic adaptation to captivity and itsimplications for reintroductions; (vii) resolvinguncertainties of taxonomic identification; (viii)defining management units based on genetic ex-change; (ix) forensics (species identification anddetection); (x) determining biological processesrelevant to species management; and (xi) out-breeding depression. All these issues can be as-sessed by extracting genetic material [e.g. DNA(deoxyribonucleic acid), RNA (ribonucleic acid)]from tissue sampled from live or dead indivi-duals (see Winchester and Wejksnora 1995 for a


means that in protein‐coding genes, nucleotidesubstitutions are either synonymous – theamino acid coded by the codon remains thesame, or non‐synonymous – the correspondingamino acid changes. Comparing the rates ofnon‐synonymous/synonymous substitutions(the o rate ratio) of a gene between species canprovide evidence of whether that gene or locusis under selection (Yang 2003). A variety ofmethods are available to estimate o ratios for agiven gene tree. When o <1, purifying selectionis inferred because non‐synonymoussubstitutions are deleterious with respect tofitness; when o = 1, neutral evolution is inferredbecause there is no difference in fitnessbetween non‐synonymous and synonymoussubstitutions; and when o >1, positive selectionis inferred because non‐synonymoussubstitutions are favored by natural selection.In their most general form, o ratios areaveraged across all nucleotide sites, butbecause non‐synonymous rates are often quitevariable across a gene, o values can also beestimated for individual codons. While it ispossible to test for significant differencesamong o values, the most conservativeinterpretation holds that adaptive evolutionhas occurred only when o values are >1.However, even when o values are >1,demographic forces can elevate o ratios if thereis an imbalance between genetic drift and

purifying selection. Because several non‐mutually exclusive factors can affect o ratios,comparisons using these data, which are alwaysonly correlative in nature, need to beinterpreted with caution.The genomics research horizon is

rapidly changing all areas of biology andconservation biology is no exception.A new arsenal of genomic and analyticaltools is now available for conservationbiologists interested in identifying adaptivedifferences between individuals andpopulations that will complement traditionalneutral marker studies in managing wildlifepopulations.

REFERENCES

Beaumont, M. A. (2005). Adaptation and speciation:what can Fst tell us? Trends in Ecology and Evolution, 20,435–440.

Kohn, M. K., Murphy, W. J., Ostrander, E. A., and Wayne,R. K. (2006). Genomics and conservation genetics.Trends in Ecology and Evolution, 21, 629–637.

Torres, T. T., Metta, M., Ottenwälder, B., and Schlötterer,C. (2008). Gene expression profiling by massively parallelsequencing. Genome Research, 18, 172–177.

Yang, Z. (2003) Adaptive molecular evolution. In D. J.Balding, M. Bishop and C. Cannings, eds Handbook ofStatistical Genetics, pp. 229–254, John Wiley and Sons,New York, NY.




good introduction to the array of methods used todo this).

Of these 11 themes, the first three are perhapsthe most widely applicable elements of conserva-tion genetics, and so deserve special mentionhere. Inbreeding depression can be thought of asan Allee effect because it exacerbates reductionsin average individual fitness as population sizebecomes small. Inbreeding is the production ofoffspring by related individuals resulting fromself-fertilization (e.g. the extreme case of ‘selfing’in plants) or by within-‘family’ (e.g. brother-sis-ter, parent-offspring, etc.) matings. In these cases,the combination of related genomes during fertil-ization can result in reductions in reproductionand survival, and this is known as inbreedingdepression. There are several ways to measureinbreeding: (i) the inbreeding coefficient (F) mea-sures the degree of parent relatedness derivedfrom a pedigree analysis (strictly – the probabilitythat an allele is common among two breedingindividuals by descent); (ii) the averageinbreeding coefficient is the F of all individualsin a population; and (iii) inbreeding relative torandom breeding compares the average related-ness of parents to what one would expect if thepopulation was breeding randomly.

The amount of genetic diversity is the extent ofheritable variation available among all indivi-duals in a population, species or group of species.Heterozygosity is the measure of the frequency ofdifferent of alleles [alternative forms of the samesegment of DNA (locus) that differ in DNA basesequence] at the same gene locus among indivi-duals and is one of the main ways genetic diver-sity is measured. Populations with few alleleshave generally had their genetic diversity re-duced by inbreeding as a result of recent popula-tion decline or historical bottlenecks. Populationsor species with low genetic diversity thereforehave a narrower genetic template from which todraw when environments change, and so theirevolutionary capacity to adapt is generallylower than for those species with higher geneticvariation.

Habitat fragmentation is the process of habitatloss (e.g. deforestation) and isolation of ‘frag-ments’, and is one of the most important direct

drivers of extinction due to reductions in habitatarea and quality (Chapter 5). Yet because frag-mentation also leads to suitable habitats for par-ticular species assemblages becoming isolatedpockets embedded within (normally) inhospita-ble terrain (matrix), the exchange of individuals,and hence, the flow of their genetic material, isimpeded. Thus, even though the entire popula-tion may encompass a large number of indivi-duals, their genetic separation via fragmentationmeans that individuals tend to breed less ran-domly and more with related conspecifics, thusincreasing the likelihood of inbreeding depres-sion and loss of genetic diversity. For a morecomprehensive technical demonstration and dis-cussion of these issues, we recommend the readerrefers to Frankham et al. (2002).

16.6 Concluding Remarks

The multidisciplinarity of conservation biologyprovides an expansive source of approaches, bor-rowed from many disciplines. As such, this inte-grative science can appear overwhelming or evenintimidating to neophyte biologists, especiallyconsidering that each approach discussed here(and many more we simply did not have spaceto describe) is constantly being reworked, im-proved, debated and critiqued by specialists.But do not despair! The empirical principles ofconservation biology (again, focusing here onthe ‘biology’ aspect) can be broadly categorizedinto three major groups: (i) measuring speciesand abundance; (ii) correlating these to indicesof environmental change; and (iii) estimatingrisk (e.g. of extinction). Almost all of the ap-proaches described herein, and their myriad var-iants and complications, relate in some way tothese aims. The specific details and choices de-pend on: (i) data quality; (ii) spatial and temporalscale; (iii) system variability; and (iv) nuance ofthe hypotheses being tested.

When it comes to the choice of a particularstatistical paradigm in which to embed thesetechniques, whether it be null hypothesis test-ing or multiple working hypotheses (Box 16.3),likelihood-based or Bayesian inference (Box


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16.4), is to some extent open to personalchoice. We have been forthright regardingour particular preferences (we consider multi-ple working hypotheses to be generally superi-or to null hypothesis testing, and Bayesianoutperforming likelihood-based inference), butthere are no hard-and-fast rules. In generalterms though, we recommend that conserva-tion biologists must at least be aware of thefollowing principles for any of their chosenanalyses:

· Adequate and representative replication of theappropriate statistical unit of measure should beplanned from the start.

· The high probability that results will vary de-pending on the spatial and temporal scale of inves-tigation must be acknowledged.

· Choosing a single model to abstract the complex-ities of ecological systems is generally prone to over-simplification (and often error of interpretation).

· Formal incorporation of previous data is a goodway of reducing uncertainty and building on pastscientific effort in a field where data are inevitablychallenging to obtain; and

· Multiple lines of evidence regarding a specificconclusion will always provide stronger inference,more certainty and better management and policyoutcomes for the conservation of biodiversity.

This chapter represents the briefest of glimpsesinto the array of techniques at the disposal ofconservation biologists. We have attempted toprovide as much classic and recent literature toguide the reader toward more detailed informa-tion, and in this spirit have provided a list of what

Box 16.6 Useful Textbook GuidesCorey J. A. Bradshaw and Barry W. Brook

It is not possible to provide in‐depthmathematical, experimental or analytical detailfor the approaches summarised in this chapter.So instead we provide here a list of importanttextbooks that do this job. The list is notexhaustive, but it will give emerging andestablished conservation biologists a solidquantitative background on the issuesdiscussed in this chapter – as well as manymore.

SUGGESTED READING

Bolker, B. M. (2008). Ecological models and data in R.Princeton University Press, Princeton, NJ.

Burnham, K. P. and Anderson, D. R. (2002).Model selectionand multimodal inference: a practical information‐theo-retic approach. 2nd edn. Springer‐Verlag, New York, NY.

Caswell, H. (2001). Matrix population models: construc-tion, analysis, and interpretation. 2nd edn. Sinauer As-sociates, Inc., Sunderland, MA.

Caughley, G. and Gunn, A. (1996). Conservation biology intheory and practice. Blackwell Science, Cambridge, MA.

Clark, J. S. (2007). Models for ecological data: an intro-duction. Princeton University Press, Princeton, NJ.

Ferson, S. and Burgman, M., eds (2002). Quantitative meth-ods for conservation biology. Springer, New York, NY.

Frankham, R., Ballou, J. D., and Briscoe, D. A. (2002).Introduction to conservation genetics. Cambridge Uni-versity Press, Cambridge, UK.

Krebs, C. J. (1999). Ecological methodology. 2nd edn.Benjamin Cummings, Upper Saddle River, NJ.

Krebs, C. J. (2009). Ecology: the experimental analysis ofdistribution and abundance. 6th edn. Benjamin Cum-mings, San Francisco, CA.

Lindenmayer, D. and Burgman, M. (2005). Practical con-servation biology. CSIRO (Australian CommonwealthScientific and Industrial Research Organization) Publish-ing, Collingwood, Australia.

McCallum, H. (2000). Population parameters: estimationfor ecological models. Blackwell Science, Oxford, UK.

McCarthy, M. A. (2007). Bayesian methods for ecology.Cambridge University Press, Cambridge, UK.

Millspaugh, J. J. and Thompson, F. R. I., eds (2008).Modelsfor planning wildlife conservation in large landscapes.Elsevier, New York, NY.

Morris, W. F. and Doak, D. F. (2002). Quantitative conser-vation biology: theory and practice of population viabil-ity analysis. Sinauer Associates, Sunderland, MA.

Turchin, P. (2003). Complex population dynamics: a theo-retical/empirical synthesis. Princeton University Press,Princeton, NJ.




we consider to be some of the better textbookguides which provide an expanded treatment ofthe different techniques considered (Box 16.6). Aparting recommendation – nomatter how sophis-ticated the analysis, the collection of rigorousdata using well-planned approaches will alwaysprovide the best scientific outcomes.

Summary

· Conservation biology is a highly multidisciplin-ary science employing methods from ecology, Earthsystems science, genetics, physiology, veterinary sci-ence, medicine, mathematics, climatology, anthropol-ogy, psychology, sociology, environmental policy,geography, political science, and resource manage-ment. Herewe focus primarily on ecological methodsand experimental design.

· It is impossible to census all species in an ecosys-tem, so many different measures exist to comparebiodiversity: these include indices such as speciesrichness, Simpson’s diversity, Shannon’s index andBrouillin’s index.Many variants of these indices exist.

· The scale of biodiversity patterns is important toconsider for biodiversity comparisons: a (local), b (be-tween-site), and g (regional or continental) diversity.

· Often surrogate species – the number, distri-bution or pattern of species in a particular taxonin a particular area thought to indicate a muchwider array of taxa – are required to simplifybiodiversity assessments.

· Many similarity, dissimilarity, clustering, andmultivariate techniques are available to comparebiodiversity indices among sites.

· Conservation biology rarely uses completelymanipulative experimental designs (althoughthere are exceptions), with mensurative (basedon existing environmental gradients) and obser-vational studies dominating.

· Two main statistical paradigms exist for com-paring biodiversity: null hypothesis testing andmultiple working hypotheses – the latter paradigmis more consistent with the constraints typical ofconservation data and so should be invoked whenpossible. Bayesian inferential methods generallyprovide more certainty when prior data exist.

· Large sample sizes, appropriate replication andrandomization are cornerstone concepts in all con-servation experiments.

· Simple relative abundance time series (sequen-tial counts of individuals) can be used to infer morecomplex ecological mechanisms that permit the esti-mation of extinction risk, population trends, andintrinsic feedbacks.

· The risk of a species going extinct or becominginvasive can be predicted using cross-taxonomiccomparisons of life history traits.

· Population viability analyses are essential toolsto estimate extinction risk over defined periodsand under particular management interventions.Many methods exist to implement these, includingcount-based, demographic, metapopulation, andgenetic.

· Many tools exist to examine how genetics affectsextinction risk, of which perhaps the measurementof inbreeding depression, gene flow among popula-tions, and the loss of genetic diversity with habitatdegradation are the most important.

Suggested reading

See Box 16.6.

Relevant websites

· Analytical and educational software for risk as-sessment: www.ramas.com.

· Population viability analysis software: www.vor-tex9.org.

· Ecological Methodology software–Krebs (1999):www.exetersoftware.com/cat/ecometh/eco-methodology.html.

· Capture-mark-recapture analysis software:http://welcome.warnercnr.colostate.edu/gwhite/mark/mark.htm.

· Analysis of data from marked individuals: www.phidot.org.

· Open-source package for statistical computing:www.r-project.org.

· Open-source Bayesian analysis software: www.mrc-bsu.cam.ac.uk/bugs/.


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Acknowledgements

We thank T. Gardner, D. Bickford, C. Mellin andS. Herrando-Pérez for contributions and assistance.

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