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regression to model the abundance conditional upon host use – our focal parameter. ... The host breadth model indicated that several insect species had high ...
Methods in Ecology and Evolution 2010, 1, 292–299

doi: 10.1111/j.2041-210X.2010.00026.x

How many hosts? Modelling host breadth from field samples Peter A. Vesk*, Michael A. McCarthy and Melinda L. Moir School of Botany, The University of Melbourne, Parkville, Vic. 3010, Australia

Summary 1. Host-specificity is important in fundamental and applied studies of biodiversity, but it is difficult to generate definitive data for many species. 2. Here, we present a model framework for estimating the realized host breadth of dependent fauna from samples collected from replicate host individuals. We use Bayesian, Zero-inflated Poisson regression to model the abundance conditional upon host use – our focal parameter. We illustrate the model using a data set of insects on threatened and non-threatened plant species from eastern Australia. Estimating co-extinction risk through threats to host organisms is a key application for the model, requiring assessment of the host-specificity of biota, whilst incorporating uncertainty. 3. The host breadth model indicated that several insect species had high probability of narrow host breadth, including several species that appeared to only have one host. Furthermore, the model distinguished polyphagous, oligophagous and monophagous insect species. Modification of the model to account for false positives also identified tourist occurrences. 4. The host breadth model can be utilized not only towards focusing conservation actions on the most co-threatened dependent invertebrate species, but also for other projects involving host-specificity, such as estimating the number of insects globally, and selecting the most likely candidates for biological control of invasive species. Further uses are likely in various data sets of associations between species. Key-words: herbivory, host range, host-specificity, insect–plant interactions, monophagous, oligophagous, parasites, polyphagous

Introduction Host-specificity is of interest for several reasons: understanding co-evolution and the importance of tight vs. weak interactions in communities (e.g. Poulin et al. 2006); estimating global biodiversity (e.g. Ødegaard 2000); assessing co-extinction risk (e.g. Koh et al. 2004; Dobson et al. 2008; Moir et al. 2010) and understanding population dynamics of affiliate species (Griebeler & Seitz 2002). Host breadth (the number of host species an affiliate is capable of using in the field) is sometimes equated with potential diet breadth (all possible host species that an affiliate may be able to use, regardless of the origin of the host species). Feeding trials remain the most effective method to determine potential diet breadth, but present several problems. Feeding trials of free-living organisms such as phytophagous insects are difficult, laborious and resource-intensive, and for internal parasites and parasitoids, infeasible. And although feeding trials are recommended, can even they be regarded as truly definitive? One may argue that successful rearing of *Correspondence author. E-mail: [email protected] Correspondence site: http://www.respond2articles.com/MEE/

putative dependents through to reproduction might be needed. Feeding trials are particularly limiting for rare species because feeding trials, identification and experimentation place conflicting demands on sampled organisms. Because of such problems compiling host-specificity data from feeding trials, there is a need for methods to determine realized host-specificity from the observed presence of an affiliate upon a host, even if this is not a definitive demonstration of host use. Moreover, realized host breadth may differ considerably from potential diet breadth because of variable apparency, sensu (Feeny 1976): diet breadth may include hosts that are not encountered by the affiliate and so do not form part of the realized host breadth (e.g. hosts that occur outside of the range of the affiliate). This concept of diet breadth is explicitly used when researchers do feeding trials before releasing biological control agents into different countries (Kluge & Gordon 2004). Inferring host use from association has several problems. Affiliates may be absent from a collection either because they do not use the putative host, or they use it but are simply not present on that individual – a false negative. Affiliates may be collected either because they do actually use the host, or through chance occurrence on a host that they do not in fact

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Modelling host breadth from samples 293 use – a false positive. So-called ‘tourist’ species are false positives, occurring through accident or mass effects (Novotny & Basset 2000). Complex protocols that have been suggested to ‘control’ for tourists include sampling strategies (sampling neighbouring plants, incorporating host plant phylogeny), incorporating knowledge of invertebrate species autecology (difficult in biodiverse and understudied regions) and abundance information (Flowers & Janzen 1997; Ødegaard 2004). Plainly, abundances should be useful for inferring host use. If an animal usually occurs in high abundance, its presence in low numbers on a single plant might suggest a chance occurrence, such that the affiliate is a ‘tourist’ on that particular plant species. However, if a species is never found at high abundance, then absence from a collection might occur simply through chance variation. In short, methods are needed to assess host use by an affiliate (and subsequently its host breadth) that do not require arbitrary decisions about numbers, but that utilize the collection data to estimate the probability that the host is used. Further, because we do not have perfect knowledge, a desirable approach would be one that accounts for, and can report, uncertainty. This paper presents just such an approach. The motivation for developing this model was the estimation of host-specificity for assessing the co-extinction risk to insects on threatened plant hosts (Moir et al. 2010). Following parameter estimation, feeding trials or other information can be applied to the question of host use. Our aim here is to describe a general modelling approach for estimating host use through the presence and abundance of affiliates.

Materials and methods Our ultimate aim is to estimate the number of plant hosts for a particular invertebrate species. We do this by first estimating the probability that an invertebrate species uses a particular plant species. The modelling is based on a matrix of counts of individual invertebrates from different species in collections from individual plants. Hence, we are not analysing use, but rather assume that use is inferred from presence and retain this interpretation throughout this article. The data Yij are observed counts of invertebrate species j in collection i from an individual plant. There is one collection per plant. We model these counts as a random realization from Poisson distributions with mean lij; the Poisson is a natural distribution used for count data, although others could be used, e.g. negative binomial. Yij  Poissonðlij Þ

eqn 1

THE HOST BREADTH MODEL

A natural model for variation in counts of invertebrates among plants that they may or may not use is one that jointly estimates the probability of use of a plant by an invertebrate and abundance of that invertebrate, given that it does use the plant. This can be thought of as a model of conditional abundance: the abundance is modelled conditional on use (Hall 2000). The specific model we use is a Zero-Inflated Poisson (ZIP) regression, the observations being counts and, as such, naturally Poisson distributed, but with an excess of zeros. The excess of zeros comes from absences of

invertebrates from plants that they do not use as hosts. The estimation of the Poisson parameter should come only from those observations where the invertebrate has a chance of occurring. Four sources of zeros exist in ecological data: design error; observer error; animal error and true absence (Martin et al. 2005). In this article, we are concerned with zeros originating from suitable but unoccupied plants, and from collections missing animals that were in fact present. We also model false positives (Royle & Link 2006) to account for tourists that occasionally occur at low abundance on individual plants. We present results from two versions of the model, M1, which does not include terms for false positives and M2, which does. One could contemplate modelling a single invertebrate at a time, but it is reasonably straightforward to model all species in a hierarchical model and this brings particular advantages (Link et al. 2002; Clark 2005). The model is hierarchical, in that particular model parameters are assumed to belong to some distribution, which has its own hyper-parameters, so the parameters belong to a hierarchy. Coincidentally, that plants and invertebrates can be hierarchically organized by taxonomy suits hierarchical modelling. Furthermore, covariates may be applied at different levels of the hierarchies. Hierarchical models are very useful because the abundance of data and hierarchical structure allows the model to estimate the parameters of particular species by using data for related species (Link et al. 2002; Clark 2005). The basic structure of the model can be represented as a Directed Acyclic Graph (Spiegelhalter & Lauritzen 1990) with nodes, which can be observed variables or parameters to be estimated, represented by ellipses, and dependencies represented by arrows pointing towards the dependent node (Fig. 1). There are three submodels in our host breadth model: one for the probability of use of the host by the invertebrate (dashed outline in Fig. 1); a second for the abundance of the invertebrate (dotted outline in Fig. 1); and a third for the probability of being a tourist and for modifying the abundance accordingly, only relevant to M2 (dot-dashed outline in Fig. 1). These three sub-models are linked to estimate the abundance of each invertebrate species on each plant, depending on whether or not it uses the plant or is a tourist thereon. The model can be expanded in various ways as each of the submodels has a linear form to which extra terms may be added. The model is as follows, and can be read in combination with Fig. 1 working from the bottom up. lij ¼ ðhk½ij þ dij  vÞ  kij

eqn 2

The mean abundance lij is a function of hk[i]j, the use of the plant species k that the individual plant i belongs to, kij (the characteristic abundance of the invertebrate), dij (whether invertebrate species j is a tourist on the individual plant i), and m, which is the relative abundance of invertebrates when found as tourists. Our notation here using square brackets indicates that plant i belongs to plant species k. The parameters hk[i]j are indicator variables, taking the value 1 when the plant species, k, that the individual plant i belongs to is used by the invertebrate, and 0 otherwise. Similarly, dij is an indicator variable for occurrence as a tourist. Thus, the mean abundance of tourists is some proportion of the abundance of those same invertebrates when occurring on plant species that they truly use. This proportion is assumed to be the same for all invertebrate–plant combinations. Use and tourist are mutually exclusive. When the plant is used, the tourist parameter d becomes 0 and the expected abundance is kij. If the plant is not used, then the tourist parameter d becomes 1 and the expected abundance is m · kij. Below, we work through each of the submodels in turn: use, abundance and tourists.

 2010 The Authors. Journal compilation  2010 British Ecological Society, Methods in Ecology and Evolution, 1, 292–299

294 P. A. Vesk, M. A. McCarthy & M. L. Moir

Fig. 1. Directed acyclic graph, showing the structure of the host breadth model. Ellipses represent nodes (parameters) of the model, while arrows (arcs) indicate causal dependencies between nodes. Dashed arrows indicate logical, deterministic calculations. Three submodels are indicated, the Use submodel (in dashes) and the Abundance submodel (in dots) and the Tourist submodel (in dashdots). Subscripts are indicated by brackets.

THE USE SUBMODEL

logðkij Þ ¼ b0 þ b1j :

Focussing on the Use submodel (dashed outline on the left side of Fig. 1):

Here, kij is the mean abundance for invertebrate species j in collection i from an individual plant. The abundance is modelled with a Poisson regression as the function of the average abundance across all invertebrate species, b0, and a (random effect) coefficient b1j for invertebrate species j. This says that each invertebrate species has a characteristic abundance with which it occurs on any plant that it uses as a host.

hkj  Bernoulliðpk½ij Þ:

eqn 3

Use is a realization of a Bernoulli trial with probability of host use pk[i]j logitðpkj Þ ¼ a0 þ a1f½kj :

eqn 4

The probability of host use pkj, can then be modelled with logistic regression and here we included an intercept term for the average prevalence of the invertebrates across the host plants, a0, and a (random effect) coefficient corresponding to the combination of the invertebrate species j by plant family f, a1f[k]j. That is, each invertebrate species j has a probability of occurring on a plant that is common to all members of a particular plant family f. Variation between plant species within a family was not modelled and so is random ‘noise’. Previous work has suggested that host plant phylogeny explains a high percentage of variation in insect herbivore communities (e.g. Ødegaard, Diserud, & Østbye 2005; Weiblen et al. 2006). In addition, there were insufficient data for modelling at the level of invertebrates by plant species. When prevalence is low, i.e. a small fraction of potential hosts are occupied, large samples are needed to determine whether absences are due to chance.

THE ABUNDANCE SUBMODEL

Turning to the Abundance submodel (dotted outline at the top right of Fig. 1):

eqn 5

THE FALSE POSITIVE OR ‘TOURIST’ SUBMODEL

The Tourist submodel (dot-dashed outline at lower right on Fig. 1) simply states that each invertebrate can occur randomly as a tourist on individual plants. The probability of being a tourist d, given that the plant species is not used as a host (h = 0), is assumed to be the same for all invertebrate–plant combinations: dij  Bernoullið/ij Þ;

eqn 6

/ij ¼ 0 if hij ¼ 1; and /ij ¼ q otherwise:

eqn 7

Inferences about host breadth are obtained through simple logical (deterministic) operations on the host use. X hkj : HBj ¼ k eqn 8 Hence host breath of the invertebrate j, HBj, is simply the number of plant species for which use hkj returns the value 1 for that invertebrate.

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Modelling host breadth from samples 295 We may also wish to determine whether an invertebrate only uses plants of family f.  P 0; if ðkefÞPðhkj Þ ¼ 0 ðeqn 9aÞ; family usef ¼ eqn 9a and b 1; if ðkefÞ ðhkj Þ>0 ðeqn 9bÞ: We also calculate whether an invertebrate only plants of family f (family usef = 1, and family usej = 0 for all j „ f). This is a quite general model form; other models could be fitted say, in which the abundance of a particular invertebrate varies between plant species. But our choice here was driven by the desire to make inferences about the probability of host use. While better fitting of abundances is certainly possible, this tends to drive the host use probabilities to be more similar, and ⁄ or uncertain. Both the abundance and host use submodels may be extended with covariates about collection site, method, functional type classification and taxonomy. For instance, one might posit that invertebrates with a particular feeding mode may have similar abundances. Our point here although is to illustrate the general modelling approach and to present some example inferences that might be made.

BAYESIAN IMPLEMENTATION, SPECIFICATION OF PRIOR DISTRIBUTIONS OF PARAMETERS

We use Bayesian inference and hence need to specify prior distributions for model parameters. We use vague priors throughout. Regression intercepts (mean abundance b0, and mean probability of use a0) were drawn from normal distributions with mean 0 and r = 1000. The regression coefficients, a1f[k]j, which model variation in probability of use of plant family f, to which plant species k belongs, by invertebrate species j were drawn from Normal distributions centred on 0 with standard deviation ra. Similarly, the coefficients for variation in average abundance among invertebrate species b1j, were drawn from a Normal distribution with mean 0 and standard deviation rb. One could specify the distribution for the variance, but the standard deviation is a more intuitive parameter, and other work has promoted its use (Gelman 2006). We specify uniform priors for each of ra and rb, stating only that it they could be anywhere between 0 and 100, with the upper limit chosen such that it has little influence on the posterior distribution. The prior distribution for q, the probability of an invertebrate species being a tourist if the plant species was not used, was assumed to be uniform between 0 and 1. The prior distribution of the relative abundance of tourists, conditional on them being present, m, was also assumed to be uniform between 0 and 1. We used Markov Chain Monte Carlo sampling to estimate the posterior probability distributions of parameters. The model was implemented in the freely available software OpenBUGS 3Æ03 (Thomas et al. 2006). Code is included as Appendix S1 (Supporting information). We routinely inspected chain traces and found that convergence occurred within 1000 samples, but we routinely rejected the first 2000 samples as a burn in and sampled the next 10 000 samples from the Markov chain.

THE EMPIRICAL STUDY AND DATA

The focal endangered plant species, Grevillea caleyi R.Br. (Proteaceae: Grevilleeae) and Pultenaea glabra Benth. (Papilionaceae: Mirbelieae), were chosen for ease of access, familial representation and previous work conducted on population dynamics. Plants were located in open dry sclerophyll forest, in the Blue Mountains (P. glabra: 3343¢S 15026¢E) and Sydney (G. caleyi: 3339¢S 15111¢E), New South Wales, Australia. For each threatened plant

species, 30 individual plants were sampled for invertebrates (15 sampled by beating, 15 sampled by vacuuming) between December 2007 and January 2008. Beating and vacuuming have been found to be the most efficient methods to sample plant-dwelling insects (in time, expense, and number of specimens). When used in combination the resultant samples are highly complementary, in that the two methods capture significantly different faunas (Moir et al. 2005). Subsequently, all individual plants were searched by hand to collect cryptic fauna, such as galls and lerps. We sampled surrounding non-threatened plants to construct a host-affiliate data base. Fourteen individuals per non-threatened plant species were sampled (seven sampled by beating, seven sampled by vacuuming) due to time limitations. Nonthreatened plants comprised at least 10 species per site, with these representing at least six of the most abundant species near the threatened plant species, two species within the same genus as the threatened species and two within the same family (Table 1). This design is preferred, because, as mentioned previously, host specificity of insects is often related to the phylogeny of the hosts (Ødegaard, Diserud, & Østbye 2005). Additionally, tourist insect species may be more likely to originate from the most abundant surrounding plants, than plant species further away from the threatened target plants – a mass effect (Shmida & Wilson 1985). We collected the predominantly herbivorous insect orders of Coleoptera (beetles), Hemiptera (bugs), Thysanoptera (thrips), Lepidoptera (butterflies) and Orthoptera (grasshoppers and stick insects), plus gall-forming species, such as some Hymenoptera. Curation followed Upton (1991) and insects were identified to species by dissecting genitalia, referring to the taxonomic literature, visiting insect collections and ⁄ or by taxonomic experts. If an insect was undescribed, they were assigned a unique species code (e.g. Poecilometis sp. 04).

Results In total, 333 individual plants were sampled from 19 species, of which 60 individuals were of the two threatened plant species. A total of 1055 insects were collected, represented by 186 species and 40 families. The most abundant and speciose orders were Hemiptera (519 individuals, 71 species) and Coleoptera Table 1. Plant species sampled for insects Family

Genus

Species

Ericaceae Gleicheniaceae Mimosaceae Mimosaceae Mimosaceae Papilionaceae Papilionaceae Papilionaceae Papilionaceae Papilionaceae Papilionaceae Papilionaceae Proteaceae Proteaceae Proteaceae Proteaceae Proteaceae Proteaceae Malvaceae

Epacris Gleichena Acacia Acacia Acacia Bossiaea Daviesia Dillwynia Phyllota Pultenaea Pultenaea Pultenaea Banksia Grevillea Grevillea Grevillea Hakea Hakea Lasiopetalum

pulchella dicarpa longifolia var. longifolia myrtifolia ulicifolia obcordata corymbosa retorta squarrosa glabra linophylla tuberculata spinulosa buxiflora caleyi sericea laevipes var. laevipes sericea ferrugineum

Those species highlighted in grey are threatened.

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296 P. A. Vesk, M. A. McCarthy & M. L. Moir (302 individuals, 61 species). From the data set, 21 species of insect were found on G. caleyi (Hemiptera, eight species; Lepidoptera, five species; Coleoptera, four species; Orthoptera, three species; Thysanoptera, one species) and 28 species on P. glabra (Hemiptera, 14 species; Coleoptera, 10 species; Lepidoptera, 3 species; Orthoptera, 1 species). Collection information and predictions from models M1 and M2 are detailed for 18 invertebrate species in Table S1 (Supporting Information).

PREDICTING HOST BREADTH

Median host breadths of particular invertebrates are often predicted to be wider under M1 than M2, which accounts for false positives (Fig. 2). Host breadth is never predicted to be greater when excluding false positives. Under M1, any occurrence of a particular invertebrate on a plant indicates use of the plant and so that plant is a host. Under M2, some occurrences are attributed to false positives, or tourists, rather than host use. For example, M2 predicts that some invertebrates that were collected with a total of four animals from P. glabra, and up to two animals from the same individual plant, were in fact false positives or tourists, and thus did not use the species P. glabra (Fig. 3). Predictions of host breadth incorporating uncertainty are made for a set of exemplar species with two versions of the model: M1, which does not account for false positives (Fig. 4), and M2, which does (Fig. 5). Under M1, median predicted host breadth ranged from one host for 10 insect species, through to nine hosts for four species. Whereas, under M2, for some invertebrates there is a good chance that they have no hosts within the set of plant species sampled (median HB is 10 individuals, 5–9, 2–4, 1), and ‘additional evidence’ such as designation as tourists by comparing samples from other neighbouring species (Flowers & Janzen 1997; Ødegaard 2004). Often the decision process of these alternative methods is yet more involved, including singletons being handled variably, depending upon feeding mode. Here, we eliminate such decisions and allow the model to predict the host breadth of the affiliates based on specified model assumptions. Nevertheless, the estimates of host breadth will be strongly influenced by the available data set, as with any empirical model. The greater the number of potential host species that are included within the data set, the more accurate the predicted host breadth of the affiliate species. Furthermore, additional host species may occur beyond the sampled region, so we may have overestimated the number of affiliates with high host-specificity. But for particular target host species, the sampling design may minimize this overestimation by attempting to account for phylogenetic and other associations between the affiliates and hosts, and ⁄ or by stratifying samples spatially (Gaston et al. 1996; Ødegaard 2004). A possible extension of this work would be to extend inferences to plant species not included in the sample, along the lines of work that estimates species richness through summaries of imperfect detection of multi-species occurrences (Dorazio et al. 2006). For our data set, the two models we have used provide upper and lower bounds on predictions of host use and host breadth. M1 overestimates host use because every occurrence defines

use of the plant species as a host. M2 might underestimate host use because single occurrences tend to be ascribed as false positives, as long as there have been collections of multiple individuals from a single plant somewhere. In an exhaustive sample, M2 would be expected to be correct, but in progressively smaller samples, single true occurrences would form a greater proportion of the sample and hence be ascribed as false positives. Increased sampling intensity of the target species would also improve accuracy and precision, most likely nonlinearly related to sample size. Broadly, a fourfold increase in sample size (at any particular level) should produce roughly a halving of the SE and hence the 95% CI associated with the parameter estimate. Yet, the relative frequency of zeroes and the distribution of non-zero counts will have strong effects on the outcomes that cannot be foreseen. Hence, it is not possible to provide general recommendations about appropriate sampling design without an exhaustive study. Without at least two collections from a plant species, the parameters cannot be estimated, and plainly, more samples within a plant species will aid estimation of the probability of use. But for a fixed effort, there is a trade-off between the number of replicate plants sampled and the number of plant species. We are unaware of any analysis of the effects of this trade-off on sampling design for zero-inflated Poisson models, such as those used here. However, zero-inflated binomial models have been analysed in the context of occupancy models with imperfect detection (Mackenzie & Royle 2005). That work suggests that at least two visits per site are needed, that the number of visits per site increases as detection probability declines and as occupancy increases (Mackenzie & Royle 2005). Further, when occupancy is low, more effort should be spent surveying more sites less intensely. The analogy for our case, where most invertebrate species have been collected from only 1 of the 19 plant species, and where most invertebrates were detected in fewer than 20% of collections from a plant species, would suggest at least seven collections per plant species are required. Yet, this has not been tested and the effects of false positives on such a result are unknown. Further work is needed. There are many possible variations on this model, including incorporating phylogeny, host and affiliate traits. One might posit that particular feeding modes or guilds (for instance, predispersal seed predation, leaf-miners vs. chewers; Novotny & Basset 2005) are more likely to be associated with narrow host breadth. Models can also be extended to examine variation in host breadth between host populations, for example, the changes in specificity of herbivorous insect assemblages of bracken (Pteridium aquilinum) across different continents (Lawton, Lewinsohn, & Compton 1993). In the case study analysed here, the host breadth estimates identify some species as host-specific to the threatened plants sampled. These are necessary, but insufficient for estimating co-extinction risks alone (Moir et al., unpublished data). An explicit risk assessment protocol developed by Moir et al. (unpublished data) includes the results from this host breadth model, in addition to cross-referencing literature and other collections, incorporating taxonomic issues and feeding trials. In other situations, such as identifying biological control

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Modelling host breadth from samples 299 agents, we foresee that the model could be critical at gauging host breadth, especially when feeding trials are not possible or successful (e.g. Kluge & Gordon 2004). The model can concentrate the worker on affiliates of interest (in this case, those with a narrow host breadth) in a time- and cost-effective manner when compared with methods normally associated with conventional host-specificity testing. This will be particularly useful in regions where affiliate diversity is high and the taxonomy of the fauna poorly known. The model would also be applicable to other biological associations including host-parasitism, host-commensalism and mutualism.

Conclusion We have shown that it is possible to estimate the host breadth of affiliate species, and perhaps more importantly, account for uncertainty in such estimates with our model. While these estimates cannot replace feeding trials, they provide an important means to assess realized host specificity, particularly in pressing cases, such as gauging the risk of co-extinction confronted by hyperdiverse insect groups.

Acknowledgements Grants from the Australian Research Council (DP0772057), Australia & Pacific Science Foundation (APSF 07 ⁄ 3), the University of Melbourne Botany Foundation, the Commonwealth Environment Research Facility,and New South Wales National Parks & Wildlife Service supported this work. We thank David Keith and Karl Brennan for assistance with field logistics. Comments from Marc Kery and an anonymous reviewer helped considerably to clarify the structure and expression.

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Supporting Information Additional Supporting Information may be found in the online version of this article. Appendix S1. Win BUGS code for host breadth model. Table S1. Model parameters and collection records for exemplar species. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

 2010 The Authors. Journal compilation  2010 British Ecological Society, Methods in Ecology and Evolution, 1, 292–299