1. In large-scale field surveys, a binary recording of each species’ detection or nondetection has been increasingly adopted for its simplicity and low cost. Because of the importance of abundance in many studies, it is desirable to obtain inferences about abundance at species-, functional group-, and community-levels from such binary data.
2. We developed a novel hierarchical multi-species abundance model based on species-level detection/nondetection data. The model accounts for the existence of undetected species, and variability in abundance and detectability among species. Species-level detection/nondetection is linked to species-level abundance via a detection model that accommodates the expectation that probability of detection (at least one individuals is detected) increases with local abundance of the species. We applied this model to a 9-year dataset composed of the detection/nondetection of forest birds, at a single post-fire site (from 7 to 15 years after fire) in a montane area of central Japan. The model allocated undetected species into one of the predefined functional groups by assuming a prior distribution on individual group membership.
3. The results suggest that 15–20 species were missed in each year, and that species richness of communities and functional groups did not change with post-fire forest succession. Overall abundance of birds and abundance of functional groups tended to increase over time, although only in the winter, while decreases in detectabilities were observed in several species.
4.Synthesis and applications. Understanding and prediction of large-scale biodiversity dynamics partly hinge on how we can use data effectively. Our hierarchical model for detection/nondetection data estimates abundance in space/time at species-, functional group-, and community-levels while accounting for undetected individuals and species. It also permits comparison of multiple communities by many types of abundance-based diversity and similarity measures under imperfect detection.
The estimation of abundance is fundamental to ecology (Williams, Nichols & Conroy 2001; Krebs 2009). For example, abundance is directly linked to persistence of populations (Hanski 1999) and ecosystem function/services (Ellison et al. 2005; Gaston & Fuller 2008). However, large-scale surveys are very costly so abundance can be expensive to count. Binary recording of species (species-level detection/nondetection) could reduce sampling effort at each site (MacKenzie et al. 2006), and yet retain some ability to study temporal population dynamics (Joseph et al. 2006; Pollock 2006). Occupancy estimated from binary data is also useful in metapopulation and landscape ecology because theoretical studies use occupancy as a state variable of populations (e.g. Hanski 1999). Collecting binary detection/nondetection data is thus increasingly adopted in large-scale field surveys (Marsh & Trenham 2008). Nevertheless, because of the relevance of abundance in many situations, it is desirable to obtain inferences about abundance from binary data (He & Gaston 2000; Royle & Nichols 2003).
Recently, Royle & Nichols (2003) developed a hierarchical model for estimating abundance of single species based on detection/nondetection data, i.e. the Royle–Nichols (RN) model. In the RN model, species-level detection/nondetection is linked to abundance via a detection model that accommodates the expectation that detection probability increases with local abundance of the species. On the contrary, Dorazio & Royle (2005) and Dorazio et al. (2006) developed a multi-species occupancy model also based on species-level detection/nondetection data, i.e. the Dorazio–Royle (DR) model. By accounting for the existence of undetected species and variability in occupancy and detectability among species, the DR model allows for estimation of species richness and community composition at a given site. Here we developed a novel hierarchical multi-species abundance model by combining these two different modelling frameworks, i.e. the Royle–Nichols and Dorazio–Royle models. Based on species-level detection/nondetection data (also called presence/absence data), our model provides estimates of abundance of each species within communities while accounting for undetected species and variability in abundance and detectability among species.
The concept of a functional group or guild, which is a group of species with similar ecological characteristics, is a basic tool in community ecology (Simberloff & Dayan 1991). It is increasingly important in understanding and predicting how biological communities drive ecosystem function/services (Violle et al. 2007; Hillebrand & Matthiessen 2009), and should be incorporated into multi-species abundance models. In our model, we do this by prescribing a prior distribution for species-level group membership in which group identity is a latent categorical covariate.
The development of this model made use of 9 years of bird monitoring data from a single site following a forest fire. Forest fires play a major role in forest ecosystems where they maintain habitat heterogeneity and species diversity at a landscape level (Turner, Gardner & O’Neill 2001). They are widely used in conservation management plans (Lindenmayer & Franklin 2002). Although the effect of fire on birds has been widely studied, most have used a chronosequence approach (but see Smucker, Hutto & Steele 2005; Haney, Apfelbaum & Burris 2009; Jacquet & Prodon 2009) where bird communities in fire and control sites are examined concurrently to identify differences due to fire. However, the assumption of a space-for-time substitution is not necessarily met due to the existence of confounding factors such as differences in initial conditions and site history among sites (Johnson & Miyanishi 2008). Therefore, long-term monitoring studies examining the effects of fire are very valuable (Brawn, Robinson & Thompson 2001).
Species detection was recorded over a 9-year period following a major (>200 ha) forest fire in Hitachi-city, central Japan (i.e. years 7–15, post-fire). Sampling included both breeding and wintering seasons, allowing comparison of bird responses between two seasons. Long-term monitoring data after forest fire are rare especially in East Asia, so these data provide a unique opportunity to understand the responses of birds to such events. The data have only a single spatial replicate (n = 1) but have temporal replications (n = 9 years), and possess two characteristics typical in long-term (or broad-spatial) data: variable sampling effort and possible changes in detectability among the samples. These factors complicate estimation of the effects of the covariates on populations and communities because, ideally, sampling should be constant across space and time (i.e. the proportionality assumption: Thompson 2002). We develop a hierarchical model that explicitly incorporates detection processes and accommodates variable sampling effort and changes in detectability, and allows inferences to be made about the post-fire changes in bird populations and communities.
Several long-term studies from temperate zones (North America: Haney, Apfelbaum & Burris 2009; Europe: Jacquet & Prodon 2009) have shown that bird communities change significantly in the first 10 years following a forest fire, after which they become relatively stable and approach pre-fire communities. Canopy trees return over this period so the abundance of a functional group feeding in the canopy layer (canopy gleaners) is also expected to increase (Haney, Apfelbaum & Burris 2009). However, the species richness and abundance of communities and other functional groups may not change markedly (Haney, Apfelbaum & Burris 2009; Jacquet & Prodon 2009). Succession could cause not only changes in bird communities but also a decline in the detectability of birds due to the development of habitat structure (Bibby & Buckland 1987; Schieck 1997), in which case we predicted that detectability of many species would decline. We tested these predictions by applying our multi-species abundance model to the 9-year monitoring data set.
Materials and methods
We describe our model using a spatially replicated sampling design as an example, although the model can be easily applied to temporally replicated sampling design by substituting space (e.g. sites) by time (e.g. years). Indeed, we apply this model to temporal dynamics in a bird community in a single site.
Detection process model
We assume a sampling design in which a number of spatial sample units –‘sites’– are visited multiple times, allowing for inferences to be made about species- and community-level state variables (e.g. occupancy, abundance and species richness) while accounting for imperfect detection (Royle & Dorazio 2008). We utilized binary recording in the field surveys to obtain encounter histories for each species. This gave a series of detection/nondetection in the visitations to each site, e.g. [1 0 1 0 1] for a certain species during five visits to a site. We compiled these encounter histories into a dataset of the number of visits in which species i are detected (yij) out of total visits (vj) for site j. Here vj needs to be larger than 1, but could vary among sites.
A key element of our model is that we link these binary detection/nondetection recordings of species to species-level abundance, following Royle & Nichols (2003). If individuals of species i in site j are detected independently of one another with probability rij, then site- and species-specific detection probability is
where pij is the ‘net’ probability of detection of species i, i.e. Pr(at least 1 individual is detected), and Zij is abundance of species i in site j that may be the object of inference either directly or indirectly. We assume that yij follows a binomial distribution in the form yij∼ Binomial(vj, pij).
Detectability could also differ among sites, depending on site-specific relevant covariates, which can also affect the abundance of each species (Bibby & Buckland 1987; Schieck 1997). In such cases, we must consider the dependency of the detection probability on the covariates (Kéry 2008):
where xj are measured covariates for site j, rij is individual-level detection probability of species i in site j, and α0i (intercept) and αi (slope) are the parameters to be estimated for species i. Because detection processes are modelled separately from ecological (i.e. abundance) processes, changes in abundance would not be confounded with changes in detectability in our model (Kéry 2008).
Ecological process model
The abundance of species i, Zij, could vary in space depending on covariates in the form Zij∼ Poisson (λij) with
where β0i and βi are the parameters to be estimated for species i. Here β0i (intercept) is a random species effect. If there are no covariates, i.e. if the right hand side of eqn 3 has only β0i, the model allows for heterogeneity only in base-line abundance among species. Deviations from such base-line abundance, which depend on covariates of each site, are modelled by xhjβhi (h = 1, 2, …, H). Note that variation in abundance might not be fully captured by measured covariates and the Poisson assumption (Royle & Dorazio 2008). To overcome this potential overdispersion, we can include (spatially structured) random site effects into the right hand side of the eqn 3 (Royle et al. 2007; Kéry et al. 2009). If this model is applied to a temporally replicated design, it can be extended to include dynamic effects, i.e. to incorporate recruitment and mortality rates, which can be approximated by linear or quadratic time trends in this equation (Kéry et al. 2009; Russell et al. 2009).
Modelling variations in parameters among species
Although parameters of well-detected species could be independently estimated, there are far too many parameters to be precisely estimated for rare species (and some species will not be detected at all). Hence, we add to the model an additional hierarchical layer and assume that parameters (e.g. αi, and βi) are independent normal random effects, each governed by community-level hyper-parameters (Kéry & Royle 2009). For example, we assume that βi∼ Normal(μβ, σβ2) where μβ is the community mean response (across species) to a covariate and σβ is the standard deviation (among species). In sum, the hyper-parameters are simply the mean and variance for each covariate as measured across species.
Using such hierarchical models we can estimate species- and community-level state variables more precisely, especially for rarely detected species (Zipkin, DeWan & Royle 2009; Zipkin et al. 2010), which is often referred to colloquially as ‘borrowing strength’, but species-level estimates (random effects) are pulled in (‘shrunk’) towards the community-level means (Sauer & Link 2002; Kéry 2010). Parameters that describe variation among species – i.e. community-level hyperparameters – are relatively well-estimated because the model effectively aggregates data from among species (Link 1999; Sauer & Link 2002). On the contrary, the precision of species-level estimates are highly variable depending on the sample sizes and are relatively more influenced by the hierarchical model structure.
Bayesian analysis by data augmentation
Let N denote the unknown number of distinct species in the sampled community and let n denote the total number of species that are detected through the sampling across sites (i.e. n ≤ N). We cannot know how many species are undetected by sampling, i.e. number of undetected species (N – n). As such, we prescribe a prior distribution for N and it is estimated along with the other model parameters by Markov chain Monte Carlo (MCMC) using a method based on data augmentation (Royle, Dorazio & Link 2007). As described above, let yi = (yi1, yi2, …, ynj) denote a vector of the j site-specific binary observations of species i (number of visits in which species i are detected in site j). We create a supercommunity of species, one that comprises the n detected species and an arbitrarily large, but known, number of undetected species (potential species) for which yi = 0 (i = n + 1, n + 2, …, N, N + 1, …, M). The supercommunity size M is fixed. Formally, data augmentation arises under a uniform prior distribution for the community size N where M is the upper bound for the uniform prior. A useful fact associated with the uniform prior is that it can be constructed ‘hierarchically’ by introducing a set of latent indicator variables, say wi, which takes the value 1 if a species in the supercommunity is a member of the community exposed to the sampling and 0 otherwise. The uniform prior for N arises by assuming that wi are independent, Bernoulli-distributed random variables indexed by parameter Ω: wi∼ Bernoulli[Ω]; Ω∼ Uniform(0,1). We can estimate N as a derived parameter, by calculating . If the assigned value of M is too low, the posterior distribution of Ω will be concentrated near the upper limit of its support, and N would be underestimated. Conversely, if M is too large, the computational burden increases (Royle & Dorazio 2008).
Under data augmentation in our multi-species abundance model, the observations for which wi = 0 are ‘structural’ or fixed 0s. This model admits that the number of visits in which species i is detected (yij) of the species exposed to the sampling (i.e. wi = 1) can be more than 0 depending on covariates, whereas those of the species unexposed to the sampling (i.e. wi = 0) is always 0, that is, Pr(yi = 0) = 1. This is a form of zero-inflation model for the augmented data set, and the model is a mixture of stochastic and structural zeros. To formulate this in the model, we modify eqn 1 so that Zijwi rather than Zij appears in the model for encounter probability. We can estimate site-specific species richness and total abundance by counting species with Zijwi > 0, and calculating , respectively. We calculated the posterior distributions of these derived parameters by MCMC.
We extended the model to include a species-level functional group attribute, as a discrete, latent variable, so that undetected species could be allocated to prescribed functional groups. To formalize this in the model, we introduce a species-level covariate, Gi, the group membership of species i, which is unobserved for the undetected species. We assume that the group membership probabilities have a conventional non-informative Dirichlet prior distribution (Spiegelhalter et al. 2003; McCarthy 2007) on functional group membership. Specifically, we assume that Gi∼ Categorical(propk) where propk is the proportion of species in group k (k = 1, 2, …, K). We used the gamma distribution to construct the Dirichlet prior (Spiegelhalter et al. 2003): gk∼ Gamma(1,1); . The parameters gk are also estimated by MCMC along with the other parameters of the model. We can estimate species richness of each functional group by calculating only for members of each group. We can also estimate site-specific species richness and abundance of each functional group by counting members with Zijwi > 0, and calculating only for the constituent species, respectively.
We applied our model to 9-years of bird monitoring data after a forest fire at a single site (N36° 35′ 32′′, E140° 37′ 20′′) by substituting time (e.g. years) for space (e.g. sites). The monitoring site was located in a montane area in Hitachi-city, Ibaraki prefecture, central Japan. The montane area dominates the western area of the city, whereas industrial and residential area dominates eastern area. The fire burnt 218 ha on 7–8 March 1991. The fire was a stand-replacing fire because many canopy trees were burned and became snags, and shrubs and forest floor vegetation was burnt out (Appendix S1, Supporting information). The dominant species before the fire were planted Japanese cedar Cryptomeria japonica and red pine Pinus densiflora, and natural broadleaved species.
A single observer (Kouji Kuboi) walked similar routes (c. 3·5 km) in the area, and recorded species detection from January 1998 to November 2006 (1176 sampling visits; 7–15 years post-fire). Routes were composed of three sections. The second section (c. 600 m) was a single segment, whereas first and third sections were composed of 2–3 segments within 500 m each other. Although the observer arbitrarily selected segments in the first and third sections (and selected routes were not recorded), the total lengths were similar (differences were <200 m). The three sections of the routes were sub-samples aggregated into single encounter histories in a single route (site) to form species-level encounter histories. That is, a species was recorded as encountered if it was observed on any section of the route. Data were pooled within breeding (May–July) and wintering (December–February) seasons separately in each year so that the data are composed of total detections out of number of visits for each species in each season (Appendix S2, Supporting information). Stand level covariates such as stand height were not recorded.
In each season, we allocated each species exclusively to one of the seven functional groups (or guilds) based on their feeding ecology and habitat associations following published literature (Amano & Yamaura 2007; Yamaura et al. 2009) and expert knowledge. For the wintering season birds were classified as bush user, canopy gleaner, edge species, floor user, open land species, seed eater, and stem prober; in the breeding season we classified birds as air searcher, bush user, canopy gleaner, edge species, flycatcher, open land species, and stem prober. We excluded water birds in both seasons, and in the breeding season we excluded species that did not breed in the study area (i.e. transients) from the analyses. The data set used for the analysis contained 47 and 34 bird species in the wintering and breeding seasons, respectively (Appendix S2).
Using the model described above, we estimated temporal dynamics of species richness and abundance within communities and functional groups, and abundance of each species allowing for undetected species. Here we assumed that our data were independent between years because our primary objective was the development and application of the simple model.
We augmented the data set with 100 potential species in both seasons. Median estimates of inclusion rate (Ω) were lower than 1 in both seasons (<0·45), indicating that the number of augmented species was sufficiently large (Royle & Dorazio 2008). Because Jacquet & Prodon (2009) showed that bird abundances could change nonlinearly during the 7–15 post-fire years, we modelled abundance response of each species to year since burning (Yearj; covariate) quadratically:
As succession progresses, the vegetation structure will become more complex and bird detectability will decrease (Bibby & Buckland 1987; Schieck 1997). Therefore, we also assumed that detectability of each species could change quadratically among years:
Year, which took values 1–9, was standardized to a mean 0 and a SD of 1·0. We allocated each of the undetected species into one of the seven functional groups using a categorical distribution with uninformative Dirichlet prior. We used customary vague priors that reflect ignorance about the parameter values: Ω∼ Uniform(0,1); ∼ Normal(0,1000); ∼ Normal(0,1000). We used uniform distribution for the standard deviations (Gelman 2006): ∼ Uniform(0,10); ∼ Uniform(0,10). We used WinBUGS Ver. 1·4·3 (Lunn et al. 2000) and R2WinBUGS R package Ver. 2·1–16 (Sturtz, Ligges & Gelman 2005) to fit the model using MCMC. We ran three chains of 88 000 iterations with different initial values, discarded the first 8000 and thinned by 20, which resulted in 12 000 iterations used for inference. Model convergence was assessed with values (the Gelman–Rubin statistic), and of all above described parameters were less than 1·12, indicating that our model convergence was good (Gelman & Hill 2007).
We recorded 47 and 34 bird species post-fire in the wintering and breeding seasons, respectively. The posterior median species richness () was 57 (95% credible interval [CI]: 48–109) and 55 (36–127) in each season over the whole nine years. This suggests that c. 10 (95% CI: 1–62) and 21 (2–93) species were not detected in each season throughout the survey. Consistent with previous studies (Haney, Apfelbaum & Burris 2009; Jacquet & Prodon 2009), there were no distinct post-fire annual changes in estimated species richness of communities or functional groups in both seasons (Fig. 1, Appendix S3, Supporting Information). The estimated species richness of communities suggests that 15–20 species were missed in each year. However, the estimated number of missed species varied among functional groups. While most species would have been detected in the bush user functional group in the breeding season, 5–15 species would have been consistently missed in canopy gleaners and edge species in both seasons (see also Appendix S3).
In the winter, the abundance of canopy gleaners showed a weak increasing trend, which was consistent with our prediction (Fig. 2, Appendix S3). The abundance of communities (all species) and many functional groups also showed increasing trends. The abundances of constituent species also showed an increasing trend in the winter (e.g. Japanese bush warbler Cettia diphone for bush user; great tit Parus major for canopy gleaner), indicating that changes in their abundance contributed to the increases in the abundance of communities and functional groups (Fig. 3, Appendix S3). In contrast, few annual changes in the abundance of communities and functional groups were observed in the breeding season, and few species showed annual changes in their abundance (Fig. 3, Appendix S3).
Annual changes in detectability varied among species. The detectabilities of many species were quite low and unchanged across years, and these species were rarely detected in the survey (Appendices S1 and S3). Brown-eared bulbul Hypsipetes amaurotis was the only species whose detectability increased with years in both seasons (Appendix S3). However, as predicted, the detectability of many well-detected species decreased with year since fire, particularly in the later years (Fig. 3, Appendix S3). For example, detection probabilities of the black-faced bunting Emberiza spodocephala, Japanese bush warbler, and the Siberian meadow bunting Emberiza cioides decreased as a function of time in the wintering, breeding, and both seasons, respectively.
It is important to combine ecological and detection processes in statistical models because ignoring imperfect detection (e.g. false absence) could lead not only to underestimation of occupancy/abundance (MacKenzie et al. 2006; McCarthy 2007; Royle & Dorazio 2008), but also to a misunderstanding of the effects of covariates (Tyre et al. 2003; Mazerolle, Desrochers & Rochefort 2005) and undesirable management outcomes (Yoccoz, Nichols & Boulinier 2001). Here we develop a method to examine the effects of covariates on population and community structure while accounting for imperfect detection of individuals. We build on earlier development of such models (e.g. Kéry & Royle 2008; Russell et al. 2009; Zipkin, DeWan & Royle 2009); specifically, our model is novel in that it is the first community-level abundance model based on species-level binary detection/nondetection data that accommodates the existence of undetected species (Appendix S4, Supporting Information). Consideration of abundance and undetected species in community models is important because abundance is a fundamental state variable in basic and applied ecology, and undetected species commonly occur in most practical community sampling scenarios. The model also accommodates functional group structure by assuming a prior distribution of functional group membership and estimating the parameters of that distribution.
We applied this model to bird monitoring data collected after a forest fire. The results suggested that 10 (95% CI: 1–62) and 21 (2–93) species remained undetected throughout the survey in the wintering and breeding seasons, respectively, and 15–20 species were also missed in each year. Estimates of the number of undetected species throughout the survey were similar to those derived from the regional species pool. Systematic survey of birds in Ibaraki prefecture suggests that 5–10 and 21–29 undetected species could inhabit the area in each season (Ibaraki Branch 2008; S. I. person. comm.). This suggests that our abundance model may yield good inferences about the sampled community. The estimated number of undetected species differed among functional groups. We found few annual changes in the estimated species richness of communities and functional groups in both seasons, which is consistent with previous studies (Haney, Apfelbaum & Burris 2009; Jacquet & Prodon 2009).
As predicted, the abundance of canopy gleaners showed a trend towards a slight increase across years. The abundance of communities, many functional groups and species also showed consistent increasing trends, but only in the wintering season. Foraging resources, including those in canopy layers, would have increased as succession progressed. In contrast, we found few annual changes in species abundances during the breeding season. Under conditions of severe weather and limited food resources, habitat and landscape structure in winter could have?large effects on bird populations and communities (e.g. Doherty & Grubb 2002; Johnson et al. 2006) with further effects in the subsequent breeding season (Greenberg & Marra 2005). Bird–habitat relationships in post-fire sites may also be important in winter.
Previous studies have shown that bird communities are relatively stable after the first 10 years post-fire in the United States and Europe (Haney, Apfelbaum & Burris 2009; Jacquet & Prodon 2009). Although we found that bird responses to the year since burning differed between seasons, our study in East Asia confirmed this by accounting for detectabilities over this period. The first 5–10 years after a forest fire are the most dynamic, during which open-land species (granivores), flycatchers, and woodpeckers colonize, and some of them desert the site (Brawn, Robinson & Thompson 2001; Jacquet & Prodon 2009). It is thought that disturbed/early successional habitats and the species inhabiting them are now declining in many countries (Askins 2001; Yamaura et al. 2009), therefore future studies should examine the responses of birds to such short-lived disturbed habitats at multiple scales, preferably using complementary chronosequence and long-term (revisiting) approaches (e.g. Donner, Ribic & Probst 2010).
In our model, we assumed the unit of detection was a single individual of a species (Zij = number of individuals). However, many bird species form flocks in winter, for which the observers detect groups of birds rather than single individuals (Zij = number of ‘functional individuals’). When estimating abundance of communities and/or comparing abundance among species, group size should be considered whenever possible. However, obtaining explicit information about group size entails additional sampling protocol modifications and also additional model assumptions. The development of methods that can accommodate group size would be worthwhile.
Rarely detected species had low detectabilities, and the credible intervals (CIs) of community-level state variables (i.e. species richness and abundance of communities and functional groups) were very wide. These results are attributable to the low densities of many species in the community, factors that cause low detectability (e.g. topographic complexity along the census route, poor census ability of the observer), short length of the census route, and the limited amount of information provided by binary detection/nondetection data. In addition, our model is highly parameterized relative to the sparse data available; however, this is partly a consequence of biological considerations. In order to accommodate temporal variability in the parameters in the model, it is necessary to consider heterogeneity in model parameters among species. In our case, we considered a quadratic trend containing species-level linear and quadratic parameters. For many species, these species-level parameters are poorly informed by the sparseness of available data. Indeed, narrower CIs could have been achieved if we assumed constant detectability across years, i.e. by using ri rather than rij (results not shown). Such a model might be reasonable in a standard design where spatial units with similar habitat structure are used as replicates, and sampled within the same year. However, in our case, such a model could not account for the decreases in detectabilities in the later years, and estimated bird abundances showed slight decreases in that period especially in the winter. If we use count data rather than binary detection/nondetection, sparse data availability would be partially resolved. For example, in each site, we may obtain count data such as counts of individuals in the series of the visits, e.g. [2 1 3 0 2] (Kéry, Royle & Schmid 2005). Let yijt (t = 1, 2, …, T) be independent counts of individuals of species i made at sites j = 1, 2, …, J so that
where Zij and rij is abundance and individual-level detectability of species i in site j, respectively. Development of multi-species models for this binomial observation model is ongoing.
Because our model estimates the abundance of each species, we can compare multiple communities by many types of abundance-based diversity and similarity measures under imperfect detection (e.g. Shannon diversity index, Euclidean distance and χ2 metric: Legendre & Legendre 1998). A further extension is the estimation of α, β, and γ diversity. Using the additive partitioning framework (Lande 1996; Veech et al. 2002), the estimated species richness of the sampled community (N) could be defined as γ diversity (regional diversity), while average site-specific species richness could be defined as α diversity (local diversity). Differences between these two diversity measures could be an estimate of β diversity (among sites diversity).
Collection of detection/nondetection data for species is increasingly adopted in large-scale field surveys. Development, use, and improvement of the statistical models for such simple data should be encouraged. Our hierarchical multi-species model allows explicit modelling and estimation of abundance in space/time at species-, functional group- and community-levels accounting for undetected individuals and species.
Suggestions from two anonymous reviewers and the editor greatly improved our manuscript. We are grateful to M. Kéry, R. Russell, and E. F. Zipkin for their helpful reviews of a draft of this manuscript. We also thanks for T. Amano, K. Matsumoto, Y. Mitsuda, H. Taki, K. Okabe, and S. Sugiura for useful suggestions for this study. Y. Yamaura was supported by Research grant No. 200802 of the Forestry and Forest Products Research Institute, and JSPS KAKENHI (Grand-in-Aid for JSPS Fellows No. 21-7033).