reliability of existing reserve species records
Our best estimate of the species richness of these study areas is derived from existing reserve records that represent the efforts of highly experienced ornithologists, most resident in Ecuador year-round and working either as research scientists or professional birding guides. They combine birding records over an approximate 20-year period and records from intensive survey work in each area. As such, it is highly unlikely that more than one or two species has been missed. While species lists for temperate regions, such as the British Isles, typically include many migratory and vagrant species, a high proportion of the birds listed for the areas considered in this study are resident and can be encountered year round. The records for these reserve areas are, hence, a more accurate reflection of the species richness of the areas surveyed at any given point in time than they would be for a comparable area in temperate latitudes. Additionally, both nocturnal species, systematically missed by daytime surveys, and Nearctic migratory species, not expected to be present during the survey period, were excluded, removing that fraction of species that we could not expect our survey to capture.
The species records for the Maquipucuna–Santa Lucia reserve area represent surveying effort carried out over an altitudinal range from 1000 to 2900 m a.s.l. (Sarmiento 1993; Molina et al. 2003; Prieto 2003). The Mindo Valley species records represent birding surveys in the 1200–1600 m a.s.l. altitudinal range (Perez, Lyons & Allen 2000). Our survey covered a range in altitude from 1191 to 2017 m a.s.l., and, as such, did not reach the lower or upper bound of the altitude range potentially represented by the combined reserve records. Should the expected richness value be reduced to reflect this altitudinal limitation? Thirty-five of the 440 species in the species lists have 2100 m as the lower limit of their altitudinal range according to The Birds of Ecuador (Ridgely & Greenfield 2001), and as such we might not expect to encounter them in our survey. However, on the same basis, 54 of the 440 species in the reserve records, 18 of which were encountered in the survey, should not occur in the reserves at all because their recorded range is given as below 1000 m a.s.l. These discrepancies reflect acknowledged uncertainties concerning the altitudinal range limits of species in the bird guides (Stattersfield et al. 1998; Ridgely & Greenfield 2001) and may also reflect distributional anomalies related to mesoclimatic conditions in the areas surveyed. Hence, we have retained the figure of 440 species as the observed ‘true’ richness of the system unadjusted for the slight discrepancy between the altitudinal limits of the reserve records and the point count data, whilst acknowledging this as a small potential source of error.
non-parametric species richness estimators
The non-parametric species richness estimators applied consistently underestimated the total species richness of the reserve areas by more than 50%. As such, they appear inappropriate for estimating total species richness in a given area from a modest sample, although often credited with the capacity do so (cf. Bhatta 1997; Toti, Coyle & Miller 2000; Hofer & Bersier 2001; Smith 2001; Johnson & Ward 2002). The intended purpose of these estimators is to predict the true number of species in a statistical population from a random sample of individuals (Colwell & Coddington 1994). In practice, however, the spatial boundaries of the sampled population are often impossible to determine. Failure to meet this assumption of a closed population is rarely cited in explaining why non-parametric estimators give biased results (Walther & Martin 2001; Brose, Martinez & Williams 2003; Chiarucci et al. 2003), but is, we argue, a key factor in determining their validity. Consequently, where sampling effort is the same or comparable across sites, the most valuable thing these estimators provide is a legitimate means of comparing richness per unit effort. Authors have used these measures to compare diversity among sites for the purpose of either site prioritization exercises or for answering more fundamental scientific questions about patterns of diversity (Coddington, Young & Coyle 1996; Poulsen & Krabbe 1997; Arnott, Magnuson & Yan 1998; Herzog, Kessler & Cahill 2002; Brehm, Sussenbach & Fiedler 2003). Used in this context, they are appropriate and useful.
extrapolation from species-accumulation and t-s curves
Unlike non-parametric estimators, the extrapolation procedures used herein reflect patterns in the entire data set. Extrapolations of species richness are based mostly on two models: the semi-log model (Gleason 1922), in which species richness is treated as a linear function of the logarithm of area, and the log-log model (Arrhenius 1921; but see Tjørve 2003 for other potentially useful models). Palmer (1990, 1991) found, for temperate hardwood forest plants. that the log-log model produced massive overestimates of species richness, while the semi-log estimate was much less biased and more precise, although also an overestimate. The debate between proponents of these models is ongoing (Hubbell 2001) but it has been argued that the choice is really a practical one based on the goodness-of-fit of the model to the data (Connor & McCoy 1979; Colwell & Coddington 1994; He & Legendre 1996). It may also be related to the sampling design (Scheiner 2003; Gray, Ugland & Lambshead 2004) or scale range of the study (Lomolino 2000).
For our data, log-log approximations of species accumulation and models produced from T-S curves explained between 93% and 98% of the variance, but consistently had a poorer fit than corresponding semi-log models. Based on goodness-of-fit, extrapolation of species richness from the semi-log models seemed most appropriate, if we, like Ugland, Gray & Ellingsen (2003), assume that the same relationship of area sampled and species richness will hold when extrapolated to a larger area. However, among semi-log models, the magnitude of the R2 value had no relationship with the accuracy of the estimate produced relative to the recorded richness of 440 species. As such, curve-fitting alone cannot guide us in the selection of appropriate models of species richness extrapolation.
Establishing appropriate bounds of extrapolation is a further challenge to the application of these techniques. Ugland, Gray & Ellingsen (2003) set out to estimate invertebrate species richness for the entire Norwegian shelf, extrapolating from their available sample by a factor of more than 2000 million. This degree of extrapolation applied to our data would be equivalent to extrapolating to the avian diversity of an area four times the total land area of earth; clearly beyond the limits Ugland, Gray & Ellingsen (2003) may have envisaged. Gray (2000) argues that in order to achieve accurate estimates of species richness for large areas and biogeographical provinces ‘the area covered or province boundaries have to be clearly defined and sampling design must be appropriate to the scale of the features sampled’. In our area, it would appear that the spatial scope and extent of sampling employed was sufficient to provide a reasonable extrapolation model. However, it should be acknowledged that the spatial boundaries set for our study system correspond to spatial planning units rather than a biologically defined entity.
incorporating spatial heterogeneity
Stratifying sites into habitat and altitude subsets resulted in T-S curves with significantly higher slopes than the standard species accumulation curve, indicating that spatial heterogeneity in species composition was associated with spatial heterogeneity in environmental factors. Further, random subdivision of sites for null T-S curves produced curves with slopes that did not differ significantly from the standard species accumulation curve, demonstrating that the subdivision itself did not impose an artificially higher heterogeneity on the data. Indeed, species richness extrapolated from null models varied less than 3% from that of the standard species accumulation curve.
Among stratified T-S curves, those generated from uneven-sized subsets gave more accurate richness estimates than those for even subsets. While we might infer that this increased accuracy reflected a more correct subdivision of sites, it is difficult to say, for instance, why dividing sites into subsets based on 200-m altitudinal intervals is any more legitimate than dividing them into equal-sized subsets along the altitudinal gradient. We argue that it is actually the rarefaction approach applied in generating the T-S curves that produces these lowered estimates. Rarefaction results in data loss and cuts the subset accumulation curve at a smaller sample size, where it is likely to be steeper. As such, it reduces the slope of the T-S curve relative to the fixed total observed species value (189 species) and, thereby, gives a lower estimate of species richness relative to evenly divided subsets where all the existing heterogeneity is expressed.
For our survey area, incorporating spatial heterogeneity through the T-S method overestimated species richness, in extreme cases by almost 80 species. In contrast, the estimate produced by extrapolation of the standard species accumulation curve was among the most accurate and required no assumptions about what might structure the heterogeneity of the system. Spatial heterogeneity in environmental factors exists and has a significant effect on species richness and patterns of species accumulation. However, the species–area relationship for large areas already takes account of this; indeed, increased spatial heterogeneity with increased area is a key underlying mechanism of increased diversity (Colwell & Coddington 1994; Rosenzweig 1995). As such, we argue that the standard species accumulation model implicitly takes account of beta-diversity in its formulation, provided that the initial deployment of sample sites is appropriately designed. The work of Brose, Martinez & Williams (2003) points to a similar conclusion; testing both simulated and empirical data sets, they found that neither the strength of species compositional gradients (similar to our first axis DCA scores) nor spatial autocorrelation (similar to our habitat and altitude subsets) were correlated with unexplained variance between known and estimator-predicted species richness.
In this context, results from our single study indicate that stratification of sites within the T-S accumulation method may be unnecessary, and even counter-productive, to refining estimates of richness, at least for study systems like this. There are many possible ways of subdividing sites within a landscape that will reflect significant differences in bird species composition. Take the extreme example of dividing sites along the axis of maximum variation in species composition. Stratifying by first-axis DCA scores produced a maximum estimate of 518 species, almost 20% greater than the recorded species richness. In this case, within-subset beta-diversity is minimized because each subset's species composition is relatively homogeneous, while between-subset beta-diversity is maximized. Consequently, the slope of accumulation curves for any one subset will be quite gentle but will become increasingly steep as more subsets are combined because of the high beta-diversity between subsets. The T-S curve generated by interpolating among the endpoints of these curves will then inevitably have a much higher slope than the standard species accumulation curve. Amplifying beta-diversity in this way is what leads to the apparent overestimate of species richness for our study system.
Even if we are wrong in the above arguments and in trusting the reserve records as the independent measure of actual richness, there exists no objective means of deciding an appropriate stratification of sites. Habitat type and altitude are both known to exert strong influences on patterns of species composition within the landscape (Terborgh 1977; Canaday 1996; Sekercioglu 2002; Watson, Whittaker & Dawson 2004). While a stratification that captures either type of environmental heterogeneity might improve estimates of landscape species richness, we have no means of determining a priori which is best. Without this knowledge we could have no confidence in the estimates of species richness produced.
In effect, the difference in slope between the randomized species accumulation curve (or null T-S models) and the T-S models employing environmental or compositional site stratification served as a measure of the beta-diversity produced by these gradients. This measure, however, did not improve the accuracy or precision of extrapolated species richness estimates for the overall reserve area.
While non-parametric species richness estimators give little basis on which to assess the total species richness of large areas, they do give a basis on which to compare the diversity of sites for a given level of sampling. As such, they are particularly useful in rapid site assessments (Poulsen et al. 1997a,b; Poulsen & Krabbe 1998; Herzog, Kessler & Cahill 2002). However, the numbers they generate have a purely comparative value; it is not possible to determine the geographical bounds of the system for which they are estimating richness. Consequently, non-parametric estimators cannot legitimately be used to derive estimates of inventory richness of an entire landscape.
Extrapolation methods considered herein have the advantage of explicitly incorporating area in the calculation of total species richness, thereby allowing inferences to be drawn about the total number of species residing within, for instance, a protected area, based on a limited set of standardized samples. This facilitates the comparison of real geopolitical entities and has the virtue of providing an immediately meaningful figure (e.g. ‘This reserve contains 440 species of birds’), although it is important to note that there is an unknown error margin in estimates of this sort. Where exhaustive inventories of species are simply not possible, because of constraints of time, money and other resources, these methods offer a means of projecting a realistic quantitative estimate of the diversity of geographical areas substantially greater than covered in actual surveys.
Estimating species richness for high-diversity ecological assemblages is important both in the context of conservation (Whittaker et al. 2005) and for basic ecological research purposes, and great latitude remains in determining the best means to achieve this end. The T-S method, although it does not appear from our analysis of Ecuadorian birds to improve significantly estimates of total species richness for large areas over standard species accumulation methods, nevertheless represents a valuable contribution to the development of such techniques. In the context of both conservation and ecological research, what is most important is that we know what each estimator is estimating so that when we characterize or compare sites based on these figures, we know what we are talking about. Our examination of the T-S method indicates, contrary to Ugland, Gray & Ellingsen's (2003) expectation, that, when analysing survey data designed to capture the major gradients in assemblage composition, homogenizing beta-diversity among samples, rather than explicitly incorporating it as a separate adjustment term, is necessary to estimating species richness accurately. However, where the study system is less well prescribed, and the factors structuring beta-diversity less well understood, the stratified forms of the T-S method provide means of estimating the potential range of values according to different assumptions about the pattern of beta-diversity across a region, and thus generating a family of richness estimates rather than a single projection. Further empirical tests are required to judge whether extrapolations based on standard species accumulation curves are more generally valid across scales and at different levels of compositional heterogeneity, as well as within different high-diversity assemblages.