Using spatial heterogeneity to extrapolate species richness: a new method tested on Ecuadorian cloud forest birds


Niall O'Dea, Biodiversity Research Group, Oxford University Centre for the Environment, South Parks Road, Oxford OX1 3QY, UK (fax + 44 1865 275885; e-mail


  • 1For most ecological assemblages, compiling complete inventories of species is difficult, if not impossible. Various methods have been developed to estimate total species richness based on the pattern of richness and relative abundance reflected in a limited sample.
  • 2We assessed the performance of a recently developed technique, the total-species (T-S) accumulation method, in estimating bird species richness for cloud forest reserves in north-west Ecuador. This technique explicitly integrates the spatial heterogeneity of samples into the estimate of species richness for large areas by grouping samples into subsets based on shared environmental characteristics.
  • 3We compared the technique's performance with that of more traditional methods of species richness estimation: non-parametric estimators and extrapolations from species-accumulation curves. Existing bird species records for the Ecuadorian cloud forest reserves served as the independent measure of total species richness.
  • 4Non-parametric estimators of species richness significantly underestimated total species richness. In contrast, extrapolation from the semi-log approximation of T-S curves, using subdivision by habitat type, altitude and first axis detrended correspondence analysis scores, overestimated total species richness, while extrapolation from null T-S models and the standard species-accumulation curve produced the most accurate results.
  • 5The T-S method overestimated species richness for our ‘hyper-diverse’ assemblage. This was probably because it adjusted the estimates upwards to account for beta-diversity, when this diversity was already captured in the design of the site selection scheme. Nevertheless, it provided a quantitative measure of the beta-diversity produced by environmental and compositional gradients. Moreover, our test indicated that factors such as sampling effort and species abundance distributions may be more important for accurate species richness estimation than heterogeneity in the spatial distribution of species.
  • 6Synthesis and applications. Our analysis demonstrates significant differences in the accuracy of different methods for estimating total species richness from a limited sample. Our work highlights the importance of knowing what an estimator is estimating so that when we characterize or compare sites, whether in ecological or conservation research, we do so with explicit knowledge of the potential biases in our chosen methodology.


Exhaustive inventories of ecological assemblages will often be unobtainable, but generating comparable indices of species diversity for different areas is important for conservation planning. To this end, various means of estimating total species richness of an area, assemblage or system from a limited sample have been derived but no one estimator has been found consistently to provide precise and unbiased estimates (Walther & Martin 2001; Brose, Martinez & Williams 2003; Chiarucci et al. 2003). In this paper, we offer an empirical test of the recently proposed total-species (T-S) accumulation method (Ugland, Gray & Ellingsen 2003) and compare it with a number of other available estimation techniques, using data collected on bird assemblages in Ecuadorian cloud forest.

Ugland, Gray & Ellingsen (2003) argue that the traditional species accumulation curve, developed to measure species richness for relatively homogeneous areas at local scales (Colwell & Coddington 1994), underestimates species richness for a large area by ignoring heterogeneity in the spatial distribution of species within that area. In practice, a species accumulation curve combining samples from spatially heterogeneous subsets of samples will lie above that for an equal number of samples taken from one subset alone. This reflects not just a higher total number of species for a given sampling effort, but a higher rate of species accumulation because of differences in species identities across the sampled area. Ugland, Gray & Ellingsen (2003) argue that this beta-diversity must be captured in order to estimate accurately richness for the large area. This is in line with other recently proposed models that aim to incorporate the beta-diversity element (Lande 1996; Loreau 2000; Hubbell 2001; Condit et al. 2002). The T-S method is unique, however, in attempting to model directly the influence of spatial heterogeneity in environmental factors (as expressed by the subdivision of sites into subsets) on spatial heterogeneity in species composition (beta-diversity) and the impact of this heterogeneity on the rate of species accumulation.

The Ugland, Gray & Ellingsen (2003) T-S accumulation method extrapolates the total species richness of a large area using a modified form of the species-accumulation curve based on local inventory sampling. Local species richness and beta-diversity across the sample region are captured simultaneously to produce an estimate for large-area species richness. The area for which species richness is estimated may range widely, from a forest landscape or coral reef to a continent or ocean shelf, covering Whittaker's (1977) γ and ɛ scales of diversity or Cody's (1975) γ-diversity.

The data we used came from bird communities in the Andean subtropics, a region harbouring some of the richest bird assemblages in the world (Fjeldsa 1994; Stattersfield et al. 1998). Spatial heterogeneity at the landscape level is thought to be among the chief drivers of this high species richness (Rahbek & Graves 2001). This study assessed whether incorporating beta-diversity, via the T-S method, improves extrapolated estimates of species richness.

Our study had three aims. First, we wanted to determine whether the T-S method of Ugland, Gray & Ellingsen (2003) provides robust estimates of total species richness for our study area. Secondly, we tested whether the estimates were significantly more accurate than those provided by traditional species richness estimation methods. Finally, our overarching aim was to assess whether explicitly incorporating spatial heterogeneity, through the beta-diversity it generates, is necessary for accurately estimating species richness in heterogeneous landscapes.

Materials and methods

study area

Surveys were conducted in two areas on the western slope of the Andes in northern Ecuador. The first was located in the contiguous Maquipucuna and Santa Lucia Reserves and adjacent lands (0°7′N, 78°36′W), covering approximately 6736 ha between 1000 and 2900 m a.s.l. in altitude. The second was located approximately 25 km away in the Mindo Valley (0°4′S, 78°46′W). This valley ranges between 1200 and 2100 m a.s.l., but the 4058 ha area used for extrapolation lies between 1200 and 1600 m a.s.l., in which the bird species records for the Mindo area have been compiled. The actual area was calculated using a digital altitudinal model in ArcGIS 9·0 (ESRI, Redlands, California, USA) with a 40-m contour resolution based on a 1 : 50 000 scale map data provided by the Instituto Geográfico Militar del Ecuador (Quito, Ecuador). To calculate species richness for the two areas together, we used the combined reserve area of 10 794 ha, permitting direct comparison with the existing species records. Although the Mindo Valley is not a reserve in the strict sense, we refer to the two areas together as the ‘reserve area’ and to their associated bird species records as ‘reserve records’ throughout.

bird species data

Bird species abundance data were collected in a point count survey. Three-hundred point counts were performed at 75 sites in each study area, covering an altitude range from 1100 to 2000 m a.s.l., in May–July 2003. Point count survey sites were selected without prior knowledge of bird distributions. All point counts were conducted by one observer between 06:15 and 10:00, the peak period of bird activity, and, for the second set of counts, the order in which sites were visited was reversed to control for any remaining time-of-day bias in detectability. Each count was 10 min in duration, balancing maximization of the probability of detecting all species present with minimizing the probability of multiple detection (van Rensburg et al. 2000). During this period, all bird species seen and heard within a 50-m radius were registered, and their abundance and estimated distance from the observer recorded. Fifty metres is considered an appropriate radius for the detection of vocalizations (Schieck 1997) but for the present analysis we considered only those detected within 25 m for consistency with other fixed-radius point count studies (Greenberg, Bichier & Angon 2000; Reynaud & Thioulouse 2000; Gillespie & Walter 2001). Sites were located at least 200 m apart to minimize the risk of counting the same individual twice.

Considerable effort was made to examine the properties and basic reliability of the survey protocol. O'Dea, Watson & Whittaker (2004) showed that while point count surveys systematically fail to capture certain bird species of this region, they more accurately reflect the relative abundance distribution of the bird assemblage than other available techniques. Because the relative abundance distribution greatly influences estimates produced by species richness estimators it was a priority in the choice of survey protocol.


The benchmark figure against which the performance of species richness estimators was assessed was derived from existing reserve records. These records, accumulated mostly since the mid-1980s, report 457 species of bird to occur within the combined areas of the Maquipucuna and Santa Lucia reserves and the Mindo Valley (Sarmiento 1993; Perez, Lyons & Allen 2000; Molina et al. 2003; Prieto 2003). Nocturnal species, systematically missed by daytime surveying, and Neartic migrant species, not expected to be present in the survey period, were excluded from the total, giving a benchmark figure of 440 species.

All analyses were conducted on untransformed bird species abundance data collected during the point count survey. Flying birds were excluded from the analysis. Following Ugland, Gray & Ellingsen (2003), two non-parametric species richness estimators are used for comparison with the T-S method: the Chao 2 estimator (Chao 1984, 1987; Colwell & Coddington 1994) and the incidence-based coverage estimator (ICE; Chao & Lee 1992; Chazdon et al. 1998). Chao 2 estimates total species richness based on the ratio of species encountered exactly once to those encountered exactly twice. It is intended as a lower bound estimator for assemblages in which rare species predominate (Chao 1984; Colwell & Coddington 1994). ICE bases estimates on species found in 10 or fewer sampling units (Chazdon et al. 1998). Various other non-parametric species richness estimators are also available and we report the range of values generated by those estimators available in the EstimateS software package (Colwell 2004): abundance-based coverage estimator (ACE), Chao 1, first- and second-order jack-knife and Michaelis–Menten means and runs. These techniques are intended to provide accurate estimates of true richness based on small sample sizes (Colwell & Coddington 1994).

The standard species accumulation curve was generated using the analytic method of Ugland, Gray & Ellingsen (2003). This is equivalent to the method developed by Colwell, Mao & Chang (2004) and available in EstimateS version 7 (Colwell 2004). Extrapolation of total species richness from the species accumulation curve was based on the semi-log approximation of the curve: we first regressed the number of species against the log of the number of sites sampled. Then, the logarithm of the number of sites (54 987) required to cover the entire 10 794-ha reserve area was substituted into the regression equation to produce the total richness estimate (Gleason 1922; Palmer 1990, 1991; Ugland, Gray & Ellingsen 2003).

In order to produce T-S curves, sites and their associated bird species data must first be divided into subsets. An underlying assumption of the T-S method is that we know the correct subdivision of sites, but, in practice, a single ‘correct’ subdivision will rarely exist. Consequently, we applied different subdivisions of sites along environmental and species composition gradients (hereafter stratified T-S curves) to test the stability of estimates produced in response to the different subdivisions imposed. For clarity, different subdivisions are labelled as they occur in Table 1.

Table 1.  Total species richness of a 10 794-ha cloud forest reserve area in north-west Ecuador as reported in reserve records, as observed in a 2003 point count survey, and as estimated by species richness estimators. For each extrapolation estimator, the semi-log model is reported, where the number of point count survey plots required to sample the total area exhaustively is substituted in place of ‘a’ to extrapolate species richness. R2 values, measuring the degree of fit of each model to its associated data, are also reported
  Species richnessModelR2
Reserve records 440  
Species observed in point count survey  189 
Non-parametric estimators:
Chao 2 203  
Incidence-based coverage estimator 202  
Extrapolation estimators:
Species accumulation curve 43541·2 ln(a) – 14·70·9915
Null T-S curvesThree subsets41437·9 ln(a) – 0·10·9960
Four subsets42539·8 ln(a) – 8·80·9942
Five subsets43441·1 ln(a) – 14·40·9938
10 subsets44642·9 ln(a) – 22·30·9941
T-S curve with stratification by1) Habitat type   
a) Three subsets52256·2 ln(a) – 91·60·9982
b) Four subsets44141·9 ln(a) – 16·30·9639
2) Altitude   
a) Four subsets43440·6 ln(a) – 9·50·9708
b) Five subsets51654·5 ln(a) – 79·30·9970
c) 10 subsets48549·5 ln(a) – 55·50·9968
3) DCA scores   
a) Three subsets45144·3 ln(a) – 32·20·9995
b) Five subsets51855·4 ln(a) – 86·90·9979
c) 10 subsets49250·6 ln(a) – 60·90·9961

We first divided the sites into subsets based on their habitat type. The landscape comprised a mosaic of primary forest (undisturbed by human activities for at least 50 years), secondary forest (regenerating following agricultural abandonment 15–20 years previous) and agricultural land (still in use for crops or livestock). The survey had been designed to sample these habitats equally, giving 50 sites per subset (Table 1, model 1a). In half the agricultural sites continuous forest occurred within 50 m of the site centre. For additional analysis, splitting agricultural sites into these edge sites and remaining open-land sites produced a total of four subsets (Table 1, model 1b). We also ordered and divided sites in three ways based on their altitude: four altitudinal bands of 200 m (Table 1, model 2a) and each of five (Table 1, model 2b) and 10 (Table 1, 2c) equal-sized subsets. Sites were similarly divided along a gradient of species composition derived from detrended correspondence analysis (DCA; Hill 1979) of the species abundance data (using canoco 4·5; ter Braak & Smilauer 2002). Using standard deviation scores from the first axis of the DCA, sites were ordered along the maximum gradient of species turnover. Sites were subdivided in three ways: into three subsets representing increments of two standard deviation units (Table 1, model 3a), and into each of five (Table 1, model 3b) and 10 (Table 1, model 3c) equal-sized subsets.

To produce the stratified T-S curves we used a version of the Ugland, Gray & Ellingsen (2003) program, modified to allow division of sites into any number of subsets. T-S curves are constructed in two stages, best explained by example. Take a set of 150 sites divided into four subsets, containing 25, 30, 45 and 50 sites, respectively. First, subset species accumulation curves are constructed (Fig. 1a). The shortest curve represents the species accumulation curve for all combinations of one subset of sites, rarefied to the smallest site number; as such, it will be the mean species accumulation curve of each of the four subsets, rarefied to 25 sites each. The second shortest curve represents all combinations of two subsets of sites, similarly rarefied to the number of sites in the smallest such combination; in our example, 25 plus 30 sites giving 55. Similar curves are constructed for each successively larger combination of subsets. The longest curve is generated from the combination of all subsets, and therefore all sites. As such, it is the standard species accumulation curve for the 150 sites. The T-S curve itself is a line interpolated between the endpoints of the subset species accumulation curves, fitted by linear regression of species number on log site number (Fig. 1b). Estimates of total species richness for the entire reserve area were derived from T-S curves as from the standard species accumulation curve, by substituting the log total site number into the regression equation.

Figure 1.

Illustration of the T-S curve method for species richness estimation, using a four-way subdivision of sites. (a) Species accumulation curves for all combinations of one, two, three and four subsets of sites (denoted by successively lighter shaded lines). (b) The T-S is a straight line regressed through the endpoints of the subset species accumulation curves by semi-log regression. The equation of this line is used to estimate total species richness.

To confirm that differences between estimates from stratified T-S and the standard species accumulation curve were not a matter of chance or a consequence of subdivision alone, we produced T-S curves that were null with respect to environmental and species compositional gradients by randomly allocating sites among each of three, four, five and 10 even-sized subsets. Each randomization was repeated 1000 times to generate mean null T-S curve values for each number of subdivisions, as well as associated standard deviations. Analysis of covariance (ancova; Dytham 1999) was used to test the significance of differences in slope between the standard species accumulation curve and each of the null and stratified T-S curves in SPSS version 11·5·1. A linear model was fitted using estimated species richness as the dependent variable, subdivision type as the categorical variable and log site number as the covariable.


In total, 189 bird species in 3830 individual records were encountered within a 25-m radius of point count sites during the survey (Table 1). When sites were subdivided at random to produce null T-S curves, mean accumulated species richness values for a given number of sites were very similar, irrespective of how the sites were subdivided. Moreover, they deviated little, if at all, from values for that number of sites from the randomized species accumulation curves (Fig. 2a). No null model had a significantly different slope from the standard species accumulation curve (P > 0·05).

Figure 2.

Variability of endpoint values for null and stratified T-S curves relative to the standard species accumulation curve (grey circles). Values for null T-S curves, derived by random site subdivision (a), deviate little from the standard species accumulation curve, while values for stratified T-S curves, derived by stratifying sites on habitat (b), altitude (c) and species composition gradients (d), deviate substantially from it.

Stratification with respect to environmental and compositional gradients produced greater heterogeneity in species accumulation than would be expected by chance. Mean accumulated species richness values for a given number of sites for T-S curves with sites stratified by habitat type, altitudinal band and first axis DCA score, deviated substantially from the standard species accumulation curve (Fig. 2b–d). Their slopes were significantly higher (P < 0·001) than those of the null models and the standard species accumulation curve, except where the subsets contained unequal numbers of samples: the four-way habitat stratification, four-way altitude stratification and three-way DCA stratification.

The regression of species number against the log of the corresponding number of sites produced a line explaining more than 99% of the variability among data points for the standard species accumulation curve and all T-S curves, with the exception of the uneven habitat and altitude stratifications, with R2 values of 0·96 and 0·97, respectively. All regressions were highly significant (P < 0·001).

Relative to the existing reserve species records, the non-parametric estimators, Chao 2 and ICE, gave considerable underestimates of the recorded species richness, at 203 and 202 species, respectively (Table 1). Other non-parametric estimators gave values between 202 and 216: in all cases less than half the 440 species reported in the reserve records. In contrast, species richness values extrapolated from species accumulation and T-S curves provided estimates ranging between 414 and 522 species, within 20% either side of the known species richness. Notably, estimates of richness derived from the standard species accumulation curve and the null T-S curves ranged just 6% either side of the known richness. These were considerably more accurate than most of the estimates from stratified T-S curves, although estimates generated from uneven site stratification also produced estimates very close to the recorded richness of the area.


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.


We thank Kate Ballem, Charles Marsh, William Perez, Andy Taylor and Anna Whitfield for assistance in the field, and Parris Lyew-Ayee for GIS expertise. For hospitality and access to land, we thank Fundación Maquipucuna, Cooperativa Santa Lucia and the Mindo Biological Station. Mike W. Palmer and James E. M. Watson provided insightful criticisms of earlier drafts of the manuscript. This research was funded in part by Fundación Maquipucuna, the Rhodes Trust, the Natural Science and Engineering Research Council of Canada, the Vaughan Cornish Bequest, and Exeter College, Oxford.