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Biodivers Conserv (2010) 19:1417–1436 DOI 10.1007/s10531-009-9770-8 ORIGINAL PAPER

Assessing the performance of nonparametric estimators of species richness in meadows Jose´ Antonio Gonza´lez-Oreja • Carlos Garbisu • Sorkunde Mendarte Ainhoa Ibarra • Isabel Albizu

•

Received: 30 June 2009 / Accepted: 5 December 2009 / Published online: 19 December 2009 Springer Science+Business Media B.V. 2009

Abstract To accurately measure the number of species in a biological community, a complete inventory should be performed, which is generally unfeasible; hopefully, estimators of species richness can help. Our main objectives were (i) to assess the performance of nonparametric estimators of plant species richness with real data from a small set of meadows located in the Basque campinã (northern Spain), and (ii) to apply the best estimator to a larger dataset to test the effects on plant species richness caused by environmental conditions and human practices. Two non-asymptotic and seven asymptotic accumulation functions were fitted to a randomized sample-based rarefaction curve computed with data from three well sampled meadows, and information theoretic methods were used to select the best fitting model; this was the Morgan-Mercer-Flodin, and its asymptote was taken as our best guess of true richness. Then, five nonparametric estimators were computed: ICE, Chao 2, Jackknife 1 and 2, and Bootstrap; MMRuns and MMMeans were also assessed. According to the criteria set for our performance assessment (i.e., bias, precision, and accuracy), the best estimator was Jackknife 1. Finally, Jackknife 1 was applied to assess the effects of terrain slope and soil parent material, and also fertilization, grazing, and mowing, on plant species richness from a larger dataset (20 meadows). Results suggested that grass cutting was causing a loss of richness close to 30%, as compared to unmowed meadows. It is concluded that the use of nonparametric estimators of species richness can improve the evaluation of biodiversity responses to human management practices. Keywords Precision

Accuracy Bias Grass mowing Managed meadows Plant diversity

J. A. Gonza´lez-Oreja (&) C. Garbisu S. Mendarte A. Ibarra I. Albizu Department of Ecosystems, NEIKER – Tecnalia, Basque Institute of Agricultural Research and Development, C/Berreaga 1, 48160 Derio, Spain e-mail: [email protected]; [email protected]

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Biodivers Conserv (2010) 19:1417–1436

Introduction Biodiversity measures have been widely used as indicators of ecosystem status, and play a critical role in studies dealing with the assessment of human impacts on ecological systems (Leitner and Turner 2001). However, since the biodiversity of any ecosystem is far too complex to be comprehensively quantified, suitable indicators (Duelli and Obrist 2003) or surrogates (Sarkar 2002) of biodiversity are needed. Conceptually, species richness (i.e., the number of species present in a spatially and temporally homogeneous community) appears as the most intuitive and straightforward parameter to measure biodiversity (Gotelli and Colwell 2001). Nonetheless, for several reasons, to determine the true richness of a community is not an easy task (Magurran 2004). For example, it is known that the number of observed species increases with sampling effort; as a result, to get an accurate measurement of the true richness in a biological community, one should perform an exhaustive, complete inventory. This objective is generally not feasible, and estimation by sampling is frequently the best available option, even when we are dealing with the species richness of well-known groups of organisms, such as vascular plants (Colwell and Coddington 1994; Leitner and Turner 2001; Chiarucci and Palmer 2006). Estimators of species richness attempt to estimate the number of species of a certain biological community from an incomplete survey (Colwell and Coddington 1994; Gotelli and Colwell 2001; Leitner and Turner 2001; O’Hara 2005). A staggering number of methods have been proposed for estimating richness in a local community, but approaches generally used in ecological contexts can be classified as follows: (i) extrapolation of species accumulation curves as a function of sampling effort, where total richness is considered as the number of species that would be found with a hypothetical infinite sampling effort; (ii) estimation of the number of still unreported species after computing species-abundance distributions, and (iii) use of nonparametric estimators that, based on the prevalence of rare species, allow the estimation of the number of unreported species that could be added to the list of those already discovered (Colwell and Coddington 1994; Chazdon et al. 1998; Leitner and Turner 2001; Chao 2005). Nonparametric estimators have been considered by some authors the most significant advance in biodiversity measurement in more than a decade (Magurran 2004), and result suitable for the estimation of plant species richness (Chiarucci and Palmer 2006). Plant species richness and structure are known to change as a consequence of many factors, including human management and perturbation regimes (Canals and Sebastia` 2001); however, the links between plant richness and agricultural practices in managed ecosystems are highly complex and still largely unknown. Estimators of species richness can be used to monitor the effects of human impacts on biodiversity (Hellmann and Fowler 1999; Chiarucci and Palmer 2006), and some authors have argued that their use improves the assessment of plant responses to human practices (Loya and Jules 2008). Although several assessments of the performance of nonparametric estimators have been carried out (see Walther and Moore (2005) for a review), there is still much need for additional comparative studies regarding their performance (Colwell and Coddington 1994; Gotelli and Colwell 2001; Leitner and Turner 2001; Walther and Martin 2001; Longino et al. 2002; Magurran 2004). Our objectives in this work are the following two: (i) to assess the performance (in terms of bias, precision, and accuracy) of several incidence-based, nonparametric estimators of species richness, by using empirical data on plant species richness from a small set of well sampled meadows located in the Basque Country (northern Spain); and (ii) to compare the patterns obtained after applying observed richness versus the best estimator to study the

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effects on the number of plant species caused by changes in natural environmental conditions and human management regimes, by using empirical data on plant species richness from a larger set of meadows in the same study area.

Materials and methods Study area and sampling The whole dataset here analyzed consisted of a 65 species 9 200 quadrats matrix of plant species found in a survey of 20 managed meadows, considered as a representative sample of this habitat within the Urdaibai Biosphere Reserve (Atlantic Basque Country, northern Spain). Meadows are an integral part of the Atlantic ‘‘campinã’’, a traditional agroecosystem composed of a patchy landscape formed by forest fragments of native species, exotic tree plantations and enriched, pastured and/or mowed meadows (Rodrı´guez-Loinaz et al. 2007; Gonza´lez-Oreja et al. in press). The 20 meadows here studied differ in both natural environmental conditions (terrain slope and soil parent material) and human management regimes (type of fertilization, main type of grazing animal, and absence or presence of mowing; Table 1). To minimize the possible effects of temporal heterogeneity on plant species richness, our plant survey was performed in an intensive fashion between May and June 2008. Ten randomly placed quadrats (50 9 50 cm) were sampled at each of the 20 sites, where all plant species were identified according to Aizpuru et al. (2000) and their percent cover was visually estimated. Following Brower et al. (1997), an importance value (IV) was obtained for each plant species: IV = relative frequency of the meadows where a species was present 9 relative frequency of the quadrats in those meadows where a species was

Table 1 Number of meadows classified by natural environmental conditions (terrain slope and soil parental material) and human management regimes (fertilization, main type of grazing animal, and mowing)

Natural environmental conditions Terrain slope High ([20%)

14

Low (\20%)

6

Soil parental material Mixed calcareous rocks

10

Pure calcareous rocks

10

Human management regime Fertilization No fertilization Organic (manure) fertilization

5 10

Mineral fertilizer

2

Unknown

3

Main type of grazing animal Cows

16

Horses

4

Mowing Unmowed Mowed

18 2

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present 9 mean percent cover in those quadrats. As a result, IV values measure the mean percent cover of a particular plant species within the sampled area. Assessment of the performance (1): estimating total species richness In order to test the validity of estimators with real data, one prerequisite is to have an idea of the true number of species underlying those data (Leitner and Turner 2001; Walther and Moore 2005). However, to determine true richness, sampling must be complete; otherwise, a randomized sample-based rarefaction curve (i.e., a expected species accumulation curve), which represents the statistical expectation from repeated re-sampling of all pooled sampling units (Gotelli and Colwell 2001), can be fitted to curvilinear accumulation models and extrapolated to an infinite sampling effort (Soberoń and Llorente 1993; Moreno and Halffter 2000; Dıáz-Frances and Soberoń 2005). To estimate total species richness, we first pooled data from three adjacent, well sampled meadows (44 species 9 30 quadrats); then, a sample-based expected species accumulation curve was constructed, and finally it was fitted to a collection of non-asymptotic and asymptotic accumulation functions (see below). Following Gotelli and Colwell (2001), the sample-based expected species accumulation curve was produced by randomly re-sampling the pool of quadrats from the three selected meadows and plotting the average number of species for increasing sampling efforts (i.e., for one, two, three… 30 quadrats). Theoretically, species accumulation curves reach an asymptote when the probability of adding a new species to the inventory approaches zero; then, the asymptote represents true species richness; on the other hand, those curves are non-asymptotic if such probability never reaches zero (Soberoń and Llorente 1993). A large number of possible models can be fitted to species accumulation data (Tjorve 2003), but extrapolations from these models (and their corresponding asymptotes, if they exist) normally diverge, especially if curves are not approaching a clear plateau (Flather 1996; Thompson et al. 2003). Following a suggestion by Walther and Moore (2005), we used model selection techniques based on Kullback-Leibler (K-L) information theory and maximum likelihood approaches to choose the best one among several candidate models (see Jimeńez-Valverde et al. (2006) for a similar approach). A set of R = 9 models commonly used in the literature were fitted to the sample-based expected species accumulation curve from the three selected meadows by non-linear regression techniques using STATISTICA 7.0 (StatSoft 2004); two of the models were non-asymptotic (i.e., power and exponential), whereas the remaining ones were asymptotic (i.e., negative exponential, logistic, MorganMercer-Flodin, Chapman-Richards, cumulative Weibull distribution, and cumulative betaP distribution; Table 2). Models with a low number of parameters were easily fitted using the ‘Simplex’ or ‘Simplex & quasi-Newton’ algorithms; however, we used the ‘HookeJeeves and quasi-Newton’ or the ‘Rosenbrock and quasi-Newton’ algorithms to fit more complex functions. For each model i, the corresponding Akaike’s Information Criterion corrected for small samples (AICc) was computed, which enabled the ranking of models according to their K-L information content; AIC values were rescaled as DAICci = AICci - minAICc. The larger the DAICc, the less plausible is model i as being the best approximating one in the set of candidate models; as a rule of thumb, models having DAICc \ 2 have substantial support (evidence). Moreover, DAICc values were used to assess the likelihood of each model given the data, by calculating the Akaike weights, which are useful as the ‘weight of evidence’ in favor of model i as being the best K-L model in the set of R models. For mathematical formulas and a detailed explanation on

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Table 2 Candidate models for species-accumulation functions fitted to data collected at three meadows, and results from the non-linear regression analyses performed on these data Model

Function

k SS

Morgan-Mercer- a(1 - (1 ? (x/c)d)-b) Flodin Beta-P

axc/b ? xc c

R2 (%) AICc

DAICc Support

Asymptote

3

0.28 99.96

-133.32

0.00 1

48.3

4

0.27 99.97

-131.72

1.61 4.5 9 10-1

48.8

-77.92

55.41 9.3 9 10-13

Cumulative Weibull

a(1 - exp(-bx ))

3

1.77 99.93

Clench

a x/(1 ? bx)

2

3.44 99.79

-60.56

72.76 1.6 9 10-16

ChapmanRichards

a(1 - exp(-bx))c

3

4.54 99.80

-49.71

83.62 7.0 9 10-19

Exponential

a ? b log(x)

2 28.37 98.17

2.76 136.09 2.8 9 10-30

Logistic

a/(1 ? exp(-bx ? c)) 3 40.76 97.46

16.12 149.44 3.5 9 10-33

Negative exponential

a(1 - exp(-bx))

2 82.06 95.08

34.63 167.95 3.4 9 10-37

Power

axb

2 89.29 93.78

37.17 170.49 9.5 9 10-38

In all cases, the independent variable (x) was the number of quadrats up to a given sampling effort, whereas the response variable (y) was the corresponding observed number of species. For each model, k is the number of parameters, SS is the total sum of squares, R2 (%) is the coefficient of determination, AICc is the Akaike Information Criterion corrected for small samples, DAICc is the change in AIC between each model and the one with the lowest AIC, and Support is the evidence ratio. For the two best-ranking models (those with the highest Support), Asymptote is the number of species predicted with an infinite sampling effort

information theoretic and AIC-based methods, see Anderson et al. (2000), Burnham and Anderson (2001), and Johnson and Omland (2004). Assessment of the performance (2): calculating nonparametric estimators For increasing levels of sampling efforts, an expected species accumulation curve for the pooled data from the three meadows was computed. In plant communities, individualbased accumulation or rarefaction curves are seldom calculated, since for most groups of plants it is difficult (if not impossible) to recognized individuals (Chiarucci and Palmer 2006). Therefore, estimates of richness were computed using the following incidencebased nonparametric estimators (Colwell and Coddington 1994): (1) incidence-based coverage estimator (ICE); (2) Chao 2; (3) first-order jackknife estimator (Jack 1); (4) second-order jackknife estimator (Jack 2); and (5) the bootstrap estimator (Bootstrap). ICE is based on the number of rare species (those found in less than 10 sampling units; in our case, quadrats), whereas Chao 2 takes into account the number of unique and duplicate species (those occurring in exactly 1 or 2 sampling units, respectively). Jack 1 is also a function of the number of uniques, while Jack 2 considers the number of uniques and duplicates, as well as the number of sampling units; finally, Bootstrap is based on the proportion of samples containing each species (Chazdon et al. 1998). The effect of the order in which samples are added to the pooled curve was removed by randomly re-sampling data (Colwell and Coddington 1994; Colwell 2006). In addition, two different Michaelis-Menten estimators were computed: (6) Michaelis-Menten Runs (MMRuns) and (7) Michaelis-Menten Means (MMMeans). MMRuns computes estimates of species richness for each pooling level (i.e., for one, two, three… 30 quadrats) for each randomization run, and then averages over all the randomization runs; MMMeans estimates

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species richness for each pooling level only once, by using the mean species accumulation curve (Colwell 2006). Following Walther and Moore (2005) and Colwell (2006), for all computations involving multiple orderings of samples, 50 randomizations were used, with replacement; all these analyses were carried out by using the EstimateS 8.0 freeware (Colwell 2006), and results from each individual run were exported to a different file, allowing computation of bias, precision, and accuracy. Assessment of the performance (3): computing bias, precision, and accuracy A robust and accurate estimator should be reasonably insensitive to sample size and, beyond a threshold of sampling units, should remain stable as sampling effort increases (Chazdon et al. 1998; Leitner and Turner 2001). Moreover, an ideal estimator should reach its own asymptote much sooner than the expected species accumulation curve, approximating the empirical asymptote in an unbiased way (Chazdon et al. 1998; Gotelli and Colwell 2001; Hortal et al. 2006). Following Colwell and Coddington (1994), Chazdon et al. (1998) and Longino et al. (2002), we visually evaluated the performance of each estimator by inspecting how well it approximated true richness along successively larger numbers of accumulated samples. In addition, for increasing sampling efforts (i.e., for one, two, three… 30 quadrats), the following relative measures of estimator performance were calculated (see Walther and Moore 2005 for mathematical formulas and a detailed explanation): (i) bias, or the systematic error measuring the difference between an estimated and the true value; we expressed bias as percent of actual richness (PAR): PAR = 100 9 SME ? 100, where SME is the scaled mean error; (ii) precision, measured as the coefficient of variation (CV) of all the estimated values; it measures the repeatability of independent estimates, whether it is biased or not; and (iii) accuracy, or the overall distance between the observed value and the true one, quantified as the scaled mean squared error (SMSE). A low SMSE indicates that individual estimates are on average close to the true value, which implies both a low mean bias and a high mean precision; therefore, accuracy is generally the most desirable of the three parameters, because a highly accurate estimator is neither systematically biased nor highly variable (Hellmann and Fowler 1999; Walther and Moore 2005). Application of estimators: contrasting plant species richness in meadows under diverse environmental conditions To test if the use of species richness estimators improves the assessment of plant responses to human practices, both observed richness and the best estimator (i.e., the one producing the highest accuracy) were applied to study the effects of changes in environmental conditions and human management regimes on species richness in the larger, whole set of studied meadows. To this aim, plant species data from the 20 meadows were pooled in a smaller number of data subsets, as necessary (for classes of meadows, and number of sites per class, see Table 1); then, observed and expected richness sample-based rarefaction curves were constructed as previously explained; finally, at comparable levels of sampling effort, mean values and corresponding 95% confidence intervals (CI) were contrasted between classes of sites defined by natural environmental conditions or human management regimes. Following Colwell et al. (2004), differences were judged as statistically significant (P \ 0.05) if CI did not overlap. We used 95% CI for observed richness expected species accumulation curves as supplied by EstimateS 8.0 (Colwell 2006); for the

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best estimator, we calculated 95% CI as estimator ± 1.96 9 standard deviation of the estimator (Robert K. Colwell 2009; personal communication). If differences were found to be statistically significant, effect size for the maximum sampling effort available was expressed as a percent loss of species: DS = 100 9 (SMAX - SMIN)/SMAX, where S = observed, or estimated, richness at the corresponding sampling effort.

Results General description of the vegetation In the whole dataset studied, a total of 65 plant species were identified (Appendix). In terms of importance values (IV), only three species were dominant (IV [ 10): Agrostis capillaris, Trifolium repens, and Lolium perenne. Twenty-four species exhibited IV values between 1 and 10, like Ranunculus acris, Bellis perennis, or Veronica chamaedrys. Finally, 38 species could be deemed of minor importance (IV \ 1), including, for instance, Potentilla erecta, Prunella vulgaris, or the locally very rare Digitaria sanguinalis (Appendix). Assessment of the performance In the small dataset selected to test the performance of estimators, a total of 44 plant species were found. Goodness-of-fit of the nine candidate models adjusted to the sampledbased expected species accumulation curve was high, as judged by their coefficients of determination (in all cases, R2 [ 90%; Table 2). However, the best-fitting function was the Morgan-Mercer-Flodin (MMF; AICc = -166.32; R2 = 99.96%), and the second bestfitting model was the cumulative beta-P distribution (DAICc: 1.61; R2 = 99.97%; 4.5 9 10-1 times less probable; Table 2). The remaining models exhibited considerable less support by the data at hand, as compared to the MMF function; this was particularly true for the non-asymptotic models (exponential: support *10-30; and power: support *10-38). Commonly used functions, like the Clench model or the negative exponential, were not a good option for modeling our data on plant species richness (Table 2). The asymptote of the MMF function was 48.25 species; this value was considered as our best guess of the true number of species in the set of meadows selected to assess the performance of estimators. Notably, the asymptote of the beta-P function was very close to that value (48.8; Table 2). The visual inspection of the sample-based expected species accumulation curves for observed richness (Sobs), and for the seven estimators here studied, shows that most of them gently increased towards our best guess of true richness, but generally underestimated it (Fig. 1). Sobs increased from a mean value of 14.4 species for a sampling effort of only 1 quadrat, to a mean of 42.6 species for 30 quadrats (i.e., 88.3% of the estimated true richness). Moreover, the whole 95% confidence interval (CI) for Sobs was always below true richness, even at very high sampling efforts (Fig. 1). Therefore, irrespective of sampling effort, Sobs was a biased estimator (Fig. 1; Table 3). The number of uniques and duplicates decreased from initial values above or close to 10, to final values below 4 (Fig. 1). At very small sampling efforts, ICE, Chao 2, and MMRuns overestimated asymptotic richness (Fig. 1), but underestimated it from ca. 5 quadrats onwards (Fig. 1; Table 3); the remaining estimators gently increased towards true richness but, as Sobs, systematically

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Fig. 1 Sample-based rarefaction curves for observed richness (Sobs; thick red line) and the estimators c studied here (ICE, Chao 2, Jackknife 1, Jackknife 2, Bootstrap, MMRuns and MMMeans; thick blue lines), obtained from data collected at three meadows, for increasing sampling efforts (pooled data from three meadows; from 1 to 30 quadrats). Except for MMMeans (data not available), 95% confidence intervals for all the estimators are also shown (doted, thin red or thin blue lines above and below the estimator curve). Curves for uniques (i.e., number of species that occur in only one quadrat) and duplicates (number of species that occur in only two quadrats) are shown in the panel for Sobs. In all panels, Sobs is included as a baseline against which the performance of the estimators can be visually compared (continuous, thin red line below the estimator curve), whereas the horizontal, thin green line at 48.25 species represents the asymptotic estimate of the true species richness calculated according to the best species-accumulation model (MorganMercer-Flodin function; see Table 1)

underestimated it as well (Fig. 1). Above a threshold between 5 and 10 quadrats (from 16.7 to 33.3% of the total sampling effort), ICE, Jack 2, MMRuns, and MMMeans were practically independent of sampling effort. In terms of bias, Sobs was always the mostbiased estimator of true richness, since the corresponding sample-based expected species accumulation curves for all the estimators were located above the curve for Sobs (Fig. 1); the bootstrap estimator was generally the second most-biased (Fig. 1; Table 2). Only Jack 1 (from a sampling effort above 66.7% of the total), and Jack 2 (from a lower sampling effort, above 50% of the total), exhibited PAR values [95% (Table 3). Given the way MMMeans works, it was impossible to assess its precision as computed in this paper; therefore, it was removed from further analyses. In terms of precision, MMRuns was the worst estimator at very low or low sampling efforts, whereas Chao 2 or Jack 2 were the most variable estimators at medium and high sampling efforts (Fig. 1; Table 2). Irrespective of sampling effort, the most precise estimator was Sobs, followed by Bootstrap, ICE, and Jack 1 (Fig. 1; Table 2). As for Sobs, and irrespective of sampling effort, the 95% CI for Bootstrap did not include the best guess of true richness (Fig. 1). Finally, in terms of accuracy, and irrespective of sampling effort, the worst estimator was always Sobs (Table 3). The best estimator with very small sampling efforts was Jack 2 (for example, with 5 quadrats, 100 9 SMSE = 32.8%); however, from that number of sampling units onwards, the most accurate estimator was always Jack 1 (Table 3). In fact, Jack 1 was the only estimator with 100 9 SMSE \ 5%: the accuracy of Jack 1 ranged from 100 9 SMSE = 16.3% (with 10 quadrats, 33.3% of the total sampling effort) to a final value of only 3.8% (with 100% of the total sampling effort). In consequence, because of its good performance (i.e., low bias and high accuracy) in the set of meadows used to assess the behavior of nonparametric estimators of species richness, Jack 1 was selected to test if species richness estimators improve the evaluation of plant responses to natural environmental conditions and human management regimes, when compared to observed species richness. Application of estimators A total of 56 plant species were reported from the 14 meadows (140 quadrats) located on low slope terrains, whereas 46 species were found in the six meadows (60 quadrats) on high slopes. The sampled-based expected species accumulation curve for the observed number of species in low-slope sites was always above that for high-slope sites; however, this difference was not statistically significant (P [ 0.05), since the 95% CI for these two classes of meadows did extensively overlap (Fig. 2). On the other hand, according to the Jack 1 estimator, a total of 61.05 species were expected in the set of low-slope meadows, whereas 49.05 species were estimated for high-slope ones. The sample-based rarefaction

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Biodivers Conserv (2010) 19:1417–1436 60

1425 60

Sobs

50

50

40

40

30

30

20

ICE

20

Uniques 10

10

Duplicates

0

Richness (number of species)

60

0 60

Chao 2

50

50

40

40

30

30

20

20

10

10

0

0

60

Jack 1

60

Jack 2

50

50

40

40

30

30

20

20

10

10

0

0

60

60

MMRuns

50

50

40

40

30

30

20

20

10

10

0

Bootstrap

MMMeans

0 0

5

10

15

20

25

30

0

5

10

15

20

25

30

Sampling effort (number of quadrats)

123

123

84.2

78.4

81.6

87.1

72.7

101.9

Chao 2

Jack 1

Jack 2

Bootstrap

MMRuns

93.4

82.4

93.7

89.6

86.6

86.4

75.2

91.8

87.7

96.1

93.8

88.3

89.5

81.1

50.0

15

92.1

90.3

97.8

95.6

91.3

91.1

84.5

66.7

20

92.8

91.6

95.9

95.4

91.4

92.2

86.7

83.3

25

93.3

92.6

95.8

95.7

91.4

92.8

88.3

100

30

32.5

10.2

14.6

11.6

17.7

15.3

9.2

16.7

5

CV (%)

16.3

6.7

12.8

8.2

19.2

9.3

6.1

33.3

10

11.2

6.0

11.8

7.5

8.5

7.9

5.2

50.0

15

8.9

4.1

9.7

5.3

7.8

5.1

3.7

66.7

20

7.2

3.8

10.3

5.7

8.5

5.6

3.0

83.3

25

6.1

2.9

8.5

4.6

4.3

4.5

2.4

100

30

123.8

79.8

32.8

42.9

66.1

41.6

132.3

16.7

5

27.8

34.1

18.2

16.3

45.4

25.0

63.8

33.3

10

SMSE 9 100

6.2 7.7

9.6 12.9

10.8

8.3 17.9 17.3

3.8 8.3 11.4

9.5 14.4

5.1

4.5

8.8

8.9

6.9 13.4

14.2 8.8

100

30

18.3

83.3

25

12.7

10.1

25.0

66.7

20

19.4

16.1

37.4

50.0

15

PAR percent of actual richness, CV coefficient of variation, SMSE scaled mean squared error

The following subjective scale for sampling effort was used throughout the text: ‘very low’ if sampling effort \ 16.7%; ‘low’ if 16.7% \ sampling effort \ 33.3%; ‘medium’ if 33.3% \ sampling effort \ 66.7%, and ‘high’ if sampling effort [ 66.7%. Bold italic values indicate the most accurate estimators for different sampling efforts (values of SMSE 9 100 \ 10%)

64.2

33.3

16.7

ICE

10

5

Sobs

Sampling effort (no. quadrats): Sampling effort (% of total):

PAR (%)

Table 3 Scaled performance measures of observed species richness (Sobs) and the estimators of species richness studied here, obtained from data collected at three meadows, for increasing sampling efforts (measured as both number of quadrats, up to 30, and percent of total effort)

1426 Biodivers Conserv (2010) 19:1417–1436


1427

Observed richness (Sobs) 70

Estimated richness (Jack 1) 70

60

60

50

50

Low slope

40

High slope

30

40 30

20

20

10

10

0

0

70

70

Mixed calcareous

60 50

∆S = 16.2%

Mixed calcareous

60

Pure calcareous

50

Pure calcareous

40

40

30

30

20

20

10

10

0

Low slope High slope

0

20

40

60

80

100

120

140

0

∆S = 16.5%

0

20

40

60

80

100

120

140

Sampling effort (number of quadrats) Fig. 2 Sample-based rarefaction curves for observed (Sobs; left panels) and estimated (Jack 1; right panels) richness, obtained from data collected at 20 meadows differing in natural environmental conditions; 95% confidence intervals for all the estimators are also shown (doted, thin green or thin red lines above and below the estimator curve). The vertical, dotted lines on the estimated richness panels mark the maximum number of inventories useful for comparison purposes; at that sample size, DS (expressed as %loss of species) quantifies the effect of the corresponding environmental condition on species richness. Above: slope (six meadows with high slope versus 14 meadows with low slope); below: soil parent material (10 meadows on pure calcareous rocks versus 10 meadows on mixed calcareous rocks)

curve for Jack 1 showed that, with a maximum common sampling effort of 60 quadrats, the difference was statistically significant, since the corresponding 95% CI did not overlap: on average, estimated richness in meadows located on high slope terrains was 16% inferior than that for low slopes (Fig. 2). Irrespective of sampling effort, the number of plant species observed in the 10 sites with soils over mixed calcareous rocks was always higher than that for the 10 sites with soils over pure calcareous rocks; a total of 57 and 49 species were observed in those two classes of meadows, respectively; this difference, nonetheless, was not statistically significant, even for the greatest sampling effort (Fig. 3). However, by using the Jack 1 estimator at a maximum common sampling effort of 100 quadrats, meadows on soils over pure calcareous rocks were, on average, 16.5% less rich than those over mixed calcareous rocks (Fig. 2).

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Observed richness (Sobs)

Estimated richness (Jack 1)

70

70

60

60

Organic

Organic

50 40

50

Mineral

30

30

20

20

10

10

0

0

70

70

60

60

50

50

Cows

40

Horses

30

Cows

40

Horses

30

20

20

10

10

0

0

70

70

60

60

50

50

No mowing

40

No mowing

40

Mowing

30

20

10

10 0

30

60

Mowing

30

20

0

No Fertilizer Mineral

40

No Fertilizer

90

120

150

180

0

∆S = 30.6%

0

30

60

90

120

150

180

Sampling effort (number of quadrats)

Fig. 3 Sample-based rarefaction curves for observed (Sobs; left panels) and estimated (Jack 1; right panels) richness, obtained from data collected at 20 meadows differing in human management regimes; 95% confidence intervals for all the estimators are also shown (doted, thin green, thin blue, or thin red lines above and below the estimator curve). The vertical, dotted line on the estimated richness bottom panel marks the maximum number of inventories useful for comparison purposes; at that sample size, DS (expressed as %loss of species) quantifies the effect of the corresponding human management regime on species richness. Uppermost panels: type of fertilization (10 meadows with organic fertilization versus five meadows with no fertilizer versus two meadows with mineral fertilization); middle panels: grazing animals (mainly cows in 16 meadows versus mainly horses in four meadows); bottom panels: effect of mowing (18 unmowed meadows versus two mowed meadows)

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1429

Irrespective of sampling effort, no differences in both observed and estimated samplebased rarefaction curves were found between non-fertilized meadows and those subjected to organic fertilization (manure; Fig. 3). On the other hand, and regardless of sampling effort, observed and estimated plant species richness in meadows subjected to mineral fertilization were always below the corresponding values from non-fertilized or organically-fertilized meadows. However, at a maximum common sampling effort of only 20 quadrats, these differences were not statistically significant (Fig. 3). In addition, observed and estimated species richness seemed independent of the type of main animal grazing (cows versus horses; Fig. 3). Finally, although more species were found in meadows with no mowing versus those actually mowed, the observed richness rarefaction curves for these two classes of meadows were not statistically different (Fig. 3). However, after applying the Jack 1 nonparametric estimator, it seemed apparent that mowing had a striking effect on estimated species richness: with a sampling effort of only 20 quadrats, estimated species richness at mowed sites was close to 36 species (and it looked as approaching a plateau), whereas in the absence of mowing it was close to 52 (and it even raised up to 66 species, but only with a final sampling effort of 180 quadrats); the difference between unmowed and mowed meadows was statistically significant (DS = 30.6%; Fig. 3).

Discussion There are basic and applied reasons in favor of the use of species richness in ecological and environmental studies (Hellmann and Fowler 1999; Dale and Beyeler 2001; Duelli and Obrist 2003; Chiarucci and Palmer 2006). However, since simple richness measures exhibit high sample-size dependence and, usually, underestimate true richness (Colwell and Coddington 1994; Gotelli and Colwell 2001; Leitner and Turner 2001), robust methods are needed to accurately estimate the number of species at a variety of spatial and temporal scales (Colwell and Coddington 1994; Cao et al. 2004; Magurran 2004). Hopefully, modern methods to estimate species richness, like the nonparametric estimators here evaluated, can reduce the bias associated with species richness determination (but see O’Hara 2005 for a different opinion). Many estimators have been put forward, leaving the investigator with the question of which ones are more suitable for use with a given dataset. Assessment of the performance To evaluate the performance of estimators with real datasets, prior knowledge of the total number of species is necessary (Walther and Moore 2005), an ideal usually not feasible (for a rare exception, see Lo´pez-Go´mez and Williams-Linera (2006), who counted all individual trees in two small coffee plantations). As a consequence, this information must be obtained using other approaches, like the well-informed opinion of an expert (i.e., a guesstimate; Walther and Moore 2005; for an example of its application, see Hortal et al. 2006), or the extrapolation from collector’s (Sobs) curves (for example, see Soberoń and Llorente 1993; Moreno and Halffter 2000; Dıáz-Frances and Soberoń 2005). Unless the assemblage has been exhaustively sampled, Sobs curves underestimate true richness (Magurran 2004). Therefore, it is crucial that the extrapolation function fits reasonably well the empirical data, although little attention has been given to this point in the literature (Thompson et al. 2003; O’Hara 2005). Soberoń and Llorente (1993) provided a theoretical, a priori justification for using several extrapolation equations. On the other hand, Colwell and Coddington (1994),

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Flather (1996), Thompson et al. (2003), and Jimeńez-Valverde et al. (2006) argued for a pragmatic approach that tests different reasonable models against inventories with diverse degrees of completeness. In the first part of our study, we fitted the sample-based rarefaction curve from a reasonably well sampled set of meadows, which represents the expected number of species in a small collection of quadrats drawn at random from a larger pool of sampling units, to two non-asymptotic and seven asymptotic models, and used model selection techniques based on the principle of parsimony to choose the best function to be used for inference. After comparing the plausibility of all these functions with our dataset, there was strong evidence in favor of the asymptotic Morgan-Mercer-Flodin (MMF) model as the best one; conversely, we found very little empirical support for the much used Clench and other simpler models. These findings are not new in the literature of species richness (see Jimeńez-Valverde et al. 2006). In addition, Jimeńez-Valverde and Hortal (2003) suggested that, for a sampling to be considered as adequately reliable, the slope of the curve should be 0.1, or below. For our small dataset, the actual rate of increase in the number of species at the end of the sampling was 0.13, when a total number of 44 species was observed; according to the MMF model, a doubling of the sampling effort (30 new quadrats) would increase the number of species by adding only 1.3 new species. Therefore, we considered the asymptote of the MMF function as a very good estimate of true richness. With a reliable estimate of true richness, we compared the performance of several nonparametric incidence-based estimators of species richness. There is no estimator that is appropriate for all situations or taxa (Walther and Moore 2005), and different authors have found contrasting results (see, for example, O’Hara 2005; Hortal et al. 2006; Lo´pez-Go´mez and Williams-Linera 2006; Canning-Clode et al. 2008 or Williams 2008). Walther and Moore (2005) reviewed 14 studies that compared estimator performance and concluded that Sobs was generally the worst of all measures describing species richness, whereas the Chao estimators (including Chao 2) and the jackknife estimators (including Jack 1 and Jack 2) usually performed better than the other methods (including the bootstrap estimator). Our study showed that, in general, all the estimators underestimated true richness; even so, the amount of underestimation gradually decreased with increasing sampling efforts. In terms of bias, and irrespective of sampling effort, the worst estimator was always Sobs, and Bootstrap was the second worst: it was apparent that Bootstrap did not reveal anything that Sobs had not told in advance. Chazdon et al. (1998) and Herzog et al. (2002) also reported the extreme sample-size dependence of the Bootstrap estimator (in fact, it was not recommended for studies of plant species richness). In the studied meadows, Sobs has to be considered a biased estimator of species richness, since it inevitably underestimated the true number of species. In addition, our study showed that all the nonparametric estimators were useful to reduce bias (versus Sobs), as has been reported by other authors (Palmer 1991; Colwell and Coddington 1994; Brose and Martinez 2004). However, in terms of accuracy, our analyses revealed that the best estimator was Jack 1, for low, medium and high sampling efforts. It is important to note that, if the asymptote of the second best fitting model (the beta-P function) had been considered as our best guess of true richness, instead of that from the best model (the Morgan-MercierFlodin), then the ranking of nonparametric estimators according to the criteria set for our performance assessment (i.e., bias, precision, and accuracy) would have remain the same, Jack 1 being also the most accurate (analyses not shown).

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Application of estimators Species richness has been suggested as a useful indicator to monitor changes in ecological integrity (Dale and Beyeler 2001), and as a necessary tool to make informed decisions in conservation biology (Hellmann and Fowler 1999; Walther and Martin 2001). However, ecologists have only recently begun to incorporate the techniques of species accumulation, rarefaction and richness estimation into their measurements of biodiversity (Gotelli and Colwell 2001). This fact is true especially in agroecosystems, where biodiversity has been usually measured by using diversity indices such as the Shannon-Wiener (but see Brose 2002; Lo´pez-Go´mez and Williams-Linera 2006). Nevertheless, to assess biodiversity in agroecosystems, to properly evaluate their contribution to regional diversity, and to estimate the effects of changes in soil uses and other management practices on such biodiversity, it is necessary to have reliable estimates of the number of species (Lo´pez-Go´mez and Williams-Linera 2006). Some authors have argued that the use of species richness estimators can improve the evaluation of plant responses to human practices (Loya and Jules 2008). In the second part of the current study, we found that differences in observed richness in several classes of meadows (formed by both natural environmental conditions and human management practices) were considered as statistically not significant. However, after computing rarefaction curves for estimated richness (using the Jack 1 nonparametric estimator), some of those differences were judged as statistically significant, involving a loss of species that ranged from ca. 15% (for instance, between meadows on low slopes versus high slopes) to ca. 30% (between uncut and cut meadows). Some words of caution on these results are needed. Ours was not a manipulative, experimental study, but a correlational, observational one; at best, it could be considered a ‘‘natural’’ experiment (Gotelli and Ellison 2004). As a consequence, we could not cross factors in a statistically proper design, and it was more challenging to clarify cause-and-effect relationships, especially where contrasting numbers of species were reported with very different sampling efforts. This was the case for the effect of grass mowing, because only two meadows could be found in the whole study area where this traditional practice in the Basque campinã is still observed (see Alberdi Collantes 2001). Nevertheless, by considering the other factors as covariates, the effects due to meadow cutting on plant richness could be deemed as real, not only the consequence of spurious relations. The loss of species due to grass cutting was observed in two meadows that were both located on low slope terrains, although, as previously explained, meadows on low slopes tend to have more species than those on high slopes (Fig. 3). At the same time, the parental rocks at these two sites were mixed calcareous, even though, in general, soils over mixed calcareous rocks tend to be richer in species than those over pure calcareous rocks (Fig. 3). On the other hand, more sampling effort is needed to test if nonparametric estimators like Jack 1 can find statistically significant differences in plant species richness due to the application of mineral fertilizers versus organic manure or no fertilization at all (Fig. 3). In any case, it has been previously reported that human intervention in agroecosystems, such as mineral fertilization or mowing, provokes a loss of biodiversity at different scales (Ferrer et al. 2001; Norris 2008). Likewise, we have recently suggested a negative effect on plant diversity of high levels of phosphorus in soils, as revealed by a direct gradient analysis linking plant community structure to soil physicochemical parameters (Gonza´lez-Oreja et al. 2009).

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Conclusion Agroecosystems have been recognized as an important biodiversity reservoir in areas with strong human presence (Clergue et al. 2005), like the Basque Country. Nonetheless, even in the European Union, where a long history of agrarian practices can be traced, agriculture is acknowledged as one of the main drivers of biodiversity loss (European Environment Agency 2007; Henle et al. 2008; Norris 2008). The need for agroecosystems to play a major role in biodiversity conservation is becoming increasingly recognized, and addressing this need is presenting conservation science with new challenges and opportunities (Clergue et al. 2005; Norris 2008). The evidence here presented strongly suggests that nonparametric estimators of species richness, like those here assessed, can be successfully applied to monitor the effects on the number of plant species caused by changes in both environmental conditions and human practices. Acknowledgements This work has been financially supported by the ‘Plan Nacional de I?D?i 2004– 2007’, through the CGL2005-08046-C03-02/BOS Project. We sincerely thank Jose´ Antonio Elorrieta for his company and technical assistance during field work in Urdaibai and Robert K. Colwell for his help with the EstimateS software. Constructive comments and suggestions by two anonymous referees greatly improved a previous version of the manuscript.

Appendix See Table 4.

Table 4 List of the 65 plant species found in the whole data set (200 quadrats), ordered by decreasing Importance Value (IV): IV = M 9 Q 9 MC (%). M is the relative frequency of the meadows where a species was present; Q is relative frequency of the quadrats in those meadows where a species was present, and MC (%) is the mean percent cover of every species in those quadrats where it was present M

Q

MC (%)

IV

Agrostis capillaris L.

0.95

0.94

46.58

41.46

Trifolium repens L.

1.00

0.88

40.41

35.36

Lolium perenne L.

0.90

0.67

29.71

17.83

IV [ 10

1 \ IV \ 10 Ranunculus acris L.

1.00

0.78

12.21

9.52

Holcus lannatus L.

0.80

0.58

19.54

8.99

Plantago lanceolata L.

1.00

0.57

15.37

8.69

Poa pratensis L.

0.70

0.49

20.82

7.08

Lotus corniculatus L.

0.75

0.34

21.20

5.41

Dactylis glomerata L.

0.75

0.46

12.35

4.26

Festuca arundinacea Schreber

0.65

0.38

16.26

4.07

Gaudinia fragilis (L.) Beauv.

0.60

0.48

11.83

3.43

Bellis perennis L.

0.75

0.35

12.91

3.42

Taraxacum gr. officinale Weber

0.90

0.52

7.33

3.41

Poa annua L.

0.45

0.47

14.71

3.09

Bromus mollis L.

0.85

0.40

8.37

2.85

Trifolium pratense L.

0.55

0.39

12.84

2.76

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1433

Table 4 continued M

Q

MC (%)

IV

Carex sp.

0.95

0.42

6.86

2.75

Cynosurus cristatus L.

0.70

0.35

11.08

2.72

Hypochoeris radicata L.

0.60

0.42

10.16

2.54

Rumex sp.

0.70

0.48

7.46

2.50

Festuca rubra L.

0.40

0.31

17.16

2.15

Anthoxanthum odoratum L.

0.50

0.41

10.00

2.05

Paspalum dilatatum Poiret

0.55

0.29

11.56

1.85

Geranium molle L.

0.90

0.32

5.77

1.65

Medicago lupulina L.

0.40

0.21

15.06

1.28

Mentha arvensis L.

0.45

0.27

10.38

1.25

Veronica chamaedrys L.

0.85

0.30

4.80

1.23

IV \ 1 Potentilla erecta (L.) Raeuschel

0.65

0.27

5.46

0.96

Daucus carota L.

0.40

0.34

6.22

0.84

Plantago major L.

0.35

0.16

14.09

0.78

Cerastium fontanum Baumg., subsp. Triviale (Spenner) Jalas

0.80

0.27

3.56

0.77

Potentilla reptans L.

0.40

0.28

6.59

0.73

Poa trivialis L.

0.15

0.37

12.73

0.70

Plantago media L.

0.50

0.16

7.75

0.62

Ranunculus repens L.

0.60

0.21

4.92

0.62

Prunella vulgaris L.

0.65

0.15

4.95

0.50

Convulvulus arvensis L.

0.25

0.42

4.48

0.47

Luzula campestris (L.) DC.

0.25

0.20

6.00

0.30

Crepis capillaris (L.) Wallr

0.15

0.27

7.00

0.28

Vicia villosa Roth subsp. Pseudocracca (Bertol.) P.W. Ball

0.15

0.30

5.22

0.24

Cirsium vulgare (Savi) Ten.

0.20

0.13

9.20

0.23

Verbena officinalis L.

0.25

0.12

6.67

0.20

Brachypodium pinnatum (L.) Beauv.

0.05

0.10

40.00

0.20

Capsella bursa-pastoris (L.) Medicus

0.20

0.18

3.86

0.14

Galium mollugo L.

0.15

0.13

6.50

0.13

Veronica arvensis L.

0.25

0.12

4.17

0.13

Linum catharcticum L.

0.05

0.30

8.00

0.12

Sonchus asper (L.) Hill

0.10

0.15

7.33

0.11

Potentilla sterilis (L.) Garcke

0.10

0.15

6.67

0.10

Briza media L.

0.05

0.30

6.67

0.10

Indet.

0.10

0.15

6.00

0.09

Centaurea nigra L.

0.05

0.10

15.00

0.08

Medicago sativa L.

0.05

0.10

15.00

0.08

Oxalis acetosella L.

0.05

0.10

15.00

0.08

Lathyrus pratensis L.

0.15

0.10

4.67

0.07

Veronica officinalis L.

0.15

0.17

2.60

0.07

Potentilla montana Brot.

0.05

0.10

10.00

0.05

123

1434


Table 4 continued M

Q

MC (%)

IV

Stellaria media (L.) Vill.

0.25

0.10

1.80

0.05

Linum bienne Miller

0.05

0.30

2.67

0.04

Danthonia decumbens (L.) DC.

0.10

0.10

2.50

0.03

Phleum pratense L.

0.05

0.10

5.00

0.03

Aquilegia vulgaris L.

0.05

0.10

3.00

0.02

Picris hieracioides L.

0.05

0.10

3.00

0.02

Achillea millefolium L.

0.05

0.10

2.00

0.01

Digitaria sanguinalis (L.) Scop.

0.05

0.10

1.00

0.01

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