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Evaluation and monitoring of the flora in a nature reserve by estimation methods
Biological Conservation 101 (2001) 305–314 www.elsevier.com/locate/biocon
Evaluation and monitoring of the flora in a nature reserve by estimation methods Alessandro Chiarucci*, Simona Maccherini, Vincenzo De Dominicis Dipartimento di Scienze Ambientali, Universita` di Siena, Via P.A. Mattioli 4, 53100 Siena Italy Received 23 May 2000; received in revised form 26 January 2001; accepted 23 February 2001
Abstract We tested the use of non-parametric estimators of species richness to evaluate the flora of a relatively large (431 ha) nature reserve, using a sampling area much lower than that used in previous studies. Different estimation methods were applied to floristic data obtained from 50 random plots: the number of observed species, the extrapolated accumulation curves based on the Michaelis–Menten model and the non-parametric estimators based on incidence data (Chao2, first-order Jackknife, second-order Jackknife and bootstrap). To test the performance of the estimators, five data sets were created on the basis of life-forms. The estimates were compared with reference values obtained by traditional floristic and vegetation sampling. The power of the different estimation methods could not definitively be determined, but the first- and second-order Jackknives seem to be the most precise. Although total species richness was underestimated, the sample-based approach provided accurate information for quantitative comparison of time series of data related to ecological changes, vegetation dynamics and environmental changes. This sample-based data included basic statistics on species richness and species frequency distributions as well as the life-form spectrum, at the plot and the whole site scales. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Biodiversity; Monitoring; Nature reserves; Species richness; Species richness estimation
1. Introduction Nature reserves are managed with the aim of preserving and restoring biodiversity. To do this, it is essential to quantify and monitor the effects of management using reliable estimates of biodiversity. Biodiversity may be monitored by a range of approaches; one of the most frequently used being maps of vegetation or habitat types. The resolution and subjectivity in delimiting polygons and classifying units limit the validity of this approach. New techniques employing automatic mapping (e.g. Carmel and Kadmon, 1998) have aimed to solve these problems. Since standard floras exist for many countries, there is less subjectivity in using a species diversity approach. Many authors agree that species richness and complementarity are the most straightforward components of biodiversity for evaluation and monitoring, in a landscape context (Magurran, 1988; Colwell and Coddington, 1994; Gaston, 1996a). Moreover, * Corresponding author. Tel.: +39-0577-232872; fax: +39-0577232860. E-mail addresses: [email protected] (A. Chiarucci).
estimating biodiversity through species diversity does not require assumptions about any model of community or landscape structure (Colwell and Coddington, 1994). However, it is difficult, if not impossible, to assess the completeness of species lists (Palmer, 1995; Gaston, 1996a). Estimation methods are useful tools for predicting species richness in large areas based on sampled information (Colwell and Coddington, 1994), Jackknife and bootstrap estimators being the most widely used (Efron and Thisted, 1976; Heltse and Forrester, 1983; Smith and van Belle, 1984). Most tests of these estimation methods have been done using simulated data-sets (Burnham and Overton, 1979; Heltse and Forrester, 1983; Pollock and Otto, 1983; Balta´nas,1992; Mingoti and Meeden, 1992; Norris and Pollock, 1996; Polulin, 1998; Walther and Morand, 1998; Zelmer and Esch, 1999). Authors working with real data have only investigated relatively species-poor assemblages and, as far as plants are concerned, small spatial scales (Palmer, 1990, 1991; Keating and Quinn, 1998; Hellmann and Fowler, 1999). A test of these estimation methods is, therefore needed, over relatively large areas to assess their performance (Palmer, 1990, 1991; Gaston, 1996a).
0006-3207/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(01)00073-8
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The aims of the present study are: (1) to test species richness estimators in a relatively large area, using a limited sample and (2) to verify the use of a sample for the assessment of special components of species diversity, such as the life-form spectrum, frequently used to characterise species assemblages (Orshan, 1986).
2. Material and methods 2.1. Study site The nature reserve of Poggio all’Olmo was selected for this study. The reserve is located in southern Tuscany (Italy, 42 520 0600 N, 11 280 1900 E); it is 431 ha, with an altitude range between 654 and 1016 m. The vegetation (Maccherini et al., 1999; Angiolini et al., 2001) consists of grasslands (22.8%); scrub colonising unmanaged grasslands (26.9%); different woodland types managed as coppice (24.8%); chestnut groves (6%); conifer plantations (16.2%); traditionally managed farmlands (3%) and settlements (0.3%). As a general trend, there is progressive re-naturalisation due to reduced grazing pressure and declining agriculture. Many open areas were planted with conifers and most of the coppiced woods are developing into groves. The site was chosen because of the existence of a comprehensive floristic list (Maccherini et al., 2001), which provided an opportunity to test estimation methods against an assumed ‘‘total’’ reference total value (511 sub-generic taxa). 2.2. Sampling design A random design was chosen to obtain a representative sample. As no vegetation map was yet available, stratified sampling was not used. Two problems were encountered in sampling design: plot size and sample size (number of plots). Since it was not possible to extend specific tests on the effect of plot size to all of the nature reserve, this issue was solved pragmatically. It was decided to use 50-m2 plots, a size intermediate between those recommended for descriptive sampling in herbaceous and woody communities (Kent and Coker, 1992). Almost all the species growing in such an area could be identified in a 30–60 min survey. After having performed a computer simulation (Fattorini, unpublished data), taking into account habitat heterogeneity and costs considerations, a sample size of 50 plots was selected. Plots were located by using random co-ordinates. This design enabled straightforward statistical analysis, since it provides independent and identically distributed data. Plots were marked on detailed aerial photographs and then located on the ground; when it was difficult to locate the point exactly, a location was chosen using random numbers from the nearest point
located. GPS was not used because its error was greater than visual location. 2.3. Data collection Plots were located in the field between 15 March and 15 April 1998. Each site was marked with a wooden post. Plot area was delimited as a circle of 50 m2; early flowering species in the plot were recorded and their cover estimated. Each plot was visited a second time in the period 15 June–10 July 1998, at the height of the vegetative period, when other species were recorded and their cover estimated. Plant specimens are preserved in the Herbarium Universitatis Senensis (SIENA). 2.4. Data analysis Only presence/absence data was used here. Basic statistics on species richness per plot and species frequency were used to characterise the site and for future comparisons. Different estimators of species richness were computed with the program EstimateS# 5 (Colwell, 1997): the extrapolated accumulation curves based on the Michaelis–Menten model (Raaijmakers, 1987; hereafter referred as MMmean) and non-parametric estimators based on incidence data (Colwell and Coddington, 1994), namely first-order Jackknife (Jack1), secondorder Jackknife (Jack2), bootstrap (Boot; Burnham and Overton, 1979; Heltse and Forrester, 1983; Smith and van Belle, 1984) and the bias-corrected Chao2 (Chao, 1987, performed by the program upgrade, available at the same URL). The number of species observed (Sobs) was also calculated. For details on estimators see Colwell and Coddington (1994) and Chazdon et al. (1997). All estimations were averaged over 1000 randomised plot sequences. Since one data-set was available, statistical comparison between sites, as done by others (Palmer, 1990; Keating and Quinn, 1998; Walther and Morand, 1998), was not possible. For explorative aims, the data matrix was divided into five data sets, based on Raunkiaer’s (1934) life forms, each showing different species richness and frequency distributions (Table 1). Although these matrices were not independent, they were useful to test estimator performance on data sets with different properties, as in the case of different types of organisms or sites. Relative error (RE) and square relative deviation (SRD) were used to evaluate the performances of the estimators. RE is a measure of the relative difference between the value estimated and the true value, as given by the formula:
RE ¼
Sest St St
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where Sest is the estimated value and St is the true value of species richness. SRD is the square of RE and measures the closeness of the estimator to the true value, without considering the sign of the deviation: it weighs estimates further from St more heavily. Estimator performances over the life-form data sets were assessed by the mean value of RE (MRE) and SRD (MSRD), and by the ‘‘percentage of overestimation’’ (OVER). MRE is equivalent to the ‘‘mean deviation’’ of Palmer (1990) and to the ‘‘bias’’ of Hellmann and Fowler (1999), except that it is scaled by the true value, being equivalent to the ‘‘bias’’ used by Walther and Morand (1998). MSRD is equivalent to the ‘‘mean square proportional deviation’’ of Palmer (1990) and the ‘‘deviation’’ of Walther and Morand (1998). If all RE values have the same sign, MRE and MSRD are related. However, if an estimator has a range of estimations above and below the true value, it may have a low MRE but a high MSRD. An unbiased estimator has and MRE and an MSRD of zero an OVER of 50% (Palmer, 1990; Walther and Morand, 1998). The estimates from the life-form matrices, were used to estimate the life-form spectrum of the flora, by preparing life-form spectra (in%) with the numbers of species in each life-form estimated by the different estimators. The correlation coefficient between each of these spectra and the spectrum calculated on the complete flora, was calculated.
3. Results 3.1. Floristic data The 50 plots sampled, constituting 0.058% of the total area, produced a list of 342 sub-generic taxa (hereafter referred to as ‘‘species’’), which was 66.9% of the species recorded in the reserve. Species richness per plot showed a wide range of values, from a minimum of two (in a conifer plantation, where only the two planted
species were found) to a maximum of 93 (in sparse Prunus spinosa L. shrubland, invading a species-rich grassland). Total number of occurrences (speciesplots) was 1998. Mean species richness per plot was 39.8; distribution of species richness per plot, although rather uneven, was not significantly different from a normal distribution (test Shapiro-Wilk W=0.987, P < 0.450). Most species recorded had very low frequencies (Fig. 1). Ninety-five species (27.8% of the species recorded) were found in a single plot (‘‘unique species’’, Colwell and Coddington, 1994) and 209 species (61.1%) were found in five or less plots; a further 71 species (20.8%) were found in the frequency class from six to 10 plots. Only six species had a frequency higher than 25/ 50, and the highest frequency (by Crataegus monogyna Jacq. and Rosa canina L.) was 32/50. 3.2. Species richness estimation Hardly any of the estimators reached an asymptotic pattern in the 50 plots (Fig. 2). Sobs was obviously the lowest pattern with the worst RE (0.331). The MMmean and the Boot estimators showed highly biased negative estimates: 388.7 and 384.7 species, respectively. The Boot curve was constantly the second worst, and the MMmean curve gave the highest estimation when few plots were sampled, except for Chao2 in one–two plots, but it quickly became one of the worst curves. The other estimators gave better results, although all underestimated the true number of species. Jack1 and Chao2 gave very similar estimations (435.1 and 431.3 species, respectively), and had similar patterns, except for very few plots. Jack2 gave the best estimation (480.2 species) which, however, was negatively biased (RE=0.056). With one exception, all the estimators provided negative estimates for the life-form data sets with 50 plots (Table 2). Sobs gave the lowest estimates, with the highest negative MRE and 0% overestimation. Chao2 was the second worst estimator, with a very biased MRE and an
Table 1 Descriptive statistics for the different data sets, from the Poggio all’Olmo Nature Reserve, used for the analyses; Ch, chamaephytes; G, geophytes; H, hemicryptophytes; P, phanerophytes; T, therophytes Data set
Total number of species in the sample
Species frequency classes in 50 plots (% of species found in the n plots) Very rare (1–10)
Rare (11–20)
Average (21–30)
Frequent (31–40)
Very frequent (41–50)
Mean species richness per plot
S.D. of species richness per plot
Range in species richness per plot
Ch G H P T
9 31 148 41 113
77.8 90.3 78.4 70.7 88.5
22.2 9.7 18.2 17.1 10.6
0 0 3.4 9.8 0.9
0 0 0 2.4 0
0 0 0 0 0
1.0 3.0 18.1 7.0 10.7
1.4 2.0 11.3 3.6 10.9
0–5 0–12 0–47 1–14 0–39
Total
342
81.9
14.9
2.6
0.6
0
39.8
21.7
2–93
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MSRD worse than Sobs, indicating very low precision. Boot and MMmean had similar values of MSRD and MRE, constantly underestimated true species richness and had intermediate precision. Jack1 and Jack2 had
the best performances. Jack1 was less close to the true value, with a constant underestimation, but was slightly more precise (lower MSRD) than Jack2. The only overestimation was by Jack2 for the H data set (the
Fig. 1. Relationship between species rank and species frequency.
Fig. 2. Species richness according to different estimators in relation to the number of plots sampled and averaged after 1000 randomised plot sequences. Symbols are as follows: circles, number of observed species (Sobs); squares, Michaelis–Menten model (MMean); asterisks, Bootstrap (Boot); triangles, first-order Jackknife (Jack1); diamonds, second-order Jackknife (Jack2); crosses, Chao2 (Chao2). The bold line represents the reference ‘‘total’’ value.
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richest and intermediately skewed). When checking the behaviour of the estimators in each data-set (Fig. 3), interesting results emerge. For chamaephytes, Jack 2 and Jack 1 showed a declining phase, after reaching the true value, because the very rare species of this group were still lacking in the sample and the increasing weight of duplicates. Less than half of the geophytic species were found in the sample and all estimators gave highly biased negative estimates. For hemicryptophytes, the richest data set, Jack1, Jack2 and Chao2 showed no sign of a decrease in their ascending phase. The other two data sets provided results similar to the whole data set.
the whole flora. Geophytes were the most (negatively) biased, leading to overrepresentation of the other groups. The weight of some life forms changed substantially from the plot to the whole sample (Fig. 4): relative importance of phanerophytes was higher at plot level (17.6%) than for the whole sample (12.0%) and at flora level (11.2%), indicating that this life form is important in structuring vegetation on a small spatial scale, but has low differentiation diversity (the b-diversity of Whittaker, 1972). On the other hand, annual species had an opposite trend: although about one fifth of the species were therophytes in any plot, this life form accounted for one third of the flora, indicating a very high differentiation diversity.
3.3. Life form spectrum All the life-form spectra, calculated on the basis of the number of species estimated in the matrix, were very highly correlated with the true one (Table 3). The following reasoning is based only on the spectrum obtained by Sobs; similar conclusions also hold for the other spectra. The life-form proportions, in the spectrum based on Sobs were already relatively stable with 20–25 plots (Fig. 4), which seem enough to obtain a good approximation to the life-form spectrum based on
4. Discussion 4.1. Floristic data Many authors have observed species frequency distributions similar to that found in our sample. Rabinowitz et al. (1986) found a similar picture of species frequency, using a grain of 10 km and an extent of over 500 km, many hundred-fold larger than the present
Table 2 Relative error (RE) of the different estimators over the five life-form data sets investigateda Statistics
Data set
Sobs
Chao2
Jack1
Jack2
Boot
MMmean
Ch G H P T
0.182 0.544 0.308 0.281 0.289
0.179 0.506 0.008 0.147 0.156
0.093 0.458 0.093 0.109 0.098
0.262 0.442 0.052 0.023 0.035
0.111 0.500 0.216 0.202 0.197
0.023 0.433 0.230 0.245 0.142
0.321 0.117 0
0.196 0.067 20
0.170 0.050 0
0.142 0.054 20
0.245 0.078 0
0.215 0.064 0
MRE MSRD OVER
a The mean relative error (MRE), mean square relative deviation (MSRD) and percentage of overestimation (OVER) of each estimators are also reported. The two overestimated values observed are in bold type. Ch, chamaephytes; G, geophytes; H, hemicryptophytes; P, phanerophytes; T, therophytes.
Table 3 Life form spectra emerging from the flora and from the number of species estimated by the estimators for each life form, based on 50 plotsa Life form
Flora
Sobs
Chao2
Jack1
Jack2
Bootstrap
MMmean
Ch G H I P T
2.2 13.3 41.9 0.4 11.2 31.1
2.6 9.1 43.3 0.0 12.0 33.0
0.7 7.9 49.0 0.0 11.0 31.4
2.3 8.5 44.5 0.0 11.6 33.1
1.7 8.1 46.6 0.0 11.4 32.3
2.5 8.8 43.6 0.0 11.9 33.2
2.8 9.7 41.9 0.0 10.9 34.7
0.993
r a
0.989
0.992
0.991
0.993
0.992
Spearman correlation coefficients for the estimated and true spectra are reported. Ch, chamaephytes; G, geophytes; H, hemicryptophytes; P, phanerophytes; T, therophytes.
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survey. Palmer and White (1994), using a variety of grains and extents, all smaller than ours, obtained similar pictures (Palmer, 1995). Our findings were in line with the rule that most species are infrequent and few are widespread (Pielou, 1969; Gaston, 1994, 1996b, 1999). This rule (Raunkiaer, 1934), has been named the ‘‘Law of infrequency’’ (Palmer, 1995) and has negative implications for biodiversity monitoring, implying that any inventory program based on plots, will inevitably miss rare species (Gaston, 1999). Given the limited resource, Gaston (1999) suggested focusing on stratified
random sampling, such as gradsects (Gillison and Brewer, 1985; Austin and Heyligers, 1989) to maximise the information collected and the possibilities of extrapolation. However, at the spatial scale of our work, a few hundreds of hectares (the scale of many nature reserves at least in Europe), random sampling gave encouraging results. The 50 plots, constituting 0.058% of the area of the reserve, took 15–16 days of field activity by two botanists to survey and produced a list of more than two thirds of the total flora. Although the rarest species were certainly missed, a good picture of
Fig. 3. Species richness estimated in the life-form matrices by the various estimators in relation to the number of plots sampled and averaged after 1000 randomised plot sequences. Symbols are as follows: circles, number of observed species (Sobs); quadrates, Michaelis–Menten model (MMean); asterisks, Bootstrap (Boot); triangles, first-order Jackknife (Jack1); diamonds, second-order Jackknife (Jack2); crosses, Chao2 (Chao2). The bold lines represents the reference ‘‘total’’ value.
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the flora was obtained with relatively little field work. Sparks et al. (1997) reported that in 22 grasslands, measuring from 0.2 to 6 ha, 0.13–0.55% of the area needed to be surveyed to collect 90% of the flora using small plots; although grasslands and a reserve do not lead themselves to direct comparison, this would imply that 62–424 further plots are needed to collect 90% of the species, indicating that an enormous work is required to collect a further 23% of species. Species richness per plot has frequently been used for monitoring vegetation stands, but it has rarely been applied to large areas. Future comparison of distribution of species richness values per plot may, however, provide interesting data on ecological trends in the whole reserve. This is particularly important since processes at the scale of plots may have major effects at larger scales (Herben, 2000). 4.2. Species richness estimation The behaviour of the estimators, was rather inconstant in the different data sets, first- and second-order Jackknives giving the best overall performances. Second-order Jackknife gave the best estimate of total species richness, but it was slightly less precise than the first-order Jackknife when applied to data sets with different properties. First-order Jackknife had a higher and always negative, bias but slightly better precision, as already observed (Palmer, 1990, 1991). Walther and Morand (1998) found the first-order Jackknife and
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Chao2 estimators to be the best performers in field trials on parasites, whereas in simulated data sets the firstorder Jackknife gave good results only at smaller sample size, being outperformed by Bootstrap at larger sample sizes. In simulated communities, Zelmer and Esch (1999) found the appropriate kth order Jackknife estimator to be less biased and less influenced by rare species and total species richness, than Bootstrap. The approach used by them was, however, significantly different and cannot be compared with ours. The Chao2 estimator had the lowest precision and a high negative bias. Chazdon et al. (1997) found Chao2 to be the second best performer, after ICE (not tested, since it needs an arbitrary level to define ‘‘rare species’’), giving a stable estimation with only a small number of plots. Chazdon et al. (1997) observed that Chao2 provided a good level of approximation, being relatively insensitive to the number of plots and patchy species distribution. Walther and Morand (1998) also found good performance of Chao2. Our different findings may be due to the different version used (Section 2). The Michaelis–Menten estimator, gave a relatively poor performance. Sobero´n and Llorente (1992) argued that this model was the most appropriate for estimating species richness of large heterogeneous communities, since their structure resembles a lognormal (Preston, 1962) or random-fraction distribution (May, 1975; Tokeshi, 1990, 1996). Keating and Quinn (1998) suggested that the Michaelis–Menten model assumes very even community structure and concluded that it should
Fig. 4. Approximation of the estimated life-form spectrum, based on Sobs and averaged after 1000 randomisation. Error bars represent 99% confidence intervals. Symbols are as follows: diamonds, chamaephytes; squares, geophytes; triangles, phanerophytes; circles, hemicryptophytes; asterisks, therophytes.
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perform well in moderately large species pools where species abundances have a broken-stick distribution. Chazdon et al. (1997) found that the Michaelis–Menten estimator climbed constantly without reaching any asymptotic trend. In our survey, it only performed well in the poorest data set. Bootstrap always gave, negatively biased, poor estimates. Chazdon et al (1997) found the bootstrap estimator climbed constantly without reaching any asymptotic trend. Bootstrap showed a different behaviour, sometimes reaching an asymptotic pattern, but yielding constantly poor estimates. In the present survey, first and second-order Jackknives seemed to be the most reliable applying to sample from limited proportion of the area. Palmer (1990) sampled 8% of an area, more than one hundred fold greater than the percentage sampled by us, obtaining similar results. In five 0.4 ha-large sites, Hellmann and Fowler (1999) reported that for small sample sizes, the least biased estimator was the second-order Jackknife, followed by the first-order Jackknife and Bootstrap. With increases in sample size, these estimators became positively biased in the same order. Hellmann and Fowler (1999) also observed that second-order Jackknife was the least precise estimator, followed by firstorder Jackknife and Bootstrap. However, the sample used by Hellmann and Fowler (1999) was highly biased, since it was based on complete sampling of the area without replacement, limiting the validity of the Jackknife and Bootstrap estimates. 4.3. Estimation of life form spectrum Despite some differences, the sample based life-form spectrum correlated well with that based on the whole flora. The most significant difference was with the geophytes, which were under-represented in the sample based spectrum. The short life cycle of some species in this group and the restricted distribution of others (e.g. Orchidaceae and some wetland plants) reduced their detectability leading to the overrepresentation of other groups. Life forms have been used to describe the features of species assemblages (Cain, 1950). Raunkiaer (1934) and recent authors have demonstrated the dependence of the proportions of life forms on climatic parameters, particularly annual rainfall (Danin and Orshan, 1990, Cabido et al., 1993) or air humidity (Pavo´n et al., 2000). Danin and Orshan (1990) also found a good correlation between the ratios of some life forms and climatic data, the ratios P/Ch and H+G/T being positively related to total annual rainfall. Estimated life-form spectra, or ratios between selected life forms, may be useful indicators for comparing different sites and/or evaluating a given site over time. Temporal comparison of these values may be used to detect changes in the species assemblage at plot and whole sample scales. Relation-
ship to reserve management, vegetation dynamics and environmental changes may be assessed quantitatively by the indications emerging from life-form spectrum (Raunkiaer, 1934; Cain, 1950).
5. Conclusion Although the estimates of species richness were not encouraging in the total data-set or in the five data sets based on life forms, the sample-based evaluation of the flora provided useful information on species richness and complementarity. More than two thirds of the species recorded for the nature reserve were found and a life-form spectrum perfectly related to that based on the whole flora was obtained. The most underrepresented species group was geophytes, presumably less detectable because of their short life cycle and their rarity. This data will enable quantitative estimations of future changes in the flora of the reserve through comparison of basic statistics of species richness, species frequency distributions and life-form spectra and through calculation of derived indices, such as those of beta diversity. The species richness estimates were less significant. As noted by other authors, standard methods to assess species richness over large areas have not been developed. Palmer (1995) observed that we do not yet know how to count species for biodiversity monitoring and Gaston (1996a) commented on our lack of understanding of the relations between relative and absolute values of species richness. The performances of species richness estimators cannot be evaluated definitively. Their application to large data sets is, however, just beginning and some answers may emerge with the accumulation of data. A few attempts have been made for larger spatial scales and species-rich groups, e.g. evaluation of litter-dwelling beetles in the Ouachita Highlands of Arkansas, USA (Carlton and Robinson, 1998). For plants, such studies have only been done for trees (Gimaret-Carpentier et al., 1998; Schreuder et al., 1999), namely for reduced number of species than a whole flora; moreover, for trees it is possible to count individual plants. To our knowledge, estimation methods for the evaluation of plant species richness in relatively large nature reserves have never been tested. Progress in this direction, especially for the landscape or ‘‘park size’’ units, would be useful because decisions on land use are often made on this scale (Colwell and Coddington, 1994).
Acknowledgements We thank Professor Lorenzo Fattorini and Dr. Luana D’Alessandro for useful discussion on sampling strategy. Two anonymous referees and R.H. Marrs provided
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useful criticisms. We thank Dr. Valeria Zoni, Dr. Michele Riccucci, Mr. Adalberto Maccherini, Mr. Fausto Romi and Mr. Elenio Maestripieri for help during field sampling. This research was partly financed by the Municipality of Cinigiano (Grosseto).
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Hellmann, J.J., Fowler, G.W., 1999. Bias, precision, and accuracy of four measures of species richness. Ecological Applications 9, 824–834. Heltse, J.F., Forrester, N.E., 1983. Estimating species richness using the jackknife procedure. Biometrics 39, 1–12. Herben, T., 2000. Correlation between richness per unit area and the species pool cannot be used to demonstrate the species pool effect. Journal of Vegetation Science 11, 123–126. Keating, K.A., Quinn, J.F., 1998. Estimating species richness: the Michaelis–Menten model revisited. Oikos 81, 411–416. Kent M., Coker P., 1992. Vegetation Description and Analysis. A Practical Approach. John Wiley. Maccherini, S., Chiarucci, A., Selvi F., De Dominicis, V., 2001. Flora vascolare della riserva naturale di Poggio all’Olmo (Cinigiano, Grosseto). Atti Soc. Tosc. Sci. Nat. Mem., Serie B (in press). Maccherini, S., Gabellini, A., Morrocchi, Chiarucci, A., De Dominicis, V., 1999. Carta della vegetazione della Riserva Naturale di Poggio all’Olmo. Selca Firenze. Magurran, A.E., 1988. Ecological Diversity and its Measurement. Chapman and Hall, London. May, R.M., 1975. Patterns of species abundance and diversity. In: Cody, M.L., Diamond, J.M. (Eds.), Ecology and Evolution of Communities. Belknap Press, Cambridge, MA, pp. 81–120. Mingoti, S.A., Meeden, G., 192. Estimating the total number of distinct species using presence and absence data. Biometrics 192, 863–875. Norris III, J.L., Pollock, K.H., 1996. Nonparametric MLE under two closed capture–recapture models with heterogeneity. Biometrics 52, 639–649. Orshan, G., 1986. Plant forms as describing vegetation and expressing adaptation to the environment. Annali di Botanica (Roma) 44, 7–38. Palmer, M.W., 1990. The estimation of species richness by extrapolation. Ecology 71, 1195–1198. Palmer, M.W., 1991. Estimating species richness: the second order jackknife reconsidered. Ecology 72, 1512–1513. Palmer, M.W., 1995. How should one count species? Natural Areas Journal 15, 124–135. Palmer, M.W., White, P.S., 1994. Scale dependence and the species– area relationship. American Naturalist 144, 717–740. Pavo´n, N.P., Herna´ndez-Trejo, H., Rico-Gray, V., 2000. Distribution of plant life forms along an altitudinal gradient in the semi-arid valley of Zapotutla´n, Mexico. Journal of Vegetation Science 11, 39–42. Pielou, E.C., 1969. An Introduction to Mathematical Ecology. Wiley Interscience, New York. Pollock, K.H., Otto, M.C., 1983. Robust estimation of population size in closed animal populations from capture–recapture experiments. Biometrics 39, 1035–1049. Polulin, R., 1998. Comparison of three estimators of species richness in parasite component communities. Journal of Parasitology 8, 485–490. Preston, F.W., 1962. The canonical distribution of commonness and rarity. Ecology, 43, 185–215 and 410–432. Raaijmakers, J.G.W., 1987. Statistical analysis of the Michaelis–Menten equation. Biometrics 43, 793–803. Rabinowitz, D., Cairns, D.S., Dillon, T., 1986. Seven forms of rarity and their frequency in the flora of British Isles. In: Soule´, M.E. (Ed.), Conservation Biology. Wiley, New York, pp. 182–204. Raunkiaer, C., 1934. The Life Forms of Plants and Statistical Plant Geography. Clarendon, Oxford. Schreuder, H.T., Williams, M.S., Reich, R.M., 1999. Estimating the number of tree species in a forest community using survey data. Environmental Monitoring and Assessment 56, 293–303. Smith, E.P., van Belle, G., 1984. Nonparametric estimation of species richness. Biometrics 40, 119–129. Sobero´n, J.M., Llorente, J.B., 1992. The use of species accumulation curves for the prediction of species richness. Conservation Biology 7, 480–488. Sparks, T.H., Mountford, J.O., Manchester, S.J., Rothery, P., Treweek, J.R., 1997. Sample size for estimating species lists in vegetation surveys. The Statistician 46, 253–260.
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Tokeshi, M., 1990. Niche apportionment or random assortment: species abundance patterns revisited. Journal of Animal Ecology 59, 1129–1146. Tokeshi, M., 1996. Power fraction: a new explanation of relative abundance patterns in species-rich assemblages. Oikos 75, 543– 550.
Walther, B.A., Morand, S., 1998. Comparative performance of species estimation methods. Parasitology 116, 395–405. Whittaker, R.H., 1972. Evolution and measurement of species diversity. Taxon 21, 213–251. Zelmer, D.A., Esch, G.W., 1999. Robust estimation of parasite component community richness. Journal of Parasitology 85, 592–594.
Evaluation and monitoring of the flora in a nature reserve by estimation methods Alessandro Chiarucci*, Simona Maccherini, Vincenzo De Dominicis Dipartimento di Scienze Ambientali, Universita` di Siena, Via P.A. Mattioli 4, 53100 Siena Italy Received 23 May 2000; received in revised form 26 January 2001; accepted 23 February 2001
Abstract We tested the use of non-parametric estimators of species richness to evaluate the flora of a relatively large (431 ha) nature reserve, using a sampling area much lower than that used in previous studies. Different estimation methods were applied to floristic data obtained from 50 random plots: the number of observed species, the extrapolated accumulation curves based on the Michaelis–Menten model and the non-parametric estimators based on incidence data (Chao2, first-order Jackknife, second-order Jackknife and bootstrap). To test the performance of the estimators, five data sets were created on the basis of life-forms. The estimates were compared with reference values obtained by traditional floristic and vegetation sampling. The power of the different estimation methods could not definitively be determined, but the first- and second-order Jackknives seem to be the most precise. Although total species richness was underestimated, the sample-based approach provided accurate information for quantitative comparison of time series of data related to ecological changes, vegetation dynamics and environmental changes. This sample-based data included basic statistics on species richness and species frequency distributions as well as the life-form spectrum, at the plot and the whole site scales. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Biodiversity; Monitoring; Nature reserves; Species richness; Species richness estimation
1. Introduction Nature reserves are managed with the aim of preserving and restoring biodiversity. To do this, it is essential to quantify and monitor the effects of management using reliable estimates of biodiversity. Biodiversity may be monitored by a range of approaches; one of the most frequently used being maps of vegetation or habitat types. The resolution and subjectivity in delimiting polygons and classifying units limit the validity of this approach. New techniques employing automatic mapping (e.g. Carmel and Kadmon, 1998) have aimed to solve these problems. Since standard floras exist for many countries, there is less subjectivity in using a species diversity approach. Many authors agree that species richness and complementarity are the most straightforward components of biodiversity for evaluation and monitoring, in a landscape context (Magurran, 1988; Colwell and Coddington, 1994; Gaston, 1996a). Moreover, * Corresponding author. Tel.: +39-0577-232872; fax: +39-0577232860. E-mail addresses: [email protected] (A. Chiarucci).
estimating biodiversity through species diversity does not require assumptions about any model of community or landscape structure (Colwell and Coddington, 1994). However, it is difficult, if not impossible, to assess the completeness of species lists (Palmer, 1995; Gaston, 1996a). Estimation methods are useful tools for predicting species richness in large areas based on sampled information (Colwell and Coddington, 1994), Jackknife and bootstrap estimators being the most widely used (Efron and Thisted, 1976; Heltse and Forrester, 1983; Smith and van Belle, 1984). Most tests of these estimation methods have been done using simulated data-sets (Burnham and Overton, 1979; Heltse and Forrester, 1983; Pollock and Otto, 1983; Balta´nas,1992; Mingoti and Meeden, 1992; Norris and Pollock, 1996; Polulin, 1998; Walther and Morand, 1998; Zelmer and Esch, 1999). Authors working with real data have only investigated relatively species-poor assemblages and, as far as plants are concerned, small spatial scales (Palmer, 1990, 1991; Keating and Quinn, 1998; Hellmann and Fowler, 1999). A test of these estimation methods is, therefore needed, over relatively large areas to assess their performance (Palmer, 1990, 1991; Gaston, 1996a).
0006-3207/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(01)00073-8
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The aims of the present study are: (1) to test species richness estimators in a relatively large area, using a limited sample and (2) to verify the use of a sample for the assessment of special components of species diversity, such as the life-form spectrum, frequently used to characterise species assemblages (Orshan, 1986).
2. Material and methods 2.1. Study site The nature reserve of Poggio all’Olmo was selected for this study. The reserve is located in southern Tuscany (Italy, 42 520 0600 N, 11 280 1900 E); it is 431 ha, with an altitude range between 654 and 1016 m. The vegetation (Maccherini et al., 1999; Angiolini et al., 2001) consists of grasslands (22.8%); scrub colonising unmanaged grasslands (26.9%); different woodland types managed as coppice (24.8%); chestnut groves (6%); conifer plantations (16.2%); traditionally managed farmlands (3%) and settlements (0.3%). As a general trend, there is progressive re-naturalisation due to reduced grazing pressure and declining agriculture. Many open areas were planted with conifers and most of the coppiced woods are developing into groves. The site was chosen because of the existence of a comprehensive floristic list (Maccherini et al., 2001), which provided an opportunity to test estimation methods against an assumed ‘‘total’’ reference total value (511 sub-generic taxa). 2.2. Sampling design A random design was chosen to obtain a representative sample. As no vegetation map was yet available, stratified sampling was not used. Two problems were encountered in sampling design: plot size and sample size (number of plots). Since it was not possible to extend specific tests on the effect of plot size to all of the nature reserve, this issue was solved pragmatically. It was decided to use 50-m2 plots, a size intermediate between those recommended for descriptive sampling in herbaceous and woody communities (Kent and Coker, 1992). Almost all the species growing in such an area could be identified in a 30–60 min survey. After having performed a computer simulation (Fattorini, unpublished data), taking into account habitat heterogeneity and costs considerations, a sample size of 50 plots was selected. Plots were located by using random co-ordinates. This design enabled straightforward statistical analysis, since it provides independent and identically distributed data. Plots were marked on detailed aerial photographs and then located on the ground; when it was difficult to locate the point exactly, a location was chosen using random numbers from the nearest point
located. GPS was not used because its error was greater than visual location. 2.3. Data collection Plots were located in the field between 15 March and 15 April 1998. Each site was marked with a wooden post. Plot area was delimited as a circle of 50 m2; early flowering species in the plot were recorded and their cover estimated. Each plot was visited a second time in the period 15 June–10 July 1998, at the height of the vegetative period, when other species were recorded and their cover estimated. Plant specimens are preserved in the Herbarium Universitatis Senensis (SIENA). 2.4. Data analysis Only presence/absence data was used here. Basic statistics on species richness per plot and species frequency were used to characterise the site and for future comparisons. Different estimators of species richness were computed with the program EstimateS# 5 (Colwell, 1997): the extrapolated accumulation curves based on the Michaelis–Menten model (Raaijmakers, 1987; hereafter referred as MMmean) and non-parametric estimators based on incidence data (Colwell and Coddington, 1994), namely first-order Jackknife (Jack1), secondorder Jackknife (Jack2), bootstrap (Boot; Burnham and Overton, 1979; Heltse and Forrester, 1983; Smith and van Belle, 1984) and the bias-corrected Chao2 (Chao, 1987, performed by the program upgrade, available at the same URL). The number of species observed (Sobs) was also calculated. For details on estimators see Colwell and Coddington (1994) and Chazdon et al. (1997). All estimations were averaged over 1000 randomised plot sequences. Since one data-set was available, statistical comparison between sites, as done by others (Palmer, 1990; Keating and Quinn, 1998; Walther and Morand, 1998), was not possible. For explorative aims, the data matrix was divided into five data sets, based on Raunkiaer’s (1934) life forms, each showing different species richness and frequency distributions (Table 1). Although these matrices were not independent, they were useful to test estimator performance on data sets with different properties, as in the case of different types of organisms or sites. Relative error (RE) and square relative deviation (SRD) were used to evaluate the performances of the estimators. RE is a measure of the relative difference between the value estimated and the true value, as given by the formula:
RE ¼
Sest St St
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where Sest is the estimated value and St is the true value of species richness. SRD is the square of RE and measures the closeness of the estimator to the true value, without considering the sign of the deviation: it weighs estimates further from St more heavily. Estimator performances over the life-form data sets were assessed by the mean value of RE (MRE) and SRD (MSRD), and by the ‘‘percentage of overestimation’’ (OVER). MRE is equivalent to the ‘‘mean deviation’’ of Palmer (1990) and to the ‘‘bias’’ of Hellmann and Fowler (1999), except that it is scaled by the true value, being equivalent to the ‘‘bias’’ used by Walther and Morand (1998). MSRD is equivalent to the ‘‘mean square proportional deviation’’ of Palmer (1990) and the ‘‘deviation’’ of Walther and Morand (1998). If all RE values have the same sign, MRE and MSRD are related. However, if an estimator has a range of estimations above and below the true value, it may have a low MRE but a high MSRD. An unbiased estimator has and MRE and an MSRD of zero an OVER of 50% (Palmer, 1990; Walther and Morand, 1998). The estimates from the life-form matrices, were used to estimate the life-form spectrum of the flora, by preparing life-form spectra (in%) with the numbers of species in each life-form estimated by the different estimators. The correlation coefficient between each of these spectra and the spectrum calculated on the complete flora, was calculated.
3. Results 3.1. Floristic data The 50 plots sampled, constituting 0.058% of the total area, produced a list of 342 sub-generic taxa (hereafter referred to as ‘‘species’’), which was 66.9% of the species recorded in the reserve. Species richness per plot showed a wide range of values, from a minimum of two (in a conifer plantation, where only the two planted
species were found) to a maximum of 93 (in sparse Prunus spinosa L. shrubland, invading a species-rich grassland). Total number of occurrences (speciesplots) was 1998. Mean species richness per plot was 39.8; distribution of species richness per plot, although rather uneven, was not significantly different from a normal distribution (test Shapiro-Wilk W=0.987, P < 0.450). Most species recorded had very low frequencies (Fig. 1). Ninety-five species (27.8% of the species recorded) were found in a single plot (‘‘unique species’’, Colwell and Coddington, 1994) and 209 species (61.1%) were found in five or less plots; a further 71 species (20.8%) were found in the frequency class from six to 10 plots. Only six species had a frequency higher than 25/ 50, and the highest frequency (by Crataegus monogyna Jacq. and Rosa canina L.) was 32/50. 3.2. Species richness estimation Hardly any of the estimators reached an asymptotic pattern in the 50 plots (Fig. 2). Sobs was obviously the lowest pattern with the worst RE (0.331). The MMmean and the Boot estimators showed highly biased negative estimates: 388.7 and 384.7 species, respectively. The Boot curve was constantly the second worst, and the MMmean curve gave the highest estimation when few plots were sampled, except for Chao2 in one–two plots, but it quickly became one of the worst curves. The other estimators gave better results, although all underestimated the true number of species. Jack1 and Chao2 gave very similar estimations (435.1 and 431.3 species, respectively), and had similar patterns, except for very few plots. Jack2 gave the best estimation (480.2 species) which, however, was negatively biased (RE=0.056). With one exception, all the estimators provided negative estimates for the life-form data sets with 50 plots (Table 2). Sobs gave the lowest estimates, with the highest negative MRE and 0% overestimation. Chao2 was the second worst estimator, with a very biased MRE and an
Table 1 Descriptive statistics for the different data sets, from the Poggio all’Olmo Nature Reserve, used for the analyses; Ch, chamaephytes; G, geophytes; H, hemicryptophytes; P, phanerophytes; T, therophytes Data set
Total number of species in the sample
Species frequency classes in 50 plots (% of species found in the n plots) Very rare (1–10)
Rare (11–20)
Average (21–30)
Frequent (31–40)
Very frequent (41–50)
Mean species richness per plot
S.D. of species richness per plot
Range in species richness per plot
Ch G H P T
9 31 148 41 113
77.8 90.3 78.4 70.7 88.5
22.2 9.7 18.2 17.1 10.6
0 0 3.4 9.8 0.9
0 0 0 2.4 0
0 0 0 0 0
1.0 3.0 18.1 7.0 10.7
1.4 2.0 11.3 3.6 10.9
0–5 0–12 0–47 1–14 0–39
Total
342
81.9
14.9
2.6
0.6
0
39.8
21.7
2–93
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MSRD worse than Sobs, indicating very low precision. Boot and MMmean had similar values of MSRD and MRE, constantly underestimated true species richness and had intermediate precision. Jack1 and Jack2 had
the best performances. Jack1 was less close to the true value, with a constant underestimation, but was slightly more precise (lower MSRD) than Jack2. The only overestimation was by Jack2 for the H data set (the
Fig. 1. Relationship between species rank and species frequency.
Fig. 2. Species richness according to different estimators in relation to the number of plots sampled and averaged after 1000 randomised plot sequences. Symbols are as follows: circles, number of observed species (Sobs); squares, Michaelis–Menten model (MMean); asterisks, Bootstrap (Boot); triangles, first-order Jackknife (Jack1); diamonds, second-order Jackknife (Jack2); crosses, Chao2 (Chao2). The bold line represents the reference ‘‘total’’ value.
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richest and intermediately skewed). When checking the behaviour of the estimators in each data-set (Fig. 3), interesting results emerge. For chamaephytes, Jack 2 and Jack 1 showed a declining phase, after reaching the true value, because the very rare species of this group were still lacking in the sample and the increasing weight of duplicates. Less than half of the geophytic species were found in the sample and all estimators gave highly biased negative estimates. For hemicryptophytes, the richest data set, Jack1, Jack2 and Chao2 showed no sign of a decrease in their ascending phase. The other two data sets provided results similar to the whole data set.
the whole flora. Geophytes were the most (negatively) biased, leading to overrepresentation of the other groups. The weight of some life forms changed substantially from the plot to the whole sample (Fig. 4): relative importance of phanerophytes was higher at plot level (17.6%) than for the whole sample (12.0%) and at flora level (11.2%), indicating that this life form is important in structuring vegetation on a small spatial scale, but has low differentiation diversity (the b-diversity of Whittaker, 1972). On the other hand, annual species had an opposite trend: although about one fifth of the species were therophytes in any plot, this life form accounted for one third of the flora, indicating a very high differentiation diversity.
3.3. Life form spectrum All the life-form spectra, calculated on the basis of the number of species estimated in the matrix, were very highly correlated with the true one (Table 3). The following reasoning is based only on the spectrum obtained by Sobs; similar conclusions also hold for the other spectra. The life-form proportions, in the spectrum based on Sobs were already relatively stable with 20–25 plots (Fig. 4), which seem enough to obtain a good approximation to the life-form spectrum based on
4. Discussion 4.1. Floristic data Many authors have observed species frequency distributions similar to that found in our sample. Rabinowitz et al. (1986) found a similar picture of species frequency, using a grain of 10 km and an extent of over 500 km, many hundred-fold larger than the present
Table 2 Relative error (RE) of the different estimators over the five life-form data sets investigateda Statistics
Data set
Sobs
Chao2
Jack1
Jack2
Boot
MMmean
Ch G H P T
0.182 0.544 0.308 0.281 0.289
0.179 0.506 0.008 0.147 0.156
0.093 0.458 0.093 0.109 0.098
0.262 0.442 0.052 0.023 0.035
0.111 0.500 0.216 0.202 0.197
0.023 0.433 0.230 0.245 0.142
0.321 0.117 0
0.196 0.067 20
0.170 0.050 0
0.142 0.054 20
0.245 0.078 0
0.215 0.064 0
MRE MSRD OVER
a The mean relative error (MRE), mean square relative deviation (MSRD) and percentage of overestimation (OVER) of each estimators are also reported. The two overestimated values observed are in bold type. Ch, chamaephytes; G, geophytes; H, hemicryptophytes; P, phanerophytes; T, therophytes.
Table 3 Life form spectra emerging from the flora and from the number of species estimated by the estimators for each life form, based on 50 plotsa Life form
Flora
Sobs
Chao2
Jack1
Jack2
Bootstrap
MMmean
Ch G H I P T
2.2 13.3 41.9 0.4 11.2 31.1
2.6 9.1 43.3 0.0 12.0 33.0
0.7 7.9 49.0 0.0 11.0 31.4
2.3 8.5 44.5 0.0 11.6 33.1
1.7 8.1 46.6 0.0 11.4 32.3
2.5 8.8 43.6 0.0 11.9 33.2
2.8 9.7 41.9 0.0 10.9 34.7
0.993
r a
0.989
0.992
0.991
0.993
0.992
Spearman correlation coefficients for the estimated and true spectra are reported. Ch, chamaephytes; G, geophytes; H, hemicryptophytes; P, phanerophytes; T, therophytes.
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survey. Palmer and White (1994), using a variety of grains and extents, all smaller than ours, obtained similar pictures (Palmer, 1995). Our findings were in line with the rule that most species are infrequent and few are widespread (Pielou, 1969; Gaston, 1994, 1996b, 1999). This rule (Raunkiaer, 1934), has been named the ‘‘Law of infrequency’’ (Palmer, 1995) and has negative implications for biodiversity monitoring, implying that any inventory program based on plots, will inevitably miss rare species (Gaston, 1999). Given the limited resource, Gaston (1999) suggested focusing on stratified
random sampling, such as gradsects (Gillison and Brewer, 1985; Austin and Heyligers, 1989) to maximise the information collected and the possibilities of extrapolation. However, at the spatial scale of our work, a few hundreds of hectares (the scale of many nature reserves at least in Europe), random sampling gave encouraging results. The 50 plots, constituting 0.058% of the area of the reserve, took 15–16 days of field activity by two botanists to survey and produced a list of more than two thirds of the total flora. Although the rarest species were certainly missed, a good picture of
Fig. 3. Species richness estimated in the life-form matrices by the various estimators in relation to the number of plots sampled and averaged after 1000 randomised plot sequences. Symbols are as follows: circles, number of observed species (Sobs); quadrates, Michaelis–Menten model (MMean); asterisks, Bootstrap (Boot); triangles, first-order Jackknife (Jack1); diamonds, second-order Jackknife (Jack2); crosses, Chao2 (Chao2). The bold lines represents the reference ‘‘total’’ value.
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the flora was obtained with relatively little field work. Sparks et al. (1997) reported that in 22 grasslands, measuring from 0.2 to 6 ha, 0.13–0.55% of the area needed to be surveyed to collect 90% of the flora using small plots; although grasslands and a reserve do not lead themselves to direct comparison, this would imply that 62–424 further plots are needed to collect 90% of the species, indicating that an enormous work is required to collect a further 23% of species. Species richness per plot has frequently been used for monitoring vegetation stands, but it has rarely been applied to large areas. Future comparison of distribution of species richness values per plot may, however, provide interesting data on ecological trends in the whole reserve. This is particularly important since processes at the scale of plots may have major effects at larger scales (Herben, 2000). 4.2. Species richness estimation The behaviour of the estimators, was rather inconstant in the different data sets, first- and second-order Jackknives giving the best overall performances. Second-order Jackknife gave the best estimate of total species richness, but it was slightly less precise than the first-order Jackknife when applied to data sets with different properties. First-order Jackknife had a higher and always negative, bias but slightly better precision, as already observed (Palmer, 1990, 1991). Walther and Morand (1998) found the first-order Jackknife and
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Chao2 estimators to be the best performers in field trials on parasites, whereas in simulated data sets the firstorder Jackknife gave good results only at smaller sample size, being outperformed by Bootstrap at larger sample sizes. In simulated communities, Zelmer and Esch (1999) found the appropriate kth order Jackknife estimator to be less biased and less influenced by rare species and total species richness, than Bootstrap. The approach used by them was, however, significantly different and cannot be compared with ours. The Chao2 estimator had the lowest precision and a high negative bias. Chazdon et al. (1997) found Chao2 to be the second best performer, after ICE (not tested, since it needs an arbitrary level to define ‘‘rare species’’), giving a stable estimation with only a small number of plots. Chazdon et al. (1997) observed that Chao2 provided a good level of approximation, being relatively insensitive to the number of plots and patchy species distribution. Walther and Morand (1998) also found good performance of Chao2. Our different findings may be due to the different version used (Section 2). The Michaelis–Menten estimator, gave a relatively poor performance. Sobero´n and Llorente (1992) argued that this model was the most appropriate for estimating species richness of large heterogeneous communities, since their structure resembles a lognormal (Preston, 1962) or random-fraction distribution (May, 1975; Tokeshi, 1990, 1996). Keating and Quinn (1998) suggested that the Michaelis–Menten model assumes very even community structure and concluded that it should
Fig. 4. Approximation of the estimated life-form spectrum, based on Sobs and averaged after 1000 randomisation. Error bars represent 99% confidence intervals. Symbols are as follows: diamonds, chamaephytes; squares, geophytes; triangles, phanerophytes; circles, hemicryptophytes; asterisks, therophytes.
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perform well in moderately large species pools where species abundances have a broken-stick distribution. Chazdon et al. (1997) found that the Michaelis–Menten estimator climbed constantly without reaching any asymptotic trend. In our survey, it only performed well in the poorest data set. Bootstrap always gave, negatively biased, poor estimates. Chazdon et al (1997) found the bootstrap estimator climbed constantly without reaching any asymptotic trend. Bootstrap showed a different behaviour, sometimes reaching an asymptotic pattern, but yielding constantly poor estimates. In the present survey, first and second-order Jackknives seemed to be the most reliable applying to sample from limited proportion of the area. Palmer (1990) sampled 8% of an area, more than one hundred fold greater than the percentage sampled by us, obtaining similar results. In five 0.4 ha-large sites, Hellmann and Fowler (1999) reported that for small sample sizes, the least biased estimator was the second-order Jackknife, followed by the first-order Jackknife and Bootstrap. With increases in sample size, these estimators became positively biased in the same order. Hellmann and Fowler (1999) also observed that second-order Jackknife was the least precise estimator, followed by firstorder Jackknife and Bootstrap. However, the sample used by Hellmann and Fowler (1999) was highly biased, since it was based on complete sampling of the area without replacement, limiting the validity of the Jackknife and Bootstrap estimates. 4.3. Estimation of life form spectrum Despite some differences, the sample based life-form spectrum correlated well with that based on the whole flora. The most significant difference was with the geophytes, which were under-represented in the sample based spectrum. The short life cycle of some species in this group and the restricted distribution of others (e.g. Orchidaceae and some wetland plants) reduced their detectability leading to the overrepresentation of other groups. Life forms have been used to describe the features of species assemblages (Cain, 1950). Raunkiaer (1934) and recent authors have demonstrated the dependence of the proportions of life forms on climatic parameters, particularly annual rainfall (Danin and Orshan, 1990, Cabido et al., 1993) or air humidity (Pavo´n et al., 2000). Danin and Orshan (1990) also found a good correlation between the ratios of some life forms and climatic data, the ratios P/Ch and H+G/T being positively related to total annual rainfall. Estimated life-form spectra, or ratios between selected life forms, may be useful indicators for comparing different sites and/or evaluating a given site over time. Temporal comparison of these values may be used to detect changes in the species assemblage at plot and whole sample scales. Relation-
ship to reserve management, vegetation dynamics and environmental changes may be assessed quantitatively by the indications emerging from life-form spectrum (Raunkiaer, 1934; Cain, 1950).
5. Conclusion Although the estimates of species richness were not encouraging in the total data-set or in the five data sets based on life forms, the sample-based evaluation of the flora provided useful information on species richness and complementarity. More than two thirds of the species recorded for the nature reserve were found and a life-form spectrum perfectly related to that based on the whole flora was obtained. The most underrepresented species group was geophytes, presumably less detectable because of their short life cycle and their rarity. This data will enable quantitative estimations of future changes in the flora of the reserve through comparison of basic statistics of species richness, species frequency distributions and life-form spectra and through calculation of derived indices, such as those of beta diversity. The species richness estimates were less significant. As noted by other authors, standard methods to assess species richness over large areas have not been developed. Palmer (1995) observed that we do not yet know how to count species for biodiversity monitoring and Gaston (1996a) commented on our lack of understanding of the relations between relative and absolute values of species richness. The performances of species richness estimators cannot be evaluated definitively. Their application to large data sets is, however, just beginning and some answers may emerge with the accumulation of data. A few attempts have been made for larger spatial scales and species-rich groups, e.g. evaluation of litter-dwelling beetles in the Ouachita Highlands of Arkansas, USA (Carlton and Robinson, 1998). For plants, such studies have only been done for trees (Gimaret-Carpentier et al., 1998; Schreuder et al., 1999), namely for reduced number of species than a whole flora; moreover, for trees it is possible to count individual plants. To our knowledge, estimation methods for the evaluation of plant species richness in relatively large nature reserves have never been tested. Progress in this direction, especially for the landscape or ‘‘park size’’ units, would be useful because decisions on land use are often made on this scale (Colwell and Coddington, 1994).
Acknowledgements We thank Professor Lorenzo Fattorini and Dr. Luana D’Alessandro for useful discussion on sampling strategy. Two anonymous referees and R.H. Marrs provided
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useful criticisms. We thank Dr. Valeria Zoni, Dr. Michele Riccucci, Mr. Adalberto Maccherini, Mr. Fausto Romi and Mr. Elenio Maestripieri for help during field sampling. This research was partly financed by the Municipality of Cinigiano (Grosseto).
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