Small-island effect in snake communities on islands of an inundated lake: The need to include zeroes

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Basic and Applied Ecology xxx (2014) xxx–xxx

mall-island effect in snake communities on islands of annundated lake: The need to include zeroesanping Wanga, Qiang Wua, Xi Wanga, Chao Liua, Lingbing Wua,huanwu Chena, Dapeng Gea, Xiao Songa, Cangsong Chena,b,ichun Xua,c, Ping Dinga,∗

The Key Laboratory of Conservation Biology for Endangered Wildlife of the Ministry of Education, College of Lifeciences, Zhejiang University, Hangzhou 310058, ChinaZhejiang Museum of Natural History, Hangzhou 310012, ChinaCollege of Life Sciences, China Jiliang University, Hangzhou 310018, China

eceived 30 April 2014; received in revised form 16 October 2014; accepted 17 October 2014

bstract

The small-island effect (SIE), i.e. the pattern that species richness on islands below a certain threshold area varies independentlyf area, has become a widely accepted part of the theoretical framework of island biogeography and biodiversity research.owever, because very few previously published datasets include islands without species, the role of S = 0 in generating the SIE

s rarely examined. Here, we tested the role of S = 0 in generating the SIE for the first time by using snake data collected on 48slands in the Thousand Island Lake, China. To determine the role of S = 0 in generating the SIE, we used regression analysisnd path analysis to conduct separate analyses for all the islands (including islands with no snake records) and for the 29 islandsnhabited by snakes. When including islands with no snakes, model selection based on AICc identified the left-horizontal SIEodel as the most parsimonious model. When excluding islands with no snakes, model selection based on AICc identified

he simple logarithm model without an SIE as the best model. Path analysis detected an SIE for the full dataset, but none forhe dataset excluding islands with no snakes. Our results suggest that S = 0 plays an important role in generating the SIE andxcluding islands with no snakes can lead to erroneously not detecting an SIE when in fact an SIE exists. We conclude that, forhe robust detection of the SIE, islands with no species should not be excluded in future studies.

usammenfassung

Der ‘small-island-effect’ (SIE), d.h., der Befund, dass der Artenreichtum auf Inseln mit einer Fläche unterhalb eines bes-immten Schwellenwerts unabhängig von der Inselfläche variiert, ist zu einem weithin akzeptierten Teil des theoretischen

Please cite this article in press as: Wang, Y., et al. Small-island effect in snake communities on islands of an inundated lake: The need toinclude zeroes. Basic and Applied Ecology (2014), http://dx.doi.org/10.1016/j.baae.2014.10.006

ebäudes der Insel-Biogeographie und der Biodiversitätsforschung geworden. Da indessen nur sehr wenige publizierte Daten-ätze Inseln ohne Arten einschließen, ist die Funktion von S = 0 beim Zustandekommen des SIE selten untersucht worden. Hieresteten wir erstmalig diese Funktion mit einem Datensatz über die Schlangen auf 48 Inseln im Qiandao-Stausee (China).

Wir benutzten Regressionsanalysen und Pfadanalysen und nahmen getrennte Analysen für alle Inseln (d.h. ein-chließlich der Inseln mit S = 0) und nur die 29 von Schlangen bewohnten Inseln vor. Wenn die Inseln ohne Schlangen

∗Corresponding author. Tel.: +86 571 88206468; fax: +86 571 88206468.E-mail address: [email protected] (P. Ding).

ttp://dx.doi.org/10.1016/j.baae.2014.10.006439-1791/© 2014 Gesellschaft für Ökologie. Published by Elsevier GmbH. All rights reserved.

dx.doi.org/10.1016/j.baae.2014.10.006

dx.doi.org/10.1016/j.baae.2014.10.006

mailto:[email protected]

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inbezogen wurden, identifizierten wir mit AICc das links-horizontale SIE-Modell als das sparsamste Modell. Wenn die Inselnhne Schlangen weggelassen wurden, war ein einfaches logarithmisches Modell ohne SIE das beste Modell. Die Pfadanalysentdeckte einen SIE für den vollen Datensatz, aber keinen SIE für den reduzierten Datensatz. Unsere Ergebnisse legen nahe, dass

= 0 eine wichtige Rolle bei der Bildung eines SIE spielt und dass die Nichtberücksichtigung von Inseln ohne Schlangen dazuühren kann, dass kein SIE entdeckt wird, obwohl er tatsächlich existiert. Wir schließen, dass bei zukünftigen Untersuchungenür die belastbare Identifizierung des SIE Inseln ohne Arten nicht eliminiert werden sollten.

2014 Gesellschaft für Ökologie. Published by Elsevier GmbH. All rights reserved.

eywords: Breakpoint regression; Landbridge archipelago; Multimodel inference; Path analysis; Logarithm function; Minimum area require-

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ent (MAR); Species–area relationship; Thousand Island Lake

ntroduction

The small-island effect (hereafter SIE) is a cryptic patternhat has been largely ignored by most ecologists and bio-eographers in the species–area relationship studies prior to000 (Lomolino, 2000; Lomolino & Weiser, 2001). The SIEccurs when species richness (S) on islands below a certainhreshold area varies more or less independently of area (A)Lomolino, 2000; Triantis et al., 2006). Although the pat-ern was first described almost 50 years ago (Niering, 1963;

hitehead & Jones, 1969), SIE studies only became popu-ar after Lomolino and Weiser (2001) applied the breakpointegression model for the first time to identify SIEs statisti-ally. Ever since, the SIE is becoming more and more partf the theoretical framework of island biogeography and bio-iversity research (Gentile & Argano, 2005; Triantis et al.,006; Whittaker & Fernandez-Palacios, 2007; Dengler, 2010;ang et al., 2012a).However, there are still serious debates over how to test

or SIEs and whether they occur at all (Burns, McHardy, Pledger, 2009; Dengler, 2010; Tjørve & Tjørve, 2011;riantis & Sfenthourakis, 2012). The methods for the detec-

ion of SIEs often are flawed in one way or another, includingot accounting for model complexity, not comparing all rel-vant models, not including islands with no species, andgnoring the effects of logarithmic data transformations andabitat diversity on generating SIEs (Triantis et al., 2006;urns et al., 2009; Dengler, 2010). All these methodologi-al shortcomings have drawn some attention and have beenomewhat well addressed (e.g. Triantis et al., 2006; Burnst al., 2009; Sfenthourakis & Triantis, 2009; Dengler, 2010),xcept the role of S = 0 (islands with no species) in generatinghe SIE.

Whether or not we should include islands with no speciesS = 0) is an important issue in SIE studies in particularDengler, 2010; Morrison, 2014), and in species–area rela-ionship studies in general (Williams, 1996). In most previoustudies, islands with no species are simply excluded proba-ly because such islands cause trouble when fitting a powerodel (S = cAz, where c is the intercept and z is the slope)

Please cite this article in press as: Wang, Y., et al. Small-island effect ininclude zeroes. Basic and Applied Ecology (2014), http://dx.doi.org/10.1

n its linearized form since log(0) is undefined (Dengler,010). However, islands with no species should not bexcluded at least for two reasons. First, S = 0 is within the

4ot

ormal range of the variation of species richness, especiallyn small islands (Williams, 1996; Morrison, 2011). Sec-nd, from a statistical perspective, the exclusion of islandsith no species would bias the parameter estimate of c,

, and S (Williams, 1996), thus likely lead to the erro-eous detection of SIEs (Dengler, 2010). However, becausef the paucity of studies reporting islands without speciesDengler, 2010), the role of S = 0 in generating SIEs remainsbscure.

In this study, we tested the role of S = 0 in generating SIEsor the first time using snake data from islands created by thenundation of the Thousand Island Lake, China. We used tworoad sets of analyses, i.e. regression analyses and path analy-es, to detect the SIE. First, we used an information–theoreticultimodel inference approach to compare the fit of a loga-

ithm model without an SIE with two breakpoint regressionodels with SIEs (Dengler, 2010). Second, we used a method

ased on path analysis (Fattorini, 2006a) that simultaneouslyncorporates island area and habitat diversity into detectinghe SIE (Triantis et al., 2006). We hypothesized that the exclu-ion of islands with no species would influence the detectionf the SIE because towards the far-left, the shape of thepecies–area curve is mostly determined by the increasingraction of islands with no species (Williams, 1996; Dengler,009).

aterials and methods

tudy sites

The Thousand Island Lake (29◦22′–29◦50′N,18◦34′–119◦15′E) is a large man-made hydroelectriceservoir formed in 1959 by the damming of the Xinanjiangiver in Zhejiang Province, China (Wang, Zhang, Feeley,

iang, & Ding, 2009). Construction of the Xinanjiang damnundated an area of 573 km2 when the water reached itsnal level (108 m a.s.l.), creating 1078 landbridge islands

arger than 0.25 ha out of former hilltops (Wang, Bao, Yu,u, & Ding, 2010). The total land area of the archipelago is

snake communities on islands of an inundated lake: The need to016/j.baae.2014.10.006

09 km . Forests on islands were clear cut before the creationf the dam (Wang et al., 2012a). The major vegetation onhe islands is thus now a successional forest dominated by

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he Masson pine Pinus massoniana (Wang, Chen, & Ding,


011). The climate is typical of the subtropical monsoonone and highly seasonal. The average annual temperatures 17.0 ◦C, with the daily extremes ranging from −7.6 ◦C ininter to 41.8 ◦C in summer. Annual rainfall in the study

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able 1. Characteristics of the 48 study islands in the Thousand Islandainland.

sland code Island area(ha)

Isolation (m) Number ofhabitats (n)

1289.23 897.41 7

143.19 1415.09 6

109.03 964.97 6

55.08 953.95 5

46.37 729.80 5

32.29 1936.95 5

5.69 21.85 3

3.42 583.00 4

2.90 1785.30 3

0 2.83 1238.14 4

1 2.29 973.85 4

2 2.23 3261.96 3

3 2.00 1042.38 3

4 1.93 888.05 4

5 1.74 2293.25 3

6 1.54 711.04 3

7 1.52 849.88 3

8 1.52 2849.99 3

9 1.40 1760.34 3

0 1.33 4217.10 3

1 1.26 54.86 3

2 1.20 657.72 3

3 1.20 2128.52 3

4 1.17 2453.37 3

5 1.15 847.12 3

6 1.03 1458.81 3

7 1.01 2437.85 4

8 1.01 2103.85 3

9 0.97 938.85 3

0 0.96 3133.96 3

1 0.91 1339.71 4

2 0.86 2321.51 3

3 0.83 2298.50 3

4 0.83 1098.58 4

5 0.80 2097.52 3

6 0.80 102.60 3

7 0.73 1320.40 3

8 0.67 1139.87 3

9 0.59 640.53 3

0 0.59 1018.42 3

1 0.57 3712.31 3

2 0.51 3073.21 3

3 0.43 2658.07 2

4 0.42 2073.07 2

5 0.34 2137.68 2

6 0.30 1198.58 3

7 0.30 1086.03 2

8 0.02 3093.21 2

cology xxx (2014) xxx–xxx 3

rea is 1430 mm, with an average of 155 days of precipitation


er year (Wang et al., 2009).The research was conducted across a set of 48 islands.

hese islands were selected (1) to represent a range of areand degree of isolation from mainland (Table 1); (2) to cover

Lake, China. Island isolation is given as distance to the nearest

Speciesrichness (S)

Number oftransects (n)

Total length oftransects (m)

12 8 32006 4 16006 4 16008 2 8004 2 8005 2 8003 1 3752 1 3002 1 2752 1 1501 1 3000 1 4002 1 3002 1 2501 1 3002 1 3750 1 2502 1 1751 1 3750 1 1253 1 2000 1 2252 1 2253 1 2501 1 2750 1 2503 1 2502 1 2500 1 2000 1 2500 1 2751 1 2252 1 2751 1 2501 1 3250 1 3000 1 3000 1 3250 1 2250 1 2501 1 2000 1 750 1 1150 1 450 1 401 1 1500 1 1750 1 20

dx.doi.org/10.1016/j.baae.2014.10.006


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he minimum area requirement (hereafter MAR; the smallestsland that could maintain a population) of the snakes in theegion (Table 1) (Dardanelli, Nores, & Nores, 2006); and (3)o ensure the survey effort on each island was large enough sohat all species present could be thoroughly surveyed. Eachsland was surveyed 30 times, which was sufficient to measurenake richness as demonstrated by the asymptotic behaviourf our species accumulation curve (Wang, Wang, & Ding,012b).

ampling methods

nake samplingWe used the line-transect method (Wang et al., 2012b)

o determine snake occupancy on the study islands duringhe breeding seasons between April and July from 2009 to013. To facilitate surveys, we cut transect trails (ca. 20 cmide) that traversed the small islands entirely and the moun-

ain ridges of large islands (Wang et al., 2012b). To accountor the greater habitat diversity associated with larger areaTable 1), the sampling effort was roughly proportional to logisland area) (Wang et al., 2009, 2012b). Accordingly, eightransect trails were sampled on island 1 (the largest island,rea > 1000 ha), four on islands 2–3 (1000 > area > 100 ha),wo on islands 4–6 (100 > area > 10 ha) and one on each ofhe remaining small islands (area ≈ 1 ha for most islands;able 1) (Wang et al., 2012b).Surveys were conducted both in the daytime and in the

ight because some species are diurnal while others are noc-urnal in the region (Huang, 1990; Wang et al., 2012b). Duringhe survey, an observer usually walked each transect at ateady pace (ca. 10 m min−1) searching the ground and treeoles with 8 × 42 binoculars in the daytime (8:00–14:00)nd with a 12 V DC lamp at night (19:00–24:00) (Wang etl., 2012b). Any snakes detected within 10 m of the transectrails were recorded. Once a snake was detected, the timepent in identification was excluded from the elapsed surveyime. All snakes encountered were identified according touang (1990) and Zhao (2006). A total of 12 snake speciesere found on the islands (Table 1; also see Appendix A:able 1). We used global positioning system (GPS) receivers

o record the length of each transect (Table 1). Each islandas surveyed 30 times, with 15 times in the daytime and5 times in the night. Surveys were not conducted duringnclement weather such as heavy rains or strong winds. Tovoid possible systematic sampling bias owing to observeratigue or weather conditions, the order in which islands wereurveyed and the directions in which the trails were walkedere randomized and rotated (Wang et al., 2012b).

abitat sampling


To evaluate the role of habitat diversity in generating theIE, we recorded and classified all habitat types on each

sland (Table 1). We used their number as a measure of habi-at diversity (Triantis et al., 2006; Wang et al., 2012b). We

im2t

cology xxx (2014) xxx–xxx

dentified habitat types mainly by examining the substratend the vegetation cover (Wang et al., 2012b). Photographsf all habitat types on each island were taken as a recorduring the intensive surveys from April to November in 2007Wang et al., 2010, 2012b). Considering the requirements ofnakes (Huang, 1990; Zhao, 2006; Mullin & Seigel, 2009),ll habitat types encountered on the complete areas of theslands were identified and classified as follows: (1) coniferorest, (2) broadleaved forest, (3) coniferous-broadleavedixed forest, (4) bamboo grove, (5) shrubland, (6) grassland,

nd (7) farmland (Wang et al., 2010, 2012b).

tatistical analyses

We used two broad sets of analyses, i.e. regression analysesnd path analyses, to detect the SIE in snake communities inur study system. To determine the role of S = 0 in generatinghe SIE, we conducted separate analyses for all the islandsxcluding one island that was smaller than the MAR of snakesn the region (see Morrison, 2014 and our Discussions sec-ion) and for the 29 islands with snake occurrences (Table 1).

egression analyses

To evaluate whether an SIE exists in our study system, weompared the simple linear model without an SIE (Eq. (1))ith the following two most widely used breakpoint regres-

ion models that were proposed by Lomolino and Weiser2001) (the left-horizontal SIE model; Eq. (2)) and Dengler2010) (a continuous SIE model; Eq. (3)).

= c1 + z1 log A (1)

= c1 + (log A > T ) z1 (log A − T ) (2)

= c1 + (log A ≤ T ) z1 log A

+ (log A > T )[z1 T + z2 (log A − T )

](3)

In the above equations, S stands for species richness, A forrea, while ci (intercept), zi (slopes) and T (breakpoint) aretted parameters. The logical expressions in round parenthe-es will return value 1 if they are true and 0 if they are falseDengler, 2010; Wang et al., 2012a).

We used the logarithm model (also referred to as the semi-ogarithmic or the exponential model; Eq. (1)) (Gleason,922) as the basic function to detect the SIE mainly forhree reasons. First and most important, the logarithm modelnables islands with S = 0 to be included in the analysis.lthough in some cases log(S + 1) = log C + z log A can besed to include islands with S = 0, such transformation is


nherently flawed because it leads to a strong bias in the esti-ation of residuals, Log C and z (Williams, 1995; Fattorini,

006b; Wilson, 2007). Moreover, since we want to check forhe effect of adding zeros, there is no point to use such a

dx.doi.org/10.1016/j.baae.2014.10.006


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ransformation. Therefore, such altered form of power func-ion is not used here. Second, it allows the easy creation ofariants that incorporate the SIE (Lomolino & Weiser, 2001;engler, 2010). Finally, it is widely used in many SIE studies

e.g. Niering, 1963; Whitehead & Jones, 1969; Woodroffe,986; Morrison, 1997; Lomolino & Weiser, 2001; Morrison

Spiller, 2008; Dengler, 2010), which allows comparisonsith previous literatures.We fitted all the equations with the non-linear regres-

ion module of Statistica 8.0 (StatSoft Inc., 2008). Wesed the default settings of the program (loss func-ion = (OBS − PRED)2; estimation method = quasi-Newton;onvergence criterion = 0.0001; starting values for all param-ters = 0.1; step-width for all parameters = 0.5), unless theterative process did not converge (Dengler, 2010; Wang etl., 2012a). In these cases, we altered the starting values untilhe program found a minimum. For each model, we calcu-ated the predicted values of S for all islands, which werehen used to determine the corrected AIC (AICc = AIC + 2 KK + 1)/(n − K − 1), where n is the number of observationsnd K is the number of model parameters) (Dengler, 2010;ang et al., 2012a). We used AICc to account for the bias

ntroduced when the sample size is small relative to the num-er of estimated parameters (n/K < 40) in a model (Burnham

Anderson, 2002). For model selection, we calculated theifference in AICc (�i) and Akaike weights (�i) for eachodel i among a set of candidate models. We also calculated

vidence ratio, the ratio of Akaike weights �i/�j, which rep-esents the evidence about fitted models as to which is bettern a K–L information sense (Burnham & Anderson, 2002).nly models with �i ≤ 2 are considered to have substantial

upport (Burnham & Anderson, 2002).

ath analyses


We also used the method proposed by Triantis et al. (2006)o detect the SIE. The method is based on path analysis usingn a priori theoretical model according to which island area

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able 2. Results of the non-linear regression analyses of species–area dahan the minimum area requirement (MAR) of snakes and (B) 29 islands (hina. Model performance is assessed using Akaike information criterioor each model, the fitted parameters (c, z, and T), number of estimable paAICc), Akaike differences (�i) and Akaike weights (�i) are presented. T

odel Parameter estimate

c z1 z2 T

A) All study islands excluding one island smaller than the MAR of snakeogarithm model 0.9434 2.8675

eft-horizontal SIE model 0.2222 2.9897 −ontinuous SIE model 0.0860 −0.3769 2.9897 −

B) 29 islands (excluding islands with no species)ogarithm model 1.4201 2.6598

eft-horizontal SIE model 1.0000 2.7272 −ontinuous SIE model 1.0000 −0.0093 2.7272 −


A) directly affects habitat diversity (H) and both area andabitat diversity directly affect species richness (S). An SIEould be present when the direct and/or the total effects of

rea on species richness are eliminated (Triantis et al., 2006).he main advantage of the method is that the detection of theIE is not based solely on the species–area relationship butabitat diversity is also incorporated (Triantis et al., 2006).he detection of the SIE is carried out through the sequentialxclusion of islands from the largest to the smallest and theimultaneous estimation of path coefficients of area (bA) andabitat diversity (bH). When bA was found to be bA ≤ 0, theespective area was assigned as the upper limit of the SIE (forurther details see Triantis et al., 2006).

esults

egression analyses for the detection of the SIE

When including islands with no species, an SIE in snakeommunities was detected in the Thousand Island LakeTable 2A). For all the islands excluding one island thatas smaller than the MAR of snakes (Table 1), model selec-

ion based on AICc identified the left-horizontal SIE modelFig. 1) as the most parsimonious model (Table 2A). Inontrast, there was little support for the other two regres-ion models (all �i ≥ 2.23) (Table 2A). According to Akaikeeights (�i), the evidence ratios of the left-horizontal SIEodel over the other two regression models were 3.1 and 3.5

Table 2A), respectively.However, the exclusion of islands with no species gave

pposite results (Table 2B). When excluding islands with nopecies, model selection based on AICc identified the simpleogarithm model (Fig. 2) without an SIE as the best modelTable 2B). In contrast, there was little support for the two


reakpoint regression models (all �i ≥ 2.04) (Table 2B).ccording to Akaike weights (�i), the evidence ratios of

he simple logarithm model over the other two breakpointegression models were 2.8 and 9.4 (Table 2B), respectively.

ta of snakes on (A) all study islands excluding one island smallerexcluding all islands with no species) in the Thousand Island Lake,n (AIC)-based model selection among a set of candidate models.rameters (K), the log-likelihood (log L), sample-size adjusted AICis log10 of the area in ha of the breakpoint.

Model selection

K log(L) AICc �i �i

s3 −1.2543 9.07 2.23 0.2031

0.1987 4 1.0574 6.84 0 0.61900.2169 5 1.0661 9.33 2.49 0.1779

3 0.0298 6.90 0 0.69390.1228 4 0.3642 8.94 2.04 0.25050.1228 5 0.6096 11.39 4.49 0.0735

dx.doi.org/10.1016/j.baae.2014.10.006

Please cite this article in press as: Wang, Y., et al. Small-island effect in snake communities on islands of an inundated lake: The need toinclude zeroes. Basic and Applied Ecology (2014), http://dx.doi.org/10.1016/j.baae.2014.10.006


6 Y. Wang et al. / Basic and Applied Ecology xxx (2014) xxx–xxx

Fig. 1. The three regression models of species–area relationshipsfor snakes on all study islands excluding one island smaller than theMAR of snakes in the Thousand Island Lake, China. Two breakpointregression models (B) and (C) were compared with the simple log-arithm model (A) to detect the small-island effect. The AICc valuesare shown (the lowest value denotes the best model).

Fig. 2. The three regression models of species–area relationshipsfor snakes on 29 islands (excluding islands with no species) in theThousand Island Lake, China. Two breakpoint regression models(B) and (C) were compared with the simple logarithm model (A)to detect the small-island effect. The AICc values are shown (thelowest value denotes the best model).

dx.doi.org/10.1016/j.baae.2014.10.006


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For the dataset excluding islands with no species, it seemshat the left sides of the two breakpoint regressions wereargely determined by only a single data point (Fig. 2B and C).

hat would happen if this data point (i.e. the smallest inha-ited island) were deleted from the analyses? We found thathe simple logarithm model, compared with the two break-oint regressions, remained the best model based on AICc

ven after excluding the smallest inhabited island (�i = 0)see Appendix A: Fig. 1). Our results thus were robust andot influenced by this extreme value in our system.

ath analyses for the detection of the SIE

For all the islands excluding one island that was smallerhan the MAR of snakes (Table 1), the method of Triantist al. (2006) based on path analysis detected an SIE in snakeommunities. When the islands in our system were excludedequentially from the largest to the smallest (Table 1), thestimated path coefficient of area (bA) was found to be belowero (bA = −0.025) (see Appendix A: Table 2). The upperimit of the SIE of the respective area was 0.80 ha (Table 1).

However, the exclusion of islands with no species gavepposite results (see Appendix A: Table 3). For the 29 islandsxcluding islands with no species, when the islands in ourystem were excluded sequentially from the largest to themallest (Table 1), none of the estimated path coefficients ofrea (bA) was found to be equal or smaller than zero (seeppendix A: Table 3).

iscussion

In this study we tested the role of S = 0 in generating theIE systematically in snake communities in the Thousandsland Lake, China. To date, although the exclusion of islandsith no species is widely viewed as an important method-logical shortcoming for the detection of the SIE (Dengler,010; Triantis & Sfenthourakis, 2012), the role of S = 0 inenerating SIEs is rarely examined. To our knowledge, onlyhis study and the work of Morrison (2014) have empiricallyested the role of S = 0 in generating the SIE, which thus filln a significant gap.

Our detection of the SIE in snake communities is robust asur analyses meet all the criteria necessary for the ‘unambigu-us demonstration’ of an SIE (Dengler, 2010): (1) includingslands with no species that fall within the geographical andange-size limits of the study; (2) comparing most relevantodels (one model without an SIE, and two with SIEs); (3)

electing models in the same S-space for all the models; (4)ccounting for model complexity when comparing modelsith different numbers of parameters (AICc); and (5) incor-


orating both area and habitat diversity into detecting the SIETriantis et al., 2006).

The results support our hypothesis that the detection of theIE in snake communities in our study system was influenced

Ssnt


y whether or not islands with no species were included.hen islands with no species were included, an SIE was

etected. In contrast, when islands with no species werexcluded, we found no evidence of the SIE. These resultsere consistent irrespective of whether regression analysesr path analyses were used. It seems unlikely, therefore, thatur results are an artefact. Our results indicate clearly that

= 0 plays an important role in generating the SIE in thistudy system.

Why does S = 0 play an important role in generating theIE? There are at least two main reasons. First, the exclu-ion of islands with no species would bias the estimate of SWilliams, 1996). Because small islands have typically loweralues of S, excluding islands with S = 0 has the effect ofiasing (upwards) the estimate of S for islands of that sizeWilliams, 1996). Second, the exclusion of islands with nopecies biases the parameters of c and z (Williams, 1996).he extent of this bias will increase as more islands withero species are excluded. Previous studies suggest that,owards the far-left, the shape of the species–area curve isargely determined by the increasing fraction of islands witho species (Williams, 1996; Dengler, 2009). Taken together,he exclusion of islands with no species biases the parameterstimate of c, z, and S (Williams, 1996), which in turn wouldnfluence the detection of the SIE.

We provided a case study to test the role of S = 0 in gener-ting the SIE. However, the more interesting and importantuestion is to determine the generality of these findings. Thisuestion could be solved by collecting all related data thatnclude islands with no species and then conducting a meta-nalysis. However, there are serious obstacles to such annalysis. Perhaps most seriously, very few previously pub-ished datasets include islands with no species (Dengler,010). Furthermore, for nearly all species–area datasets col-ected from islands, very few publications have explicitlyndicated the sizes of islands that do not host any speciesf the target group (e.g. Morrison, 1997; Lomolino, 2000;omolino & Weiser, 2001; Barrett, Wait, & Anderson, 2003;riantis et al., 2006; Burns et al., 2009). Therefore, the lack ofppropriate data precludes strong inference about the extentf the role of S = 0 in generating the SIE.We found that including the islands with no species could

bviously influence the detection of the SIE in snake com-unities in our study system. Our results are inconsistentith Morrison (2014), who found that the inclusion of islandsith no species had little effect on the detection of the SIE forahamas floras. The difference in the role of S = 0 in generat-

ng the SIE in these two systems probably can be explained byheir differences in the number of islands with no species andheir positions along the x-axis of the species–area curvesWilliams, 1996; Dengler, 2009). It seems that excludingslands with S = 0 does not always affect the detection of an


IE (Morrison, 2014). More data including islands with nopecies on other taxa and in other archipelagos are highlyeeded to test the generality of the role of S = 0 in generatinghe SIE.

dx.doi.org/10.1016/j.baae.2014.10.006


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Our study provides several general implications for thereatment of islands with no species for future SIE studies.irst, when S = 0 plays a large part in generating the SIEs in our system, it is important to preferentially determinehe minimum area requirement (MAR) of the target taxonDardanelli et al., 2006). In our system, the MAR of snakess 0.30 ha (Table 1). Second, for an archipelago with hundredsf islands with no species, should all these islands be includedn SIE analyses? We suggest that to interpret the data biolog-cally, only islands equal to or larger than the MAR shoulde included in SIE analyses (as done in our study) becausehese islands are habitable for the target taxon. Some of theroposed mechanisms of the SIE suggest that species mayolonize a habitable island but go extinct rapidly, or surviveonger because of marine subsidies (MacArthur & Wilson,967; Barrett et al., 2003; Burns & Neufeld, 2009). In con-rast, islands that have no species should not be included ifhey are too small and absolutely uninhabitable to supportpecies (Morrison, 2011). This will spuriously increase thevidence for an SIE because these islands fall to the far leftf the species–area curve (Williams, 1996; Dengler, 2009).inally, when it is impossible to determine whether islandsith no species are habitable for the target taxon with cer-

ainty (Morrison, 2011), the safest course is to conduct SIEnalyses both including and excluding islands with no speciesMorrison, 2014). A search of the data in several synthesesn island species distributions (Wright, Patterson, Mikkelson,utler, & Atmar, 1998; Lomolino & Weiser, 2001; Triantis,uilhaumon, & Sfenthourakis, 2012) identified the MARsf several major taxa such as reptiles (0.1 ha), birds (0.1 ha)nd mammals (0.08 ha). For these taxa, islands larger thanhe corresponding MARs, which are likely variable amongrchipelagos, should be included in SIE analyses.

In conclusion, the detection of the SIE in snake communi-ies in our system was influenced by whether the islands witho species were included. We found that the inclusion ofslands with no species provided new and interesting insightsnto the study of the SIE (Triantis & Sfenthourakis, 2012).ur analyses demonstrate clearly how excluding islands witho species leads to erroneously not detecting an SIE when inact an SIE exists. We thus conclude that, for the robust detec-ion of the SIE, islands with no species that fall within theeographical and range-size limits of the study should not bexcluded in future studies.

cknowledgements

We thank Simone Fattorini, Kevin Burns, Jürgen Dengler,ostas Triantis and an anonymous referee for helpfulomments on early versions of the manuscript. We arerateful to Chunan Forestry Bureau and the Thousand Island


ake National Forest Park for permits necessary to conducthe research. This study was supported by the Nationalatural Science Foundation of China (31100394, 31471981,1210103908), Zhejiang Provincial Natural Science

M

M

cology xxx (2014) xxx–xxx

oundation (LQ12C06001), Zhejiang Provincial Postdoc-oral Science Foundation and the Fundamental Researchunds for the Central Universities.

ppendix A. Supplementary data

Supplementary data associated with this article can beound, in the online version, at http://dx.doi.org/10.1016/.baae.2014.10.006.

eferences

arrett, K., Wait, D. A., & Anderson, W. B. (2003). Small islandbiogeography in the Gulf of California: Lizards, the subsidizedisland biogeography hypothesis, and the small island effect.Journal of Biogeography, 30, 1575–1581.

urnham, K. P., & Anderson, D. R. (2002). Model selection and mul-timodel inference: A practical information-theoretic approach(2nd ed.). New York, NY: Springer.

urns, K. C., McHardy, R. P., & Pledger, S. (2009). The small-islandeffect: Fact or artefact? Ecography, 32, 269–276.

urns, K. C., & Neufeld, C. J. (2009). Plant extinction dynamics inan insular metacommunity. Oikos, 118, 191–198.

ardanelli, S., Nores, M. L., & Nores, M. (2006). Minimum arearequirements of breeding birds in fragmented woodland of Cen-tral Argentina. Diversity and Distributions, 12, 687–693.

engler, J. (2009). Which function describes the species–area rela-tionship best? A review and empirical evaluation. Journal ofBiogeography, 36, 728–744.

engler, J. (2010). Robust methods for detecting a small islandeffect. Diversity and Distributions, 16, 256–266.

attorini, S. (2006a). Spatial patterns of diversity in thetenebrionid beetles (Coleoptera, Tenebrionidae) of theAegean Islands (Greece). Evolutionary Ecology Research, 8,237–263.

attorini, S. (2006b). Detecting biodiversity hotspots byspecies–area relationships: A case study of Mediterraneanbeetles. Conservation Biology, 20, 1169–1180.

entile, G., & Argano, R. (2005). Island biogeography of theMediterranean Sea: The species–area relationship for terrestrialisopods. Journal of Biogeography, 32, 1715–1726.

leason, H. A. (1922). On the relation between species and area.Ecology, 3, 158–162.

uang, M. H. (1990). Fauna of Zhejiang: Amphibia, Reptilia.Hangzhou: Zhejiang Science and Technology Publishing House(in Chinese).

omolino, M. V. (2000). Ecology’s most general, yet protean pat-tern: The species–area relationship. Journal of Biogeography,27, 17–26.

omolino, M. V., & Weiser, M. D. (2001). Towards a more gen-eral species–area relationship: Diversity on all islands, great andsmall. Journal of Biogeography, 28, 431–445.


acArthur, R. H., & Wilson, E. O. (1967). The theory of islandbiogeography. Princeton: Princeton University Press.

orrison, L. W. (1997). The insular biogeography of smallBahamian cays. Journal of Ecology, 85, 441–454.

dx.doi.org/10.1016/j.baae.2014.10.006

http://dx.doi.org/10.1016/j.baae.2014.10.006

http://dx.doi.org/10.1016/j.baae.2014.10.006

http://refhub.elsevier.com/S1439-1791(14)00146-7/sbref0005








































































































































































































































































































































































































plied E

M

M

M

M

N

S

S

T

T

T

T

W

W

W

W

W

W

W

W

W

W

W

W


orrison, L. W., & Spiller, D. A. (2008). Patterns and processes ininsular floras affected by hurricanes. Journal of Biogeography,35, 1701–1710.

orrison, L. W. (2011). Why do some small islands lack vegetation?Evidence from long-term introduction experiments. Ecography,34, 384–391.

orrison, L. W. (2014). The small-island effect: Empty islands,temporal variability and the importance of species composition.Journal of Biogeography, 41, 1007–1017.

ullin, S. J., & Seigel, R. A. (2009). Snakes: Ecology and conser-vation. New York, NY: Cornell University Press.

iering, W. A. (1963). Terrestrial ecology of Kapingamarangi Atoll,Caroline Islands. Ecological Monographs, 33, 131–160.

fenthourakis, S., & Triantis, K. A. (2009). Habitat diversity, eco-logical requirements of species and the Small Island Effect.Diversity and Distributions, 15, 131–140.

tatSoft, Inc. (2008). STATISTICA (data analysis software sys-tem), version 8.0. Tulsa, OK: StatSoft, Inc. Available at〈http://www.statsoft.com〉.

jørve, E., & Tjørve, K. M. (2011). Subjecting the theory of thesmall-island effect to Ockham’s razor. Journal of Biogeography,38, 1836–1839.

riantis, K. A., Vardinoyannis, K., Tsolaki, E. P., Botsaris, I., Lika,K., & Mylonas, M. (2006). Re-approaching the small islandeffect. Journal of Biogeography, 33, 915–923.

riantis, K. A., Guilhaumon, F., & Whittaker, R. J. (2012). Theisland species–area relationship: Biology and statistics. Journalof Biogeography, 39, 215–231.

riantis, K. A., & Sfenthourakis, S. (2012). Island biogeography isnot a single-variable discipline: The small island effect debate.Diversity and Distributions, 18, 92–96.


ang, Y., Zhang, J., Feeley, K. J., Jiang, P., & Ding, P. (2009).Life-history traits associated with fragmentation vulnerabilityof lizards in the Thousand Island Lake, China. Animal Conser-vation, 12, 329–337.

Z

Available online at www.s

ScienceD


ang, Y., Bao, Y., Yu, M., Xu, G., & Ding, P. (2010). Nested-ness for different reasons: The distributions of birds, lizards andsmall mammals on islands of an inundated lake. Diversity andDistributions, 16, 862–873.

ang, Y., Chen, S., & Ding, P. (2011). Testing multiple assemblyrule models in avian communities on islands of an inundatedlake, Zhejiang Province, China. Journal of Biogeography, 38,1330–1344.

ang, Y., Zhang, M., Wang, S., Ding, Z., Zhang, J., Sun, J., et al.(2012a). No evidence for the small island effect in avian commu-nities on islands of an inundated lake. Oikos, 121, 1945–1952.

ang, Y., Wang, X., & Ding, P. (2012b). Nestedness of snake assem-blages on islands of an inundated lake. Current Zoology, 58,828–836.

hitehead, D. R., & Jones, C. E. (1969). Small islands and the equi-librium theory of insular biogeography. Evolution, 23, 171–179.

hittaker, R. J., & Fernandez-Palacios, J. M. (2007). Island bio-geography: Ecology, evolution, and conservation (2nd ed.).Oxford: Oxford University Press.

illiams, M. R. (1995). An extreme-value function model ofthe species incidence and species–area relations. Ecology, 76,2607–2616.

illiams, M. R. (1996). Species–area curves: The need to includezeroes. Global Ecology and Biogeography Letters, 5, 91–93.

ilson, J. B. (2007). Priorities in statistics, the sensitive feet ofelephants, and don’t transform data. Folia Geobotanica, 42,161–167.

oodroffe, C. D. (1986). Vascular plant species–area relationshipson Nui Atoll, Tuvalu, Central Pacific: A reassessment of thesmall island effect. Australian Journal of Ecology, 11, 21–31.

right, D. H., Patterson, B. D., Mikkelson, G. M., Cutler, A.,& Atmar, W. (1998). A comparative analysis of nested subset


patterns of species composition. Oecologia, 113, 1–20.hao, E. M. (2006). Snakes of China. Hefei: Anhui Science and

Technology Publishing House (in Chinese).

ciencedirect.com

irect

dx.doi.org/10.1016/j.baae.2014.10.006


























































































































































































































































































































































































































































































































































































































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Small-island effect in snake communities on islands of an inundated lake: The need to include zeroes