Appendix I Applying the box-counting method to a ...

1

Appendix I

2

Applying the box-counting method to a diffusion growth model

3

Introduction and methods

4

We tested the robustness of the box-counting method by applying it to an expansion

5

model with known scale-dependent pattern. We chose a simple diffusion growth model in

6

which the movement of the invasion front approaches asymptotically a constant speed VF as

7

time becomes sufficiently large (Andow et al. 1990). Our model assumes a radial expansion

8

over homogeneous environment. Therefore, decadal expansion rates are invariant across

9

scales smaller than VF and should equal D2/(D-1)2 in the Dth decade. At scales larger than VF,

10

the expansion rate should rapidly decline to zero, but will occasionally rise when the range of

11

the population breaks the boundary of those larger scales.

12

In this analysis, we set the constant VF as 186 km per decade and let the population

13

expand radially for 6 decades. We randomly sampled 50 points within the population range in

14

the first decade and then consequentially increased the number of random sampling points in

15

the following decades. The increase was proportional to the increase in range size between

16

decades. We then applied the box-counting method to those sampling points to calculate the

17

expansion rate for the 2nd – 6th decade. The estimation was done at the scale of 1, 2, 5, 10,

18

20, 50, 100, 200, 500, and 1000 km scale. We expected that the estimates at 1 – 100 km scale

19

match the theoretical rate of D2/(D-1)2; the rate at 200 km scale be slightly lower than the

20

theoretical rate because the scale is slightly beyond the VF; and the rate at 500 and 1000 km

21

be zero except for decades in which the invasion front move into new squares of 500 and

22

1000 km size.

23

Estimates from the box-counting method can be sensitive to the placement of the grid.

24

We shifted the grid from its original placement (population starts at the center of the grid) in

25

16 directions (π/8 radians apart) and three distances (600m, 26km, and 108 km) in each

26

direction. Those replacements allowed us to assess how much fluctuation in estimates of

27

expansion rate can be caused by grid placement. We then averaged the estimates over all the

28

placements to examine whether those mean estimates are more reliable in representing the

29

true expansion rate.

30

Results and discussion

31

The estimated expansion rates at 1 – 100 km scale generally match their theoretical

32

values (Fig. A1). Fluctuations of the estimates due to grid replacements become noticeable at

33

scales beyond 50 km and the degree of fluctuation increases with scale. The 49 different grid

34

placements only result in a few different estimates, suggesting many placements give

35

consistent estimates. Estimates in the second decade have stronger fluctuation than those in

36

other decades, probably because of the lower number of sampling points.

37

When fluctuations in estimates are large, taking the mean over all the placements

38

gives a more reliable expansion rate (closer to the theoretical value) than using an estimate by

39

a single grid placement.

40

As predicted, the expansion rate at 200 km is lower than those at smaller scales

41

because the invasion front moves at a speed slightly slower than 200 km per decade. At 500

42

and 1000 km scale, the expansion rate is either close to zero or surges dramatically. Since

43

those two scales are much beyond the invasion speed, a quantitative interpretation of their

44

expansion rates is not very meaningful. Any surge is a qualitative indication that the invasion

45

front moved into new 500 or 1000 km squares in that decade.

46

Overall, the box-counting method is capable of reproducing the expected scale

47

dependent or independent pattern of range expansion. Its estimates can be sensitive to grid

48

placement especially at larger scales. Averaging the estimates over multiple placements can

49

ease the sensitivity and produce more reliable results.

50 51

Figure A1. Expansion rates in a diffusion growth model estimated by the box-counting method at 1 –

52

1000 km scales. Dash lines indicate the theoretical values of the expansion rate at 1 – 100 km scale.

53

Each “+” indicates an estimated expansion rate by each grid placement. Circles are the mean over

54

estimates of all grid placements.

55

References

56

Andow, D. A. et al. 1990. Spread of invading organisms. - Landscape Ecol 4: 177–188.

57 58

Appendix II

59

Quantifying sampling bias by applying box-counting method to herbarium records of

60

native species

61

Introduction and methods

62

Herbarium sampling efforts may vary across spatial scales and between decades. This

63

variation will introduce bias to our multi-scale analysis. To correct for the potential

64

spatiotemporal sampling bias, we chose herbarium records of three native winter annual

65

species (Plantago patagonica, Lepidium lasiocarpum, and Chaenactis stevioides) collected

66

between the 1950s and the 2000s and applied the box-counting method to those records. We

67

shifted the grid placement as in the analysis for Sahara mustard and for the diffusion growth

68 69

model. These three species are commonly found in the southwestern North America. We

70

assumed that the distribution of those native species were relatively stable during this period.

71

Any deviation from zero expansion rate can indicate decadal difference in sampling efforts.

72

We estimated the “expansion” rates at 1, 2, 5, 10, 20, 50, 100, 200, and 500 km scale. We

73

expected that the rates were close to zero at the 500 km scale (i.e. no sampling bias at this

74

scale) if the distribution of the native species stayed stable. It is unlikely that herbarium

75

collectors would search for those plants in a 500 x 500 km region in one decade and

76

completely ignored that region in the following decade.

77

Results and discussion

78

The “expansion” rates at 1-100 km scales substantially deviated from zero in each

79

decade for all three species (Fig. A2a-c). Estimates by different grid placements were quite

80

consistent with each other. Surprisingly, at 500 km scale, range of C. stevioides showed

81

strong contraction in the 2000s and the range of L. lasiocarpum showed expansion and

82

contraction in the 1960s and the 1970s respectively. As explained, we consider those regional

83

scale expansion and contraction unlikely a result of sampling bias but more likely a reflection

84

of true regional scale range shift by these two species. This interpretation is further supported

85

by the fact that while one species showed regional scale range shift in one decade, the other

86

two species did not show the same trend.

87

To avoid using true range shifts as indicators of sampling bias, for each decade we

88

combined records of only species whose 500 km scale range remained stable. In particular,

89

we combined records of P. patagonica and C. stevioides to calculate the native “expansion”

90

rates in the 1960s and the 1970s, records of all three species to calculate the rates in the 1980s

91

and the 1990s, and records of P. patagonica and L. lasiocarpum to calculate the rates in the

92

2000s (Fig. A2d). At each scale, we averaged the estimates over all the grid placements and

93

used this mean as a quantitative indicator of sampling bias. We subtracted those native

94

“expansion” rates from those of Sahara mustard to calculate the corrected expansion rate of

95

this invasive species (Fig. 1c in main text).

96 97

Figure A2. Decadal “expansion” rates estimated by the box-counting method for three native winter

98

annual species (a) Plantago patagonica, (b) Chaenactis stevioides, and (c) Lepidium lasciocarpum

99

representing the variation in herbarium sampling efforts between decades. C. stevioides and L.

100

lasiocarpum show range shifts at the 500 km scale in some decades, which are unlikely a result of

101

change in sampling efforts at such a large scale. (d) We derived the combined “expansion” rates to

102

represent sampling bias by combining records of P. patagonica and C. stevioides for estimates in the

103

1960s and 1970s, records of all three species for estimates in the 1980s and 1990s, and records of P.

104

patagonica and L. lasiocarpum for estimates in the 2000s.

105 106

Appendix III

107

Inquiring distribution of Sahara mustard in North America and its native range To infer the historical and current distribution of Sahara mustard in North America,

108 109

we searched a large number of online herbarium databases covering the continent (Table A1)

110

and acquired all the collection data points wherever possible. Only four databases (indicated

111

by stars in Table A1) have records of Sahara mustard and the majority of the records came

112

from SEINet and CCH. In these two databases, the total number of all plant collections and of

113

Sahara mustard varied strongly among decades and among different states (Table A2). We

114

applied the box-counting method to those herbarium records to calculate decadal expansion

115

rates across multiple spatial scales. We also acquired records from invasive plant surveys conducted in Arizona and

116 117

California in the 2000s (second section in Table A1). We used those records, combined with

118

herbarium records, to build species distribution models for inferring the climatic niche of

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Sahara mustard. To infer the distribution of Sahara mustard over its native range, we surveyed the

120 121

existing literature and inquired the Global Biodiversity Information Facility (GBIF) database.

122

Distribution inferred from each source is listed in Table A3.

123 124

Table A1. List of herbarium databases and invasive plant surveys inquired in this study. “*”

125

indicates a herbarium database in which records of Sahara mustard were used in this study. Region

Herbarium Database

Global *Global Biodiversity Information Facility (GBIF)

Southwest

*Southwest Environmental Information Network (SEINet) *Consortium of California Herbaria (CCH) *New Mexico Biodiversity Collections Consortium University of Texas Herbarium Botanical Research Institute of Texas Herbarium University of Oklahoma Vascular Plants Database University of Utah Garret Herbarium Intermountain Region Herbarium Network

Northwest

Consortium of Pacific Northwest Herbaria

Great Plains and

Great Plains Herbarium Network

Midwest

Black Hills State University Herbarium (South Dakota and Wyoming) Iowa State University Herbarium Wisconsin Botanical Information System University of Michigan Herbarium

Southeast

Southeast Regional Network of Expertise and Collections

Northeast

Consortium of Northeastern Herbaria

Region

Invasive plant surveys

Southwest

Southwest Exotic Plant Mapping Program (SWEMP) California Invasive Plant Council (Cal IPC) Saguaro National Park Survey Cameron Barrow’s study of Sahara mustard in Coachella Valley, California Author’s personal records

126

127

Table A2. The number of records of all plant collections obtained within the region between 100-121 degree west and 25-38 degree north

128

registered in the SEINet and CCH database. The number of herbarium collections of Sahara mustard is also listed in the table for comparison.

129 All

All

All

All

All

All

All

collections

collections

collections

collections

collections

collections

from CA

from CO

from Mexico from NV

from TX

from UT

(SEINet)

(SEINet)

(SEINet)

(SEINet)

(SEINet)

All collections collections Decade

Records of

from AZ & NM from CA

Total

(SEINet) (CCH)

Sahara mustard

(SEINet)

1920s

1

1930s

0

1940s

52110

32526

1524

1009

2611

1101

195

1924

93000

4

1950s

48085

29448

822

995

2779

118

64

925

83236

6

1960s

85038

76214

996

871

6265

1292

107

2133

172916

32

1970s

64130

95196

783

609

5609

1766

544

2090

170727

62

1980s

58924

81463

1359

2243

5287

1322

284

2573

153455

73

1990s

92220

122800

613

1940

2189

629

202

2379

222972

76

2000s

136487

171478

305

196

567

154

90

762

310039

279

130

Table A3. The distribution of Sahara mustard over its native range recorded in the literature and

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GBIF database. Sources

Described distribution of Sahara mustard

Jalas 1996

Along the coastal area of Mediterranean Europe, including continental coast and islands of Spain, France, Italy, and Greece.

Zohary 1966 and Zohary et al.

In Egypt: Nile Delta, Nile Valley, western desert, oasis, northwest,

1980

northeast, Northern, Central and Southern Sinai. In Saudi Arabia: Hejaz, eastern Arabia, central Arabia. Bahrein. Kuwait. In Israel, Palestine and Jordan: Mediterranean Littorals, northern, western and central Negev Desert, Acco Plain, Sharon Plain, Philistean Plain, desert of Edom, Jordan Mts, East Jordan Desert, Southern Jordan Desert. In Syria and Lebanon: coastland, Lebanon Mts, Jebel Druze, Northern Mts. Northern, southern and eastern Cyprus. In Turkey: Western Anatolia, Mesopotamian Anatolia, Aegean Islands. In Iraq: mountain region, lower Mesopotamia, northern plains and foothills, western and southern desert. In Iran: northern, southwestern mts, and central, and southern Iran.

Townsend and Guest 1980

In Iraq: occasional in the steppe region. Common in southern sector of the desert region.

Miller and Cope 1996

Saudi Arabia, Southern Yemen, Oman, UAE, Qatar, Bahrain, Kuwait, S&W Europe, N Africa and SW Asia. On sand and gravel in deserts: 0 – 2400 m

Maire 1965

Coastal and interior dunes of North Afirca. Oasis in M’zab (Algeria) of northern Sahara. The High Plateau. Saharan Atlas Mountains range. Oasis in Ahaggar Mountains (Algeria).

Rechinger 1968

Western and southern Europe, North Africa, western Syria, Iraq, Anatolia, Cyprus, Iran and Armenia.

Jafri 1977

N. Africa, S. Europe, eastwards to Pakistan. Recorded collections in coastal Libya.

Battandier and Trabut 1888-90

Coastal Algeria, High Plateau, Sahara. Mediterranean region.

Global Biodiversity

Records found in the following countries:

Information Facility

Europe (Greece, Cyprus, France, Greece, Italy, Portugal, Spain,

(data.gbif.org)

Turkey) Africa (Algeria, Burkina Faso, Egypt, Libya, Morocco, Tunisia) Asia (Iraq, Israel, Jordan, Kuwait, Lebanon, Oman, Pakistan, Qatar, Saudi Arabia, Syria, United Arab Emirates)

132 133

References

134

Battandier, J. A. and L. Trabut. 1888-90. Flore de L’Algerie: contenant la description de toutes

135

les plantes singnalee’s fusqu a ce jour comme spontanees en Algerie et catalogue des

136

plants du Maroc, Dicotyledones. Librairie Adolphe Jourdan. Alger.

137

Jafri, S.M.H. 1977. Flora of Libya: Brassicaceae. 23. Al Faatech University. Tripoli.

138

Jalas, J., J. Suominen, and R. Lampinen. 1996. Atlas Florae Europaeae: Distribution of Vascular

139

Plants in Europe. The Committe for Mapping the Flora of Europe and Societas Biologica

140

Fennica Vanamo, Helsinki.

141

Maire, R. 1965. Flore de L'Afrique du Nord. Paul Lechevalier, Paris.

142

Miller, A. G. and T. A. Cope. 1996. Flora of the Arabian Peninsula and Socotra. Edinburgh

143

University Press, Edinburgh.

144

Rechinger, Karl. H (ed.). 1968. Flora Iranica: Flora des iranischen Hochlandes und der

145

umrahmenden Gebirge. Cruciferae. 57. Akademische Druck – u. Verlagsanstalt, Graz.

146

Townsend, C. C. and E. Guest. 1980. Flora of Iraq. Ministry of Agriculture and Agrarian

147

Reform, Baghdad.

148

Zohary, M. 1966. Flora Palaestina. The Israel Academy of Sciences and Humanities, Jerusalem.

149

Zohary, M., C. C. Heyn, and D. Hller. 1980. Conspectus Florae Orientalis: An Annotated

150

Catalogue of the Flora of the Middle East. The Israel Academy of Sciences and Humanities,

151

Jerusalem.

152 153

Appendix IV

154

Using MaxEnt to model the distribution of range-expanding species

155

The expansion of a non-native species means that its range does not reflect its stable

156

relationship with the invaded environments (Elith et al. 2010a). This lack of equilibrium presents

157

challenges for modeling potential distribution using data from current distribution.

158

Solutions to this problem include using less complex models and comparing models based on

159

different background samples (Elith et al. 2010a).

160 161

We reduced the complexity of our models in three ways. First, we used only four climatic variables that are most biologically relevant to our focal species. Second, we used only the hinge

162

and quadratic features in MaxEnt. Choosing the two features means that the modeled distribution

163

is constrained by the mean and variance of the given climatic variables, may have piecewise

164

linear response to any of them, but is not constrained by any interaction between them (Elith et

165

al. 2010b). Third, we increased the regularization parameter in MaxEnt (from the default value of

166

1 to 2.5) to reduce the complexity of the surface of fitted models. Hence, our models excluded

167

complicated detail response of species distribution to climate, which is more appropriate for

168

species that have formed a stable relationship with its environment (Elith et al. 2010a).

169

To further account for ongoing range expansion, we also allowed our models to provide

170

Sahara mustard with more potential space for expansion. We did so by adding models based on a

171

much larger background than those using our standard background. Our standard background

172

was a polygon that consists of the majority of southwestern North America. The enlarged

173

background was a rectangular region containing all lower 48 states of the U.S. and the entire

174

territory of Mexico. By choosing the standard background, we asked why Sahara mustard was

175

only found in certain areas of the Southwest given the spatial climatic variation within the region

176

and whether it could further expand in the Southwest. By choosing the enlarged background, we

177

asked why this species was only found in the Southwest given the climatic conditions across

178

North America and whether it could expand beyond the Southwest. To provide approximately

179

equal spatial density of sampling for our models, we drew 10,000 random samples from the

180

standard background and 25,000, from the enlarged background.

181 182

We found that models based on both backgrounds allow us to reach the same conclusion that 1) Sahara mustard in North America is restricted by its climatic envelope (Fig. A3) and 2) the

183

climate in the invaded range generally predicts the native distribution (Fig. A4). The model

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predictions also allow us to infer the climatic range under which Sahara mustard is likely to be

185

present in both its invaded and native range (Fig. A5).

(a)

(b)

186 187 188 189

Figure A3. Distribution of Sahara mustard within its climatic niche in North America predicted by SDMs. We used background samples from (a) southwestern North America (SWNA) and (b) North America (NA) to build the models. For each background scenario, we trained two models: one using only

190 191 192 193 194

herbarium records and the other, herbarium and invasive plant survey records combined. We then derived an ensemble from the two models. Each ensemble shows the area predicted by both models (peach) and by each model alone (green or yellow). The maps also show the occurrence of Sahara mustard recorded by herbarium collections (red circles) and invasive plant surveys (blue triangles).

(a)

(b)

195 196 197 198 199 200 201

Figure A4. Projected distribution of Sahara mustard in its native continents projected by SDMs based on its invaded range in North America. We used background samples from (a) southwestern North America (SWNA) and (b) North America (NA) to build the models. The building of the models was the same as described in Fig. A3. Shaded areas represent its native range estimated from the literature and the GBIF records.

(a)

TEMPCOLDQ

TEMPWARMQ

RAINCOLDQ

RAINYEAR

202

(b)

TEMPCOLDQ

TEMPWARMQ

RAINCOLDQ

RAINYEAR

203 204 205 206 207 208 209

Figure 5A. Range of climatic variables in areas where Sahara mustard is predicted to be present in (a) North America and (b) its native continents by the SDMs. The four variables are mean temperature of the coldest quarter (TEMPCOLDQ), mean temperature of the warmest quarter (TEMPWARMQ), precipitation of the coldest quarter (RAINCOLDQ), and annual precipitation (RAINYEAR). Temperature values are shown as degree Celsius x 10 and precipitation values, millimeters. The SDMs use southwest North America as the background.

210 211 212

Climatic variables used in the model and their contribution None of the four climatic variables used in the two background regions were overly

213

correlated (if |R| > 0.85) with each other (Table A4); therefore we included all of them in each

214

model.

215

To understand which variable is most important in limiting the species’ distribution, we

216

evaluated the contribution of each variable to a model using MaxEnt’s built-in evaluation

217

algorithm (Table A5). Models based on SWNA background include summer temperature as the

218

most influential variable, whereas models based on NA background include annual precipitation

219

as the most influential variable. MaxEnt’s evaluation of each variable’s contribution to a model is

220

sensitive to correlation between variables (though the model itself is not). In our models, summer

221

temperature is correlated with winter temperature, and annual precipitation, with winter

222

precipitation (Table A4). Therefore, the results can only allow us to suggest that temperature

223

variation drives the species distribution within the Southwest, whereas precipitation is more

224

important in limiting its range to the Southwest.

225

Models based on the SWNA background predicted a smaller range than those based on the

226

NA background (Fig. A3). Since temperature is a more influential variable in SWNA

227

background models, this stronger climatic restriction suggests that Sahara mustard would have a

228

broader range in the Southwest if temperature were not a limiting factor. Given that regional

229

distributions are likely to shift following a changing global climate, Sahara mustard might be

230

predicted to expand particularly in response to elevated temperatures.

231

Table A4. Pearson coefficient of the four climatic variables used for building SDMs drawn from the

232

two background regions: a polygon that consists of the majority of southwestern region in North America

233

(SWNA) and a rectangular region containing all lower 48 states of the United States and the entire

234

territory of Mexico (NA). TEMPCOLDQ SWNA

NA

RAINCOLDQ

-0.1605

0.0523

RAINYEAR

-0.0470

TEMPWARMQ

0.7582

RAINCOLDQ SWNA

NA

0.2770

0.7382

0.7383

0.7257

-0.4071

-0.0943

RAINYEAR SWNA

NA

-0.4198

0.1275

TEMPCOLDQ

235 236

Table A5. The estimated influence of climatic variables on each SDM. To determine the “percent

237

contribution”, in each iteration of the training algorithm, the increase in regularized gain of the model is

238

added to the contribution of the corresponding variable, or subtracted from it if the gain is negative. To

239

determine the “permutation importance”, each variable was selected in turn, the values of that variable on

240

training presence and background data are randomly permuted. The model is re-evaluated on the

241

permuted data, and the resulting drop in training AUC (normalized to percentages) is shown.

242

Training Data Herbarium records Variable

Backg round SWN A

TEMPWARMQ TEMPCOLDQ RAINCOLDQ

Percent Permutation contribution importance

42.2 30.6 14.5

33.4 10.7 27.2

Herbarium and invasive plant survey records combined Percent Permutation Variable contribution importance TEMPWARMQ RAINYEAR TEMPCOLDQ

51.6 18.8 17.6

42.1 33.7 6.3

NA

RAINYEAR

12.6

28.7

RAINCOLDQ

12

17.8

RAINYEAR TEMPCOLDQ TEMPWARMQ RAINCOLDQ

41.9 30.7 19.1 8.4

71.8 14.5 4.1 9.6

RAINYEAR TEMPCOLDQ RAINCOLDQ TEMPWARMQ

61.1 27.8 6.5 4.6

67.7 18.6 6.4 7.3

243 244 245

Model validation

246

We tested our SDM models using 10-fold cross validation and used the test score of the Area

247

Under the receiver operating characteristic Curve (AUC) to judge whether each model performed

248

reasonably well (Table A6). An AUC of 0.5 means the model prediction is no better than

249

random, whereas a value closer to the maximum achievable AUC indicates better performance of

250

a model. The maximum achievable AUC is 1-a/2, where a is the prevalence of the species over

251

the sampled region (Phillips et al. 2006). This means that models trained by records of lower

252

prevalence (e.g. fewer records or larger background) will have a higher maximum achievable

253

AUC values. Therefore, models with higher AUC scores in the table are not necessarily better.

254

Unfortunately, using presence-only data means that the prevalence of a species is unknown (no

255

information on absence) and thus the maximum achievable AUC cannot be estimated. In our

256

study, we used the test AUC to affirm that each model performed reasonably well (AUC>0.5) but

257

did no judge how much the model deviates from its theoretical optimum. We note that MaxEnt

258

has been repeatedly shown to produce some of the most robust SDMs using presence-only data

259

when compared with other modeling methods (Elith et al. 2006; Phillips et al. 2006).

260

If a model passed the test, we trained the model used the entire dataset and accepted its

261

logistic output as the relative probability of the species’ presence in a spatial unit. We used the

262

logistic output threshold at which the model achieved maximum training sensitivity plus

263

specificity (minimizing the error rate for both positive and negative observations (Freeman &

264

Moisen 2008)) and treated any logistic value under this threshold as an indication of absence.

265 266

Table A6. The AUC score of the MaxEnt species distribution model based on two different backgrounds

267

(SWNA and NA) and using two different datasets: herbarium records only (H) and by combining

268

herbarium and invasive plant survey records (H+IS).

269

Background

Training Data H

H+IS

SWNA

0.903+0.016

0.879+0.006

NA

0.977+0.004

0.963+0.002

270 271

References

272

Elith, J., Graham, C.H., Anderson, R.P., Dudik, M., Ferrier, S., Guisan, A., et al. 2006. Novel methods

273

improve prediction of species’ distributions from occurrence data. Ecography, 29, 129–151.

274

Elith, J. et al. 2010a. The art of modelling range‐shifting species. - Methods in Ecology and Evolution 1: 330–

275

342.

276 277

Elith, J. et al. 2010b. A statistical explanation of MaxEnt for ecologists. - Diversity and Distributions 17: 43– 57.

278

Freeman, E. A. and Moisen, G. G. 2008. A comparison of the performance of threshold criteria for binary

279

classification in terms of predicted prevalence and kappa. - Ecological Modelling 217: 48–58.

280

Phillips, S.J., Anderson, R.P. & Schapire, R.E. 2006. Maximum entropy modeling of species geographic

281

282

distributions. Ecological Modelling, 190, 231–259.

283 284

Appendix V.

285

Examining the influence of decadal cold-season precipitation on the local expansion of

286

Sahara mustard

287

Introduction

288

As a winter annual plant, Sahara mustard experiences population boom in response to high

289

precipitation over the cold (late fall-winter-early spring) season. Moreover, precipitation in fall

290

and early winter may favor its growth more strongly than late cold-season precipitation because

291

early winter rainfall followed by later precipitation events provides a larger time window for the

292

species to outperform native annual plants (Barrows et al. 2009; Marushia et al. 2010).

293

Therefore, years of high (early) cold-season precipitation provide potential temporal niche

294

opportunities for its expansion. To examine whether such niche opportunities exist, we assessed

295

the relationship between the species’ local expansion and cold-season precipitation at the decadal

296

scale.

297

Methods

298

We located local expansion hotspots using the same box-counting method (see Method in

299

main text). We first evenly divided the southwestern North America into 100 km squares as our

300

focal cells. We then divided each focal cell into 1, 5 and 10 km square cells and calculated the

301

expansion rate within a focal cell (not adjusted for sampling effort) at those three local scales.

302

We chose the maximum expansion rate among the three as the expansion rate in a focal cell and

303

located cells that experienced high rates. We considered those focal cells as local expansion

304

hotspots in that decade (Fig. A6). The calculation was done for each of the five decades (the

305

1960s – the 2000s).

306

We evaluated the decadal cold-season precipitation in those hotspots using weather data

307

from the United States Historical Climatology Network. We acquired monthly precipitation data

308

from weather stations that are located either within or adjacent to the hotspots (Table A7). We do

309

not suggest that these stations faithfully represent the climate of each hotspot. Our interest is in

310

revealing the general trend of winter precipitation between decades, which we believe is

311

consistent over large spatial scales and therefore should be comparable between the hotspots and

312

their correspondent weather stations. For each station, we calculated the annual cold-season

313

precipitation as the mean monthly precipitation from October to April. We calculated its long-

314

term mean averaged over year 1929-2010. We then calculated the abnormality of decadal cold-

315

season precipitation (cold-season Ad) as the percent deviation of the decadal mean from the long-

316

term mean. For instance, a cold-season Ad of 0.2 means the cold-season precipitation averaged

317

over that decade is 20% higher than the long-term mean. We used Wilcox signed rank test to

318

determine whether the cold-season Ad averaged over those hotspots in each decade was

319

significantly above zero.

320

We also located focal cells that were hotspots in one decade but experienced negligible

321

expansion in the following decade. We considered those cells as local expansion coldspots for

322

that following decade and calculated cold-season Ad in those cells. We compared the cold-season

323

Ad averaged over hot- and coldspots of the same decade (Wilcox rank sum test) to examine

324

whether the former received significantly more rainfall. We only compared hot- and coldspots in

325

the 1970s – 1990s, the three decades in which similar number of hot- and coldspots were

326

detected.

327

Moreover, since high amount of rainfall early in the winter season may give Sahara mustard,

328

a species characterized by rapid phenology, an advantageous start, we performed the same

329

analyses using early cold-season Ad, namely the decadal abnormality of mean monthly

330

precipitation from October to December.

331

We repeated all the above analyses using precipitation data over the decade prior to any local

332

expansion to indicate whether a local expansion was a delayed response to historical conditions.

333

Finally we applied False Discovery Rate analysis (QVALUE in R package) to control the

334

increased chance of listing a false positive test in this multiple-hypotheses test.

335

Results

336

Neither the cold-season nor the early cold-season Ad in local expansion hotspots were

337

consistently positive across the five decades (Table A8). The cold-season Ad was significantly

338

positive in the 1970s, 80s and 90s, but not so in the 1960s and significantly negative in the

339

2000s. The early cold-season Ad was significantly positive in the 1960s and 80s, but not so in the

340

1970s and 90s, and significantly negative in the 2000s. Comparing early cold-season Ad between

341

hot- and coldspots, we found that those in hotspots were not significantly higher than in

342

coldspots in any decade.

343

Among the three decades (the 1960s, 70s and 2000s) in which Sahara mustard achieved the

344

most rapid local expansion (Fig. 1 in main text; Fig. A6), only the 1960s had local expansion

345

hotspots experiencing a substantial increase (+37.5%) in early cold-season precipitation but no

346

increase in cold-season precipitation (Table A8). The hotspots in the 1970s experienced a modest

347

increase (+5.9%) in cold-season precipitation, but the coldspots in the same decade received

348

similar amount of rainfall. The 2000s saw the highest rate of local expansion and the largest

349

number of hotspots. However, hotspots in this decade experienced a significant decline in cold-

350

season (-17.7%) and early cold-season precipitation (-19.1%).

351

Neither did results suggest that the local expansion was a delayed response to previous

352

decade’s high precipitation. Among the three decades (the 1970s, 90s and 2000s) in which either

353

cold-season or early cold-season Ad was significantly positive in the previous decade, none had

354

hotspots exceeding coldspots by their previous-decade cold-seaosn Ad (Table A8).

355 356

Discussion

357

Our results do not support the hypothesis that decadal variation in climate explains the

358

decadal change in local expansion of Sahara mustard. Neither the rapid local expansion nor the

359

difference between local expansion hotspots and coldspots can be consistently explained by

360

higher cold-season precipitation averaged over each decade or the previous decade.

361

The local population growth of Sahara mustard may respond to climatic fluctuation at a

362

much shorter time scale. One or two years of heavy seasonal rainfall is sufficient to trig a local

363

population boom of an annual species, strongly increasing the local occurrences recorded in a

364

decade, but not raising the average precipitation over the same decade. For example, herbarium

365

records of Sahara mustard in 2005 (78 records) make up more than a quarter of the 272 records

366

in the 2000s as a result of an extremely wet winter and spring in the 2004-2005. However, the

367

cold-season precipitation averaged over the 2000s is significantly below the long-term average.

368

Population data of higher temporal resolution is needed to investigate whether the local

369

expansion of this species tracks the climate at a much finer temporal scale.

370 371

References

372

Barrows, C. W. et al. 2009. Effects of an invasive plant on a desert sand dune landscape. -

373 374 375 376 377

Biological Invasions 11: 673–686. Marushia, R. G. et al. 2010. Phenology as a basis for management of exotic annual plants in desert invasions. - Journal of Applied Ecology 47: 1290–1299.

378

Table A7. Locations of weather stations in the United States Historical Climatology Network

379

that are either in or adjacent to local expansion hotspots and coldspots in each decade from 1960s

380

to 2000s. The weather data from those weather stations were used to calculate the cold-season

381

precipitation in each hot- or coldspot.

382 Decade

1960s

1970s

1980s

Ajo, AZ

Ajo, AZ

Buckeye, AZ

Buckeye, AZ Chandler Heights, AZ

Buckeye, AZ

Parker, AZ

Kingman, AZ

Yuma, AZ

Miami, AZ

Prescott, AZ

Tucson WFO, AZ

Prescott, AZ

Childs, AZ

Parker, AZ

Wickenburg, AZ

Blythe, CA

Roosevelt 1 WNW, AZ

Yuma, AZ

Chula Vista, CA

Tombstone, AZ

Blythe, CA

Cuyamaca, CA

Wickenburg, AZ

FT Valley (Flagstaff), AZ Grand Canyon NP, AZ Kingman, AZ

Indio, CA

Pasadena, CA

Blythe, CA

Miami, AZ

Redlands, CA Santa Barbara, CA Tustin Irvine RCH, CA Boulder City, NV

Redlands, CA

Brawley, CA

Parker, AZ

Indio, CA

Prescott, AZ

Roosevelt 1 WNW, AZ Sacaton, AZ Tucson WFO, AZ Brawley, CA Indio, CA Locations of weather stations that are in or adjacent to local expansion hotspots

Redlands, CA

El Paso, TX

1990s Chandler height, AZ Miami, AZ Pearce Sunsites, AZ

Needles, CA Ojai, CA Santa Barbara, CA Jornada Exp Range, NM Orogrande, NM NM State University (Las Cruces), NM

2000s Ajo, AZ Buckeye, AZ Chandler Heights, AZ

Roosevelt 1 WNW, AZ Sacaton, AZ Safford Agricultural center, AZ Tucson WFO, AZ Wickenburg, AZ Williams, AZ Blythe, CA Brawley, CA Cuyamaca, CA Indio, CA Needles, CA Newport Beach Harbar (Huntington Beach), CA Ojai, CA Pasadena, CA Santa Barbara, CA

Tustin Irvine RCH, CA Boulder City, NV Kanab, UT St George, UT Zion NP, UT Locations of weather stations that are in or adjacent to local expansion coldspots

Buckeye, AZ

Ajo, AZ

Buckeye, AZ

Pearce Sunsites, AZ

Chandler Heights, AZ

Kingman, AZ

Parker, AZ

Tombstone, AZ

Miami, AZ

Prescott, AZ

Tucson WFO, AZ

Parker, AZ

Wickenburg, AZ

Yuma, AZ

Yuma, AZ

Chula Vista, CA

Indio, CA Santa Barbara, CA Boulder City, NV El Paso, TX

Cuyamaca, CA

Roosevelt WNW, AZ

1

Tucson WFO, AZ Brawley, CA Indio, CA

383

Pasadena, CA Redlands, CA

Jornada Exp Range, NM Orogrande, NM NM State University (Las Cruces), NM

Table A8. Cold-season and early cold season Ad averaged over local expansion hotspots and coldspots in each decade. The top half of the table shows the mean decadal abnormality ( Ad ) of cold-season (Oct-Apr) and early cold-season (Oct-Dec) precipitation averaged over local expansion hotspots in each decade. The bottom half of the table shows the increase in Ad from local expansion coldspots to hotspots. “Current decade” rows show results derived from precipitation data over the same decade as the local expansion occurred, whereas “Previous decade” rows, over the decade prior to the local expansion. P-values were estimated by using Wilcox signed rank test (hotspots) and Wilcox rank sum test (hotspots vs. coldspots). Q-values were estimated by using QVALUE package in R. The q-value cut-off was set to 0.005, corresponding to a false discovery of 0.065 tests among the 13 tests that were significant. Ad that are significantly different from zero were highlighted in bold.

Current decade

Previous decade Current decade

Previous decade

Hotspots

Focal decade

Hotspots - Coldspots

384 385 386 387 388 389 390 391 392

1960s

1970s

1980s

1990s

2000s

Ad

P-value

q-value

Ad

P-value

q-value

Ad

P-value

q-value

Ad

P-value

q-value

Ad

P-value

q-value

cold-season

0.002

1

0.156

0.059

0.057

0.019

0.086

0.012

0.004

0.190

< 0.01

< 0.001

-0.177

< 0.01

< 0.001

early coldseason

0.375

< 0.01

< 0.001

0.076

0.340

0.074

0.236