Decomposing the Causes for Niche Differentiation Between Species

Home , Niche differentiation

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1 Decomposing the causes for niche differentiation between

2 species using hypervolumes

5 José Carlos Carvalho1,2,3* and Pedro Cardoso2,3

7 1CBMA – Molecular and Environmental Centre, Department of Biology, Univer-

8 sity of Minho, Gualtar Campus, 4710-057 Braga, Portugal

9 2CE3C – Centre for Ecology, Evolution and Environmental Changes / Azorean

10 Biodiversity Group, Universidade dos Açores, 9700-042 Angra do Heroísmo,

11 Portugal.

12 3LIBRe - Laboratory for Integrative Biodiversity Research, Finnish Museum of

13 Natural History, University of Helsinki, POBox 13, 00014 Helsinki, Finland.

14 * Corresponding author. Azorean Biodiversity Group–CITA-A, University of

15 Azores, Angra do Heroísmo, Portugal. Email: [email protected]

18 Abstract

19 1. Hutchinson’s n-dimensional hypervolume concept holds a central role across

20 different fields of ecology and evolution. The question of the amount of hyper-

21 volume overlap and differentiation between species is of great interest to under-

22 stand the processes that drive niche dynamics, competitive interactions and, ul-

23 timately, community assembly.

1 bioRxiv preprint doi: https://doi.org/10.1101/485920; this version posted December 4, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license.

24 2. A novel framework is proposed to decompose overall differentiation among

25 hypervolumes into two distinct components: niche shifts and niche contraction /

26 expansion processes. Niche shift corresponds to the replacement of space

27 between the hypervolumes occupied by two species, whereas niche contraction

28 / expansion processes correspond to net differences between the amount of

29 space enclosed by each hypervolume.

30 3. Hypervolumes were constructed for two Darwin' finches, Geospiza conirostris

31 and Geospiza magnirostris, using intraspecific trait data from Genovesa Island,

32 where they live in sympatry. Results showed that significant niche shifts, not

33 niche contraction, occurred between these species. This means that Geospiza

34 conirostris occupied a different niche space and not a reduced space on Genov-

35 esa.

36 4. The proposed framework allows disentangling different processes and under-

37 stand the drivers of niche partitioning between coexisting species. Niche dis-

38 placement due to competition can this way be separated from niche contraction

39 due to specialization or expansion due to lower pressure on newly occupied

40 ecological settings.

42 Keyword: Intraspecific trait variability, Fundamental niche, Morphospace, Niche

43 contraction, Niche shift, Realized niche

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44 1 | INTRODUCTION

46 The concept of species fundamental niche proposed by Hutchinson (1957) is at

47 the roots of many ecological and evolutionary theories. Hutchinson formalized

48 this concept as a multidimensional hypervolume, defined by a set of n inde-

49 pendent variables that represent biologically relevant axes. According to his

50 perspective, each point within this n-dimensional space corresponds to a pos-

51 sible state of the environment permitting the species to survive.

52 Hutchinsonian niches can be estimated by quantifying the functional trait hyper-

53 volume occupied by the individuals of a given species. In essence, a set of

54 functional traits, representing major axes of ecological strategies, are selected.

55 Then, the hypervolume is constructed to estimate the morphospace occupied

56 by the species. The hypervolume, representing the intraspecific trait variability,

57 is commonly interpreted as the realized niche of the species (e.g. Pigot, Trisos,

58 & Tobias, 2016).

59 The question of the amount of morphospace overlap and differentiation

60 between species is of great interest to understand the processes that drive

61 niche dynamics, competitive interactions and, ultimately, community assembly

62 (e.g. Ricklefs & Cox, 1977; Stubs & Wilson, 2004; Kraft, Valencia, & Ackerly,

63 2008). The hypervolume overlap corresponds to the shared space between two

64 species, whilst hypervolume differentiation corresponds to the sum of the

65 unique fractions of space belonging to each species. Niche differentiation

66 between species may be caused by two distinct processes: niche shifts and

67 niche contraction (or expansion). Niche shifts are determined by the replace-

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68 ment of niche space between species. In this case, species change their niche

69 position in order to occupy a different niche space. For example, morphological

70 displacement of traits related to food acquisition have been interpreted as a

71 strategy to reduce niche overlap and avoid competition (Huey, Pianka, Egan, &

72 Coons, 1974). On the other hand, niche contraction (or expansion) processes

73 are determined by differences in niche breadth (e.g. Pulliam, 1986). Niche con-

74 traction occurs when a species reduces its niche breadth. For example, when

75 faced with more intense competition from another species, many organisms re-

76 strict their utilization of shared microhabitats and/or other resources (Pianka,

77 2000). This might give them advantage exploring these resources over other,

78 generalist, species, as they adapt to explore them to the fullest. Niche expan-

79 sion occurs when a species augments its niche breadth when presented with

80 ecological opportunity (McCormack & Smith, 2008). Compelling examples of

81 niche expansion are given by studies in islands where species were released

82 from competition (e.g. Lister, 1976). Thus, to understand the factors that drive

83 niche differentiation between species it is important to disentangle niche shifts

84 from niche expansion (or contraction) processes.

85 In this paper, we propose a novel framework for partitioning hypervolumes via

86 pairwise comparisons into niche shifts and niche contraction (or expansion). We

87 present a case study to illustrate how these concepts can be applied to decom-

88 pose the causes for niche differentiation between species.

91 2 | MATERIAL AND METHODS

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93 2.1 | Hypervolume partitioning

94 To decompose hypervolume differentiation into different fractions, we use the

95 set theory notation, in the manner of Hutchinson. Given a pairwise hypervolume

96 system composed by hypervolumes hi and hj, the total space occupied by them

97 is given by their reunion (hi U hj). Total pairwise hypervolume corresponds to

98 the sum of hypervolume overlap given by the interception (hi ∩ hj) plus hyper-

99 volume differentiation, denoted by hi Δ hj.

100 Thus, a pairwise hypervolume system can be partitioned according to the equa-

101 tion:

102 hi U hj = hi Δ hj + hi ∩ hj (eq. 1)

103 The differentiation between the hypervolumes hi and hj (hi Δ hj) corresponds to

104 the sum of their unique fractions:

105 hi Δ hj = hi U hj - hi ∩ hj. = hi \ hj + hj \ hi (eq. 2)

106 Total differentiation (hi Δ hj) can occur as a consequence of two distinct pro-

107 cesses: i) the differentiation that results from the replacement of space between

108 hypervolumes; and, ii) differentiation that results from the net difference

109 between the amounts of space enclosed by each hypervolume.

110 The net difference between both hypervolumes is given by |hi \ hj - hj \ hi|. The

111 replacement component can be obtained by subtracting the difference fraction

112 from total differentiation, using equation 2:

113 hi \ hj + hj \ hi - |hi \ hj - hj \ hi|

114 This expression can be written in the form:

115 max (hi \ hj, hj \ hi) + min (hi \ hj, hj \ hi) - [max (hi \ hj, hj \ hi) - min (hi \ hj, hj \ hi)].

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116 By simplifying the expression, we obtain the replacement component:

117 2min(hi \ hj, hj \ hi).

118 Thus, the total differentiation component can be additively partitioned in two

119 components:

120 hi Δ hj = 2min(hi \ hj, hj \ hi) + |hi \ hj - hj \ hi|(eq. 3)

121 A total partitioning of hi U hj can be obtained by the equation (see Fig. 1):

122 hi U hj = hi ∩ hj + 2min(hi \ hj, hj \ hi) + |hi \ hj - hj \ hi|. (eq. 4)

123 The terms in equations 3 and 4 can be scaled in relation to the total space oc-

124 cupied by the hypervolume pairwise system, thus obtaining the following equi-

125 valency:

126 1 = (hi ∩ hj + hi Δ hj) / hi U hj = [hi ∩ hj + 2min(hi \ hj, hj \ hi) + |hi \ hj - hj \ hi|]/ hi

127 U hj. (eq. 5)

128 This equivalency can be summarized in the equation:

129 1 = Hẟoverlap + Hẟtotal = Hẟoverlap + Hẟrepl + Hẟdiff (eq. 6)

130 where, Hẟoverlap refers to the proportion of overlap between hypervolumes (simil-

131 arity), Hẟtotal refers to total differentiation between both hypervolumes, Hẟrepl cor-

132 responds to the proportion of differentiation that results from the replacement of

133 space between hypervolumes and Hẟdiff is the proportion of differentiation that

134 results from the net differences between the spaces occupied by both hyper-

135 volumes.

136

137 2.2 | Assessing intraspecific trait variability and niche partitioning

138 Here, we advocate that intraspecific trait variability can be used to estimate

139 niche parameters. The underlying assumption of a trait-based approach is that

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140 traits reflect species adaptations to the environment (Diaz & Cabido, 2001) and,

141 hence, should be a useful tool to quantify species' niches (Violle & Jiang, 2009).

142 In other words, we are assuming that the morphospace occupied by each spe-

143 cies is a surrogate for its realized niche.

144 Consider N individuals belonging to a given species S and measure a set of T

145 traits for each individual. The matrix N x T can be used to construct the hyper-

146 volume, which is assumed to describe the realized niche of the species. There-

147 fore, the niche breadth of species S is given by the extent of the hypervolume.

148 Obviously, hypervolumes can be calculated for a set of species. The set opera-

149 tions can be applied to hypervolumes using eqs. 1-6 for each species pair. This

150 allows obtaining a pairwise partitioning of the niche species pairs. Therefore,

151 the terms in eq. 6 mean: Hẟoverlap = niche overlap between two species; Hẟotal =

152 total niche differentiation between two species; Hẟrepl = differentiation due to the

153 replacement of niche space; Hẟdiff = differentiation due to differences of niche

154 breadth between species. Thus, higher values of Hẟrepl are indicative of niche

155 shifts between species, whereas higher values of Hẟdiff are indicative of niche

156 contraction / expansion of one of the species in relation to the other (functional

157 richness).

158

159 2.3 | Incorporating different data types in hypervolume estimation

160 A limitation to the current hypervolume algorithms, is that they require datasets

161 with continuous variables (Blonder, Lamanna, Violle, & Enquist, 2014; Blonder

162 et al., 2018). We suggest that this limitation may be overcome by applying al-

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163 ready available statistical methods to the trait matrix, from now on called T ma-

164 trix, prior to hypervolume estimation.

165 Multivariate techniques, specially developed to deal with mixed data, may be

166 used to ordinate the T matrix (e.g. Hill & Smith, 1976; Kiers, 1994). These ordi-

167 nation techniques are similar to a principal component analysis, allowing to ex-

168 tract several orthogonal axes (components) representing the variation of the T

169 matrix (e.g. PCAMIX, Chavent, Kuentz-Simonet, Labenne, & Saracco, 2017).

170 These axes can be interpreted in relation to the original variables (traits), by ex-

171 amining the matrix of eigenvectors in a similar way to a PCA. Then, the result-

172 ing axes are used as the new variables to compute hypervolumes (Fig. 2). If the

173 aim is to include all the variation of the T matrix in the analyses, one should re-

174 tain all the axes. However, most probably some of these components represent

175 little variation and are difficult to interpret. Therefore, a more parsimonious strat-

176 egy would be to select only those axes that provide a clearly interpretable re-

177 sult.

178 The distance-based framework proposed by Laliberté & Legendre (2010) is an

179 alternative to consider. Briefly, this approach is based on three steps: i) an ap-

180 propriate distance measure (Gower dissimilarity measure; Gower,1971; Podani,

181 1999; Legendre & Legendre, 2012) is computed from the T matrix; ii) this dis-

182 tance matrix is analyzed through principal coordinate analysis (PCoA); and, (3)

183 the resulting PCoA axes are used as the new variables to compute hypervol-

184 umes (Fig. 2). A comprehensive description of PCoA is given in Legendre & Le-

185 gendre (2012).

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186 Both PCAMIX and PCoA allow to extract orthogonal axes, which eliminates the

187 potential correlation among trait variables, a pre-requisite of hypervolume meth-

188 ods. Independently of which technique is used to transform the T matrix, an ad-

189 ditional point to consider is giving weights to trait variables, because a single

190 categorical trait can be coded by several dummy variables. Also, prior weights

191 can be given to trait variables, allowing to differentiate traits that contribute more

192 to the biological performance of the species. Contrary to PCAMIX, the informa-

193 tion of each trait is lost during the PCoA, because the T matrix is transformed

194 into a dissimilarity matrix of individuals (or species), prior to the calculation of

195 hypervolumes. Thus, the interpretation of these shapes is relative to the axes of

196 the PCoA analysis and not in relation to the traits. Therefore, questions about

197 which traits contribute more or less to a given hypervolume parameter are diffi-

198 cult to address.

199

200 2.4 | Case study

201 We present a demonstration analysis of hypervolume partitioning for two spe-

202 cies of Darwin’s finches: Geospiza conirostris and Geospiza magnirostris. Both

203 species inhabit Island Genovesa, but only the former is present in Island Es-

204 pañola. A well-known hypothesis for the two species is that competitive charac-

205 ter displacement occurred on Genovesa and, therefore, they should have

206 evolved to occupy dissimilar niches (Lack, 1945, 1947; Grant & Grant, 1982).

207 We tested this hypothesis on Genovesa and Española Islands with morphomet-

208 ric data collected by Lack (1945, 1947): WingL, wing length; BeakH, Beak

209 height; UbeakL, upper beak length and N-UBkL, nostril upper beak length. Data

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210 is available from Dryad Digital Repository: https://doi.org/10.5061/dryad.150.

211 The original measurements (in mm) were log10-transformed prior to the con-

212 struction of hypervolumes.

213 Hypervolumes for each species were calculated using a gaussian kernel density

214 estimator with the hypervolume R package with default parameters (see Blon-

215 der et al., 2018 for details). Then, hypervolume decomposition (eqs. 1-6) was

216 carried with the function beta.volumes of the BAT package (Cardoso, Rigal, &

217 Carvalho, 2015). Hypervolumes are reported in units of SDs to the power of the

218 number of trait dimensions used.

219

220

221 3 | RESULTS

222

223 As hypothesized, hypervolumes calculated using morphometric data for Geosp-

224 iza conirostris and Geospiza magnirostris were well differentiated on Genovesa

225 Island (Fig. 3), the niche overlap between these species being null (Hẟoverlap = 0).

226 By decomposing total differentiation (Hẟtotal = 1) into replacement and differ-

227 ences between niche breadths, we found that such differentiation was mostly

228 caused by niche replacement (Hẟrepl = 0.617) and not contraction/expansion, al-

229 though the latter was also considerable (Hẟdiff = 0.383). By comparing the niche

230 of Geospiza conirostris on Genovesa and Española, we found that they overlap

231 slightly (Hẟoverlap = 0.242) and the differentiation between both islands was

232 mainly due to the replacement of niche space (Hẟrepl = 0.711), not contraction/

233 expansion (Hẟdiff = 0.047). This result reinforces the interpretation that the pres-

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234 ence of Geospiza magnirostris on Genovesa Island led to a significant shift (not

235 contraction) of the niche of Geospiza conirostris.

236

237

238 4 | DISCUSSION

239

240 Hutchinson’s fundamental niche concept holds a central role across different

241 fields of ecology and evolution. Conceptually, the species niche corresponds to

242 an n-dimensional hypervolume enclosing the range of conditions under which

243 the species can survive and reproduce. Niche overlap occurs when species use

244 the same resources or strive under similar environmental conditions. In this re-

245 gard, a crucial question is which processes determine the differentiation

246 between species niches and, ultimately, determine species coexistence (MacAr-

247 thur & Levins, 1967; Pianka, 1973). In this paper, we propose a novel frame-

248 work to partitioning overall differentiation between hypervolumes into two dis-

249 tinct fractions: niche shifts corresponding to the differentiation that results from

250 the replacement of space between hypervolumes and niche contraction / ex-

251 pansion, corresponding to the differentiation that results from the net differences

252 between the space enclosed by hypervolumes.

253 We illustrate our framework with a classic dataset (Lack, 1945, 1947). Our res-

254 ults revealed that differentiation between Geospiza conirostris and Geospiza

255 magnirostris occurred mostly by niche shifts processes and not by the niche

256 contraction of Geospiza conirostris on Island Genovesa, where both species

257 live in sympatry. This means that Geospiza conirostris occupied a different

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258 niche space and not a reduced space on Genovesa. These results are consist-

259 ent with the hypothesis that the morphology of beaks was causally influenced

260 by interspecific competition for food resources (Lack, 1947). This hypothesis re-

261 ceived considerable support by analysing the food habits of these species

262 (Grant & Grant 1982). These authors showed that Geospiza magnirostris feeds

263 almost entirely on large-hard seeds, whilst Geospiza conirostris exploits

264 Opuntia and arthropods on Genovesa. Moreover, on Española Island, where

265 Geospiza magnirostris is absent, Geospiza conirostris consume large hard

266 seeds. Therefore, it seems that the presence of Geospiza magnirostris induces

267 a shift in the diet of Geospiza conirostris and, consequently, on its beak mor-

268 phology.

269 The functional roles and the sensitivity to environmental changes of the vast

270 majority of taxa are usually unknown (the so-called Hutchinsonian shortfall; Car-

271 doso et al., 2011). Therefore, a trait-based quantification of species niche can

272 provide a practical way to assess niche parameters for a potentially large num-

273 ber of species, making it possible to understand and predict species niche re-

274 sponses to environmental changes (Violla & Jiang, 2009; Blonder, 2018). Trait-

275 based approaches have been used successfully to integrate functional ecology

276 with community assembly and coexistence theories (e.g. McGill, Enquist, Wei-

277 her, & Westoby, 2006; Ackerly & Cornwell, 2007; Kraft, Valencia, & Ackerly,

278 2008). A major assumption of this approach is that trait dissimilarity is related to

279 decreasing niche overlap among co-existent species (e.g. Stubs & Wilson,

280 2004), a rationale related to the limiting similarity principle (MacArthur & Levins,

281 1967). This premise assumes, implicitly, that the trait space is a good surrogate

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282 for the niche space. However, linking trait patterns to niche differentiation re-

283 mains a challenge and, ultimately, depends on which traits were included in the

284 analysis (D'Andrea & Ostling, 2016). Thus, an informed choice of traits should

285 be made, based on their presumed adaptation to the species' ecological niche.

286 In conclusion, a novel framework was proposed to partition overall differenti-

287 ation between hypervolumes into distinct fractions, replacement of space (niche

288 shifts) and net differences between space amplitudes (niche contraction / ex-

289 pansion processes). The proposed framework allows disentangling different

290 processes and understand the drivers of niche partitioning between coexisting

291 species. Niche displacement due to competition can this way be separated from

292 niche contraction due to specialization or expansion due to lower pressure on

293 newly occupied ecological settings. We expect that the methods here presented

294 will allow to address a wider range of niche- and trait-based questions than was

295 possible to date.

296

297

298 Acknowledgements

299 PC is supported by Kone Foundation with the project “Trait-based prediction of

300 extinction risk”.

301

302 Authors' contributions

303 The authors contributed equally to the paper.

304

305

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17 bioRxiv preprint doi: https://doi.org/10.1101/485920; this version posted December 4, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license.

388 McGill, B. J, Enquist B. J., Weiher, E, & Westoby, M. (2006). Rebuilding com-

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398 Pigot, A. L., Trisos, C. H., & Tobias, J. A. (2016). Functional traits reveal the ex-

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401 20152013.

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403 Podani, J. (1999). Extending Gower's general coefficient of similarity to ordinal

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406 Pulliam, H. R. (1986). Niche expansion and contraction in a variable environ-

407 ment. American Zoologist, 26, 71-79.

408

18 bioRxiv preprint doi: https://doi.org/10.1101/485920; this version posted December 4, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license.

409 Ricklefs, R. E., & Cox, G. W. (1977). Morphological similarity and ecological

410 overlap among passerine birds on St. Kitts, British West Indies. Oikos, 29, 60-

411 66.

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413 Stubs W. J., & Wilson, J. B. (2004). Evidence for limiting similarity in a sand

414 dune community. Journal of Ecology, 92, 557-567.

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416 Violle, C., & Jiang, L. (2009). Towards a trait-based quantification of species

417 niche. Journal of Plant Ecology, 2, 87-93.

19 bioRxiv preprint doi: https://doi.org/10.1101/485920; this version posted December 4, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license.

418

419 Fig. 1. Diagram showing hypervolume partitioning in two dimensions. The over-

420 lap between hypervolumes hi and hj is given by the interception (hi ∩ hj) and the

421 differentiation (hi ∆ hj) is given by the sum of their unique fractions, hi \ hj and hj \

422 hi. Note that: hi ∆ hj = 2min(hi \ hj, hj \ hi) + |hi \ hj - hj \ hi|, where 2min(hi \ hj, hj \

423 hi) corresponds to the differentiation due to the replacement of space (grey

424 shaded area) and |hi \ hj - hj \ hi| refers to the net difference between both hyper-

425 volumes (white area in the hi \ hj space).

426

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428 Fig. 2. Diagram showing the construction of axes to be used in hypervolume es-

429 timation. The axes are obtained by ordination for mixed data types (PCAMIX;

430 see Chavent et al. 2017) or a PCoA carried on a Gower dissimilarity matrix of

431 individuals X traits (see Laliberté and Legendre, 2010). The eigenvalues corre-

432 spond to the amount of variance explained by each axis.

433

21 bioRxiv preprint doi: https://doi.org/10.1101/485920; this version posted December 4, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license.

434

435 Figure 3. Niche partitioning for two species of Darwin’s finches Geospiza

436 conirostris and Geospiza magnirostris. Hypervolumes shown as 2D projections

437 for all combinations of trait axis (WingL - wing length; BeakH - Beak height;

438 UbeakL - upper beak length and N-UBkL - nostril upper beak length) after log-

439 transformation of the original measurements.