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Journal Article

Constraint around Quarter-Power Allometric Scaling in Wild Tomatoes (Solanum sect. Lycopersicon; Solanaceae)

Christopher D. Muir and Meret Thomas-Huebner
The American Naturalist
Vol. 186, No. 3 (September 2015), pp. 421-433
DOI: 10.1086/682409
Stable URL:
Page Count: 13

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Topics: Phylogenetics, Species, Fecundity, Allometry, Leaf area, Drought, Plants, Statistical models, Modeling, Metabolism
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AbstractThe West-Brown-Enquist (WBE) metabolic scaling theory posits that many organismal features scale predictably with body size because of selection to minimize transport costs in resource distribution networks. Many scaling exponents are quarter-powers, as predicted by WBE, but there are also biologically significant deviations that could reflect adaptation to different environments. A central but untested prediction of the WBE model is that wide deviation from optimal scaling is penalized, leading to a pattern of constraint on scaling exponents. Here, we demonstrate, using phylogenetic comparative methods, that variation in allometric scaling between mass and leaf area across 17 wild tomato taxa is constrained around a value indistinguishable from that predicted by WBE but significantly greater than 2/3 (geometric-similarity model). The allometric-scaling exponent was highly correlated with fecundity, water use, and drought response, suggesting that it is functionally significant and therefore could be under selective constraints. However, scaling was not strictly log–log linear but rather declined during ontogeny in all species, as has been observed in many plant species. We caution that although our results supported one prediction of the WBE model, it did not strongly test the model in other important respects. Nevertheless, phylogenetic comparative methods such as those used here are powerful but underutilized tools for metabolic ecology that complement existing methods to adjudicate between models.

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Literature Cited
  • ['Ambrámoff, M. D., P. J. Magelhães, and S. J. Ram. 2004. Image processing with ImageJ. Biophotonics International 11:36–42.']
  • ['Bartoszek, K., J. Pienaar, P. Mostad, S. Andersson, and T. F. Hansen. 2012. A phylogenetic comparative method for studying multivariate adaptation. Journal of Theoretical Biology 314:204–215.']
  • ['Bates, D. M., M. Mächler, and B. M. Bolker. 2013. lme4: linear mixed-effects models using Eigen and S4.']
  • ['Boettiger, C., G. Coop, and P. Ralph. 2012. Is your phylogeny informative? measuring the power of comparative methods. Evolution 66:2240–2251.']
  • ['Bokma, F. 2004. Evidence against universal metabolic scaling. Functional Ecology 18:184–187.']
  • ['Chetelat, R. T., R. A. Pertuzé, L. Faúndex, E. B. Graham, and C. M. Jones. 2009. Distribution, ecology and reproductive biology of wild tomatoes and related nightshades from the Atacama Desert region of northern Chile. Euphytica 167:77–93.']
  • ['Chitwood, D. H., L. R. Headland, D. L. Filiault, R. Kumar, J. M. Jiminez-Gómez, A. V. Schrager, D. S. Park, J. Peng, N. R. Sinha, and J. N. Maloof. 2012. Native environment modulates leaf size and response to simulated foliar shade across wild tomato species. PLoS ONE 7:e29570. doi:10.1371/journal.pone.0029570.']
  • ['Coomes, D. A., and R. B. Allen. 2009. Testing the metabolic scaling theory of tree growth. Journal of Ecology 97:1369–1373.']
  • ['Enquist, B. J. 2002. Universal scaling in tree and vascular plant allometry: toward a general quantitative theory linking plant form and function from cells to ecosystems. Tree Physiology 22:1045–1064.']
  • ['Enquist, B. J., A. P. Allen, J. H. Brown, J. F. Gillooly III, A. J. Kerkoff, K. J. Niklas, C. A. Price, and G. B. West. 2007a. Does the exception prove the rule? Nature 445:E9–E10.']
  • ['Enquist, B. J., and L. P. Bentley. 2012. Land plants: new theoretical directions and empirical prospects. Pages 164–187 in R. M. Sibly, J. H. Brown, and A. Kodric-Brown, eds. Metabolic ecology: a scaling approach. Wiley, Chichester.']
  • ['Enquist, B. J., J. H. Brown, and G. B. West. 1998. Allometric scaling of plant energetics and population density. Nature 395:163–165.']
  • ['Enquist, B. J., A. J. Kerkhoff, S. C. Stark, N. G. Swenson, and M. C. McCarthy. 2007b. A general integrative model for scaling plant growth, carbon flux, and functional trait spectra. Nature 449:218–222.']
  • ['Enquist, B. J., and K. J. Niklas. 2002. Global allocation rules for patterns of biomass partitioning in seed plants. Science 295:1517–1519.']
  • ['Enquist, B. J., G. B. West, E. L. Charnov, and J. H. Brown. 1999. Allometric scaling of production and life-history variation in vascular plants. Nature 401:907–911.']
  • ['Estes, S., and S. J. Arnold. 2007. Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales. American Naturalist 169:227–244.']
  • ['Felsenstein, J. 1985. Phylogenies and the comparative method. American Naturalist 125:1–15.']
  • ['Glazier, D. S. 2010. A unifying explanation for diverse metabolic scaling in animals and plants. Biological Reviews 85:111–138.']
  • ['Haak, D. C., B. A. Ballenger, and L. C. Moyle. 2014. No evidence for phylogenetic constraint on natural defense evolution among wild tomatoes. Ecology 95:1633–1641.']
  • ['Hammond, S. T., and K. J. Niklas. 2012. Computer simulations support a core prediction of a contentious plant model. American Journal of Botany 99:508–516.']
  • ['Hansen, T. F. 2012. Adaptive landscapes and the comparative analysis of adaptation. Pages 205–226 in E. I. Svensson and R. Calsbeek, eds. The adaptive landscape in evolutionary biology. Oxford University Press, Oxford.']
  • ['Hansen, T. F., and K. Bartoszek. 2012. Interpreting the evolutionary regression: the interplay between observational and biological errors in phylogenetic comparative studies. Systematic Biology 61:413–425.']
  • ['Hansen, T. F., J. Pienaar, and S. H. Orzack. 2008. A comparative method for studying adaptation to a randomly evolving environment. Evolution 62:1965–1977.']
  • ['Hetherington, S. E., R. M. Smillie, and W. J. Davies. 1998. Photosynthetic activities of vegetative and fruiting tissues in tomato. Journal of Experimental Botany 324:1173–1181.']
  • ['Ho, L. S. T., and C. Ané. 2014. A linear-time algorithm for Gaussian and non-Gaussian trait evolution models. Systematic Biology 63:397–408.']
  • ['Hudson, L. N., N. J. B. Isaac, and D. C. Reuman. 2013. The relationship between body mass and field metabolic rate among individual birds and mammals. Journal of Animal Ecology 82:1009–1020.']
  • ['Kamenetzky, L., R. Asís, S. Bassi, F. de Godoy, L. Bermúdez, A. R. Fernie, M.-A. Van Sluys, et al. 2010. Genomic analysis of wild tomato introgressions determining metabolism- and yield-associated traits. Plant Physiology 152:1772–1786.']
  • ['Kerkhoff, A. J., and B. J. Enquist. 2009. Multiplicative by nature: why logarithmic transformation is necessary in allometry. Journal of Theoretical Biology 257:519–521.']
  • ['Koch, G. W., S. C. Sillett, G. M. Jennings, and S. D. Davis. 2004. The limits to tree height. Nature 428:783–876.']
  • ['Kolokotrones, T., V. Savage, E. J. Deeds, and W. Fontana. 2010. Curvature in metabolic scaling. Nature 464:753–756.']
  • ['Koyama, K., and K. Kikuzawa. 2009. Is whole-plant photosynthetic rate proportional to leaf area? a test of scalings and a logistic equation by leaf demography census. American Naturalist 173:640–649.']
  • ['Les, D. H., D. J. Crawford, E. Landolt, J. D. Gabel, and R. T. Kimball. 2002. Phylogeny and systematics of Lemnaceae, the duckweed family. Systematic Botany 27:221–240.']
  • ['Lloyd, J., K. Bloomfield, T. F. Domingues, and G. D. Farquhar. 2013. Photosynthetically relevant foliar traits correlating better on a mass vs an area basis: of ecophysiological relevance or just a case of mathematical imperatives and statistical quicksand? New Phytologist 199:311–321.']
  • ['Maynard Smith, J., R. Burian, S. Kauffman, P. Alberch, J. Campbell, B. Goodwin, R. Lande, D. Raup, and L. Wolpert. 1985. Developmental constraints and evolution. Quarterly Review of Biology 60:265–287.']
  • ['McCulloh, K. A., J. S. Sperry, and F. R. Adler. 2003. Water transport in plants obeys Murray’s law. Nature 421:939–942.']
  • ['Mori, S., K. Yamaji, A. Ishida, S. G. Prokushkin, O. V. Masyagina, A. Hagihara, A. T. M. R. Hoque, et al. 2010. Mixed-power scaling of whole-plant respiration from seedlings to giant trees. Proceedings of the National Academy of Sciences of the USA 107:1447–1451.']
  • ['Moyle, L. C. 2008. Ecological and evolutionary genomics in the wild tomatoes (Solanum sect. Lycopersicon). Evolution 62:2995–3013.']
  • ['Muir, C. D., and M. Thomas-Huebner. 2015. Data from: Constraint around quarter-power allometric scaling in wild tomatoes (Solanum sect. Lycopersicon; Solanaceae). American Naturalist, Dryad Digital Repository,']
  • ['Muller-Landau, H. C., R. S. Condit, J. Chave, S. C. Thomas, S. A. Bohlman, S. Bunyavejchewin, S. Davies, et al. 2006. Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests. Ecology Letters 9:575–588.']
  • ['Nakazato, T., M. Bogonovich, and L. C. Moyle. 2008. Environmental factors predict adaptive phenotypic differentiation within and between two wild Andean tomatoes. Evolution 62:774–792.']
  • ['Nakazato, T., R. A. Franklin, B. C. Kirk, and E. A. Housworth. 2012. Population structure, demographic history, and evolutionary patterns of a green-fruited tomato, Solanum peruvianum (Solanaceae), revealed by spatial genetics analyses. American Journal of Botany 99:1207–1216.']
  • ['Nakazato, T., and E. A. Housworth. 2011. Spatial genetics of wild tomato species reveals roles of the Andean geography on demographic history. American Journal of Botany 98:88–98.']
  • ['Nakazato, T., D. L. Warren, and L. C. Moyle. 2010. Ecological and geographic modes of species divergence in wild tomatoes. American Journal of Botany 97:680–693.']
  • ['Niklas, K. J. 1994. Plant allometry. University of Chicago Press, Chicago.']
  • ['———. 2006. A phyletic perspective on the allometry of plant biomass-partitioning patterns and functionally equivalent organ-categories. New Phytologist 171:27–40.']
  • ['Niklas, K. J., and B. J. Enquist. 2001. Invariant scaling relationships for interspecific plant biomass production rates and body size. Proceedings of the National Academy of Sciences of the USA 98:2922–2927.']
  • ['Nunn, C. L., and R. A. Barton. 2000. Allometric slopes and independent contrasts: a comparative test of Kleiber’s law in primate ranging patterns. American Naturalist 156:519–533.']
  • ['Orme, C. D. L., R. P. Freckleton, G. H. Thomas, T. Petzoldt, S. Fritz, N. J. B. Isaac, and W. D. Pearse. 2012. caper: comparative analyses of phylogenetics and evolution in R.']
  • ['Osnas, J. L. D., J. W. Lichstein, P. B. Reich, and S. W. Pacala. 2013. Global leaf trait relationships: mass, area, and the leaf economics spectrum. Science 340:741–744.']
  • ['Pagel, M. 1999. Inferring the historical patterns of biological evolution. Nature 401:877–884.']
  • ['Peng, Y., K. J. Niklas, P. B. Reich, and S. Sun. 2010. Ontogenetic shift in the scaling of dark respiration with whole-plant mass in seven shrub species. Functional Ecology 24:502–512.']
  • ['Pennell, M. W., J. M. Eastman, G. J. Slater, J. W. Brown, J. C. Uyeda, R. G. FitzJohn, M. E. Alfaro, and L. J. Harmon. 2014. geiger v2.0: an expanded suite of methods for fitting macroevolutionary models to phylogenetic trees. Bioinformatics 30:2216–2218.']
  • ['Pennell, M. W., and L. J. Harmon. 2013. An integrative view of phylogenetic comparative methods: connections to population genetics, community ecology, and paleobiology. Annals of the New York Academy of Sciences 1289:90–105.']
  • ['Peralta, I. E., D. M. Spooner, and S. Knapp. 2008. Taxonomy of wild tomatoes and their relatives (Solanum sect. Lycopersicoides, sect. Juglandifolia, sect. Lycopersicon; Solanaceae). Systematic Botany Monographs, no. 84. American Society of Plant Taxonomists, Ann Arbor, MI.']
  • ['Poorter, H., and L. Sack. 2012. Pitfalls and possibilities in the analysis of biomass allocation patterns in plants. Frontiers in Plant Science 3:259. doi:10.3389/fpls.2012.00259.']
  • ['Price, C. A., B. J. Enquist, and V. M. Savage. 2007. A general model for allometric covariation in botanical form and function. Proceedings of the National Academy of Sciences of the USA 104:13204–13209.']
  • ['Price, C. A., J. F. Gilooly, A. P. Allen, J. S. Weitz, and K. J. Niklas. 2010. The metabolic theory of ecology: prospects and challenges for plant biology. New Phytologist 188:696–710.']
  • ['Price, C. A., K. Ogle, E. P. White, and J. S. Weitz. 2009. Evaluating scaling models in biology using hierarchical Bayesian approaches. Ecology Letters 12:641–651.']
  • ['Price, C. A., J. S. Weitz, V. M. Savage, J. Stegen, A. Clarke, D. A. Coomes, P. S. Dodds, et al. 2012. Testing the metabolic theory of ecology. Ecology Letters 15:1465–1474.']
  • ['Reich, P. B., M. G. Tjoelker, J.-L. Machado, and J. Oleksyn. 2006. Universal scaling of respiratory metabolism, size and nitrogen in plants. Nature 439:457–461.']
  • ['Revell, L. J. 2010. Phylogenetic signal and linear regression on species data. Methods in Ecology and Evolution 1:319–329.']
  • ['Rodriguez, F., F. Wu, C. Ané, S. Tanksley, and D. M. Spooner. 2009. Do potatoes and tomatoes have a single evolutionary history, and what proportion of the genome supports this history? BMC Evolutionary Biology 9:191. doi:10.1186/1471-2148-9-191.']
  • ['Rüger, N., U. Berger, S. P. Hubbell, G. Vieilledent, and R. Condit. 2011. Growth strategies of tropical tree species: disentangling light and size effects. PLoS ONE 6:e25330. doi:10.1371/journal.pone.0025330.']
  • ['Särkinen, T., L. Bohs, R. G. Olmstead, and S. Knapp. 2013. A phylogenetic framework for evolutionary study of the nightshades (Solanaceae): a dated 1000-tip tree. BMC Evolutionary Biology 13:214. doi:10.1186/1471-2148-13-214.']
  • ['Savage, V. M., L. P. Bentley, B. J. Enquist, J. S. Sperry, D. D. Smith, P. B. Reich, and E. I. von Allmen. 2010. Hydraulic trade-offs and space filling enable better predictions of vascular structure and function in plants. Proceedings of the National Academy of Sciences of the USA 107:22722–22727.']
  • ['Savage, V. M., E. J. Deeds, and W. Fontana. 2008. Sizing up allometric scaling theory. PLoS Computational Biology 4(9):e1000171. doi:10.1371/journal.pcbi.1000171.']
  • ['Stamatakis, A. 2006. RAxML-VI-HPC: maximum likelihood-based phylogenetic analyses with thousands of taxa and mixed models. Bioinformatics 22:2688–2690.']
  • ['Tellier, A., S. J. Y. Laurent, H. Lainer, P. Pavlidis, and W. Stephan. 2011. Inference of seed bank parameters in two wild tomato species using ecological and genetic data. Proceedings of the National Academy of Sciences of the USA 108:17052–17057.']
  • ['Vasseur, F., C. Violle, B. J. Enquist, C. Granier, and D. Vile. 2012. A common genetic basis to the origin of the leaf economics spectrum and metabolic scaling allometry. Ecology Letters 15:1149–1157.']
  • ['Warton, D. I., R. A. Duursma, D. S. Falster, and S. Taskinen. 2012. smatr 3—an R package for estimation and inference about allometric lines. Methods in Ecology and Evolution 3:257–259.']
  • ['Warton, D. I., I. J. Wright, D. S. Falster, and M. Westoby. 2006. Bivariate line fitting for allometry. Biological Reviews 81:259–291.']
  • ['West, G. B., J. H. Brown, and B. J. Enquist. 1997. A general model for the origin of allometric scaling laws in biology. Science 276:122–126.']
  • ['———. 1999. A general model for the structure and allometry of plant vascular systems. Nature 400:664–667.']
  • ['White, C. R., and R. S. Seymour. 2003. Mammalian basal metabolic rate is proportional to body mass2/3. Proceedings of the National Academy of Sciences of the USA 100:4046–4049.']


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