Plant Ecology

, Volume 217, Issue 11, pp 1315–1329 | Cite as

A cost–benefit model for plant–plant interactions: a density-series tool to detect facilitation

  • Christopher J. LortieEmail author
  • Alessandro Filazzola
  • Clive Welham
  • Roy Turkington


Generally, only the net outcome of plant–plant interactions is measured in population and community ecology research, with few attempts to determine the relative importance of negative (competition) and positive (facilitation) interactions between subordinate species. Changes in the intensity of interactions along gradients, between life-stages, or with changing densities, and the use of selective removals enhance our capacity to infer positive and negative interactions. However, the most powerful examples at least in detecting facilitation typically involve measuring changes with or without a nurse-plant or benefactor species and often involve only a very limited numbers of species. In plant competition studies, however, greater number of species are commonly tested and density-dependent series are not an uncommon tool to test for net negative interactions. Here, we develop a cost–benefit model that can be used to comprehensively calculate the average expected net gain per individual at every point in a density series provided several response variables are recorded at each density. The utility of this model is demonstrated using both hypothetical data and several empirical data sets, and it is used to infer either both positive and negative net effects. Expected net gain can also serve as an accurate estimate of mean fitness per individual at a given density provided appropriate performance measures were recorded within the primary study. Within a single density series, both facilitation and competition can occur and were detectable using this method. This approach emphasizes the current view that both negative and positive interactions play a role in shaping plant communities. Furthermore, it is evident that facilitation can be detected using the manipulative density series typically associated with competition studies and not just using the typical target nurse-plant methodology. Finally, this method is a significant advance over the current practice of tallying up single responses within a study to estimate outcomes by providing a single, synthetic measure of the net gain or cost of interactions.


Cost–benefit Density dependence Multiplicative model Plant interactions Seeds 



Research was supported by an NSERC postgraduate scholarship and a fellowship from the Blaustein Center for Scientific Cooperation to CJL and an NSERC operating grant to RT. This is a publication of the Mitrani Department of Desert Ecology. We wish to extend special thanks to one referee in particular that provided numerous extremely useful ideas to the implications and interpretation of this model.

Supplementary material

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  1. Aksenova AA, Onipchenko VG (1998) Plant interactions in alpine tundra: 13 years of experimental removal of dominant species. Ecoscience 5:258–270Google Scholar
  2. Albert CH, Yoccoz NG, Edwards TC, Graham C, Zimmerman N, Thuiller W (2010) Sampling in ecology and evolution—bridging the gap between theory and practice. Ecography 33:1028–1037CrossRefGoogle Scholar
  3. Armas C, Pugnaire F (2005) Plant interactions govern population dynamics in a semiarid plant community. J Ecol 93:978–989CrossRefGoogle Scholar
  4. Armas C, Ordiales R, Pugnaire F (2004) Measuring plant interactions: a new comparative index. Ecology 85:2682–2686CrossRefGoogle Scholar
  5. Badano EI, Bustamante RO, Villarroel E, Marquet PA, Cavieres LA (2015) Facilitation by nurse plants regulates community invasibility in harsh environments. J Veg Sci 26:756–767CrossRefGoogle Scholar
  6. Bascompte J, Jordano P, Olensen JM (2006) Asymmetric coevolutionary networks faciliate biodiversity maintenance. Science 312:431–433CrossRefPubMedGoogle Scholar
  7. Baskin CC, Baskin JM (1998) Seeds: ecology, biogeography, and evolution of dormancy and germination. Academic Press, CambridgeGoogle Scholar
  8. Berkowitz AR, Canham CD, Kelly VR (1995) Competition vs. facilitation of tree seedling growth and survival in early successional communities. Ecology 76:1156–1168CrossRefGoogle Scholar
  9. Bertness MD, Callaway R (1994) Positive interactions in communities. Trends Ecol Evol 9:191–193CrossRefPubMedGoogle Scholar
  10. Bertness MD, Shumway SW (1993) Competition and facilitation in marsh plants. Am Nat 142:718–724CrossRefPubMedGoogle Scholar
  11. Bertness MD, Yeh SM (1994) Cooperative and competitive interactions in the recruitment of marsh elders. Ecology 75:2416–2429CrossRefGoogle Scholar
  12. Brooker RW, Kikvidze Z, Pugnaire F, Callaway RM, Choler P, Lortie CJ, Michalet R (2005) The importance of importance. Oikos 109:63–70CrossRefGoogle Scholar
  13. Brooker RW, Maestre FT, Callaway RM, Lortie CJ, Cavieres LA, Kunstler G, Liancourt P, Tielbörger K, Travis J, Anthelme F, Armas C, Coll L, Corcket E, Delzon S, Forey E, Kikvidze Z, Olofsson J, Pugnaire F, Quiroz Cl, Saccone P, Schiffers K, Seifan M, Touzard B, Michalet R (2008) Facilitation in plant communities: the past, present, and the future. J Ecol 96:18–34CrossRefGoogle Scholar
  14. Callaway RM (1995) Positive interactions among plants. Bot Rev 61:306–349CrossRefGoogle Scholar
  15. Callaway RM (2007) Positive interactions and interdependence in plant communities. Springer, DordrechtGoogle Scholar
  16. Callaway RM, Walker LR (1997) Competition and facilitation: a synthetic approach to interactions in plant communities. Ecology 78:1958–1965CrossRefGoogle Scholar
  17. Callaway RM, Brooker RW, Choler P, Kikvidze Z, Lortie CJ, Michalet R, Paolini L, Pugnaire FI, Newingham B, Aschehoug ET, Armas C, Kikidze D, Cook BJ (2002) Positive interactions among alpine plants increase with stress. Nature 417:844–848CrossRefPubMedGoogle Scholar
  18. Chamberlain SA, Bronstein JL, Rudgers JA (2014) How context dependent are species interactions? Ecol Lett 17:881–890CrossRefPubMedGoogle Scholar
  19. Cote IM, Jennions MD (2013) The procedure of meta-analysis in a nutshell. In: Koricheva J, Gurevitch J, Mengersen K (eds) Handbook of meta-analysis in ecology and evolution. Princeton University Press, Princeton, pp 14–26Google Scholar
  20. Crawley MJ (1990) The population dynamics of plants. Philos Trans R Soc Lond 330:125–140CrossRefGoogle Scholar
  21. Filazzola A, Lortie CJ (2014) A systematic review and conceptual framework for the mechanistic pathways of nurse plants. Glob Ecol Biogeogr 23:1335–1345CrossRefGoogle Scholar
  22. Goldberg DE (1996) Competitive ability: definitions, contingency, and correlated traits. Philos Trans R Soc Lond B 351:1377–1385CrossRefGoogle Scholar
  23. Goldberg DE, Turkington R, Olsvig-Whittaker L (1995) Quantifying the community-level consequences of competition. Folia Geobot Phytotax 30:231–242CrossRefGoogle Scholar
  24. Goldberg DE, Rajaniemi T, Gurevitch J, Stewart-Oaten A (1999) Empirical approaches to quantifying interaction intensity: competition and facilitation along productivity gradients. Ecology 80:1118–1131CrossRefGoogle Scholar
  25. Goldberg DE, Turkington R, Olsvig-Whittaker L, Dyer AR (2001) Density dependence in an annual plant community: variation among life history stages. Ecol Monogr 71:423–446CrossRefGoogle Scholar
  26. Goldenheim WM, Irving AD, Bertness MD (2008) Switching from negative to positive density-dependence among populations of cobble beach plant. Oecologia 158:478–482CrossRefGoogle Scholar
  27. Goodman LA (1960) On the exact variance of products. Journal of the American Statistical Association 55:708–713CrossRefGoogle Scholar
  28. Goodman LA (1962) The variance of the product of K random variables. J Am Stat Assoc 57:54–60Google Scholar
  29. Grace J, Tilman D (1990) Perspectives in Plant Competition. Academic Press, CambridgeGoogle Scholar
  30. Grime JP (1977) Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory. Am Nat 111:1169–1194CrossRefGoogle Scholar
  31. Hacker SD, Gaines SD (1997) Some implications of direct positive interactions for community species diversity. Ecology 78:1990–2003CrossRefGoogle Scholar
  32. Hamilton JG, Holzapfel C, Mahall BE (1999) Coexistence and interference between a native perennial grass and non-native annual grasses in California. Oecologia 121:518–526CrossRefGoogle Scholar
  33. He Q, Bertness MD, Altieri AH (2013) Global shifts towards positive species interactions with increasing environmental stress. Ecol Lett 16:695–706CrossRefPubMedGoogle Scholar
  34. HilleRisLambers J, Adler PB, Harpole WS, Levine JM, Mayfield MM (2012) Rethinking Community Assembly through the lens of coexistence theory. Annu Rev Ecol Evol Syst 43:227–248CrossRefGoogle Scholar
  35. Holmgren M, Scheffer M, Huston MA (1997) The interplay of facilitation and competition in plant communities. Ecology 78:1966–1975CrossRefGoogle Scholar
  36. Isbell FI, Polley HW, Wilsey BJ (2009) Species interaction mechanisms maintain grassland plant species diversity. Ecology 90:1821–1830CrossRefPubMedGoogle Scholar
  37. Jones RB (2005) TechDig. W. DigitizerGoogle Scholar
  38. Keddy PA (1989) Competition. Chapman and Hall, LondonCrossRefGoogle Scholar
  39. Koricheva J, Gurevitch J (2013) Place of meta-analysis among other methods of research synthesis. In: Koricheva J, Gurevitch J, Mengersen K (eds) Handbook of meta-analysis in ecology and evolution. Princeton University Press, Princeton, pp 3–13Google Scholar
  40. Koricheva J, Gurevitch J (2014) Uses and misuses of meta-analysis in plant ecology. J Ecol 102:828–844CrossRefGoogle Scholar
  41. Koricheva J, Gurevitch J, Mengersen K (2013) Handbook of meta-analysis in ecology and evolution. Princeton University Press, PrincetonCrossRefGoogle Scholar
  42. Körner C (1998) Alpine plants: stressed or adapted? In: Barker MG (ed) Physiological plant ecology. Blackwell Science, Hoboken, pp 297–311Google Scholar
  43. Lortie CJ (2014) Formalized synthesis opportunities for ecology: systematic reviews and meta-analyses. Oikos 123:897–902CrossRefGoogle Scholar
  44. Lortie CJ, Svenning JC (2015) The diversity of diversity studies: retrospectives and future directions. Ecography 38:330–334CrossRefGoogle Scholar
  45. Lortie CJ, Turkington R (2002) The effect of initial seed density on the structure of a desert annual plant community. J Ecol 90:435–445CrossRefGoogle Scholar
  46. Lortie CJ, Brooker RW, Choler P, Kikvidze Z, Michalet R, Pugnaire FI, Callaway RM (2004a) Rethinking plant community theory. Oikos 107:433–438CrossRefGoogle Scholar
  47. Lortie CJ, Brooker RW, Kikvidze Z, Callaway RM (2004b) The value of stress and limitation in an imperfect world: a reply to Körner. J Veg Sci 15:577–580CrossRefGoogle Scholar
  48. Lyons KG, Schwartz MW (2001) Rare species loss alters ecosystem function-invasion resistance. Ecol Lett 4:358–365CrossRefGoogle Scholar
  49. McIntire EJB (2014) Being a facilitator can be costly: teasing apart reciprocal effects. New Phytol 202:4–6CrossRefPubMedGoogle Scholar
  50. McIntire EJB, Fajardo A (2014) Facilitation as a ubiquitous driver of biodiversity. New Phytol 201:403–416CrossRefPubMedGoogle Scholar
  51. McMurray MH, Jenkins SH, Longland WS (1997) Effects of seed density on germination and establishment of a native and an introduced grass species dispersed by granivorous rodents. Am Midl Nat 138:322–330CrossRefGoogle Scholar
  52. Michalet R, Brooker RW, Cavieres LA, Kikvidze Z, Lortie CJ, Pugnaire FI, Valiente-Banuet A, Callaway RM (2006) Do biotic interactions shape both sides of the humped-back model of species richness in plant communities? Ecol Lett 9:767–773CrossRefPubMedGoogle Scholar
  53. Michalet R, Maalouf J-P, Choler P, Clément B, Rosebery D, Royer J-M, Schöb C, Lortie CJ (2014) Competition, facilitation and environmental severity shape the relationship between local and regional species richness in plant communities. Ecography 38:335–345CrossRefGoogle Scholar
  54. Olsen SL, Töpper JP, Skarpaas O, Vandvik V, Klanderud K (2016) From facilitation to competition: temperature-driven shift in dominant plant interactions affects population dynamics in semi-natural grasslands. Glob Chang Biol: n/a-n/aGoogle Scholar
  55. Palmblad IG (1968) Competition in experimental populations of weeds with emphasis on the regulation of population size. Ecology 49:26–34CrossRefGoogle Scholar
  56. Pescador DS, Chacón-Labella J, de la Cruz M, Escudero A (2014) Maintaining distances with the engineer: patterns of coexistence in plant communities beyond the patch-bare dichotomy. New Phytol 204:140–148CrossRefPubMedGoogle Scholar
  57. Pugnaire FI, Zhang L, Li R, Luo T (2015) No evidence of facilitation collapse in the Tibetan plateau. J Veg Sci 26:233–242CrossRefGoogle Scholar
  58. Schmitt RJ, Holbrook SJ (2003) Mutualism can mediate competition and promote coexistence. Ecol Lett 6:898–902CrossRefGoogle Scholar
  59. Schöb C, Michalet R, Cavieres LA, Pugnaire FI, Brooker RW, Butterfield BJ, Cook BJ, Kikvidze Z, Lortie CJ, Xiao S, Al Hayek P, Anthelme F, Cranston BH, García M-C, Le Bagousse-Pinguet Y, Reid AM, le Roux PC, Lingua E, Nyakatya MJ, Touzard B, Zhao L, Callaway RM (2014a) A global analysis of bidirectional interactions in alpine plant communities shows facilitators experiencing strong reciprocal fitness costs. New Phytol 202:95–105CrossRefPubMedGoogle Scholar
  60. Schöb C, Prieto I, Armas C, Pugnaire FI (2014b) Consequences of facilitation: one plant’s benefit is another plant’s cost. Funct Ecol 28:500–508CrossRefGoogle Scholar
  61. Soliveres S, Maestre FT (2014) Plant–plant interactions, environmental gradients and plant diversity: a global synthesis of community-level studies. Perspect Plant Ecol Evol Syst 16:154–163CrossRefPubMedPubMedCentralGoogle Scholar
  62. Sotomayor DA, Lortie CJ (2015) Indirect interactions in terrestrial plant communities: emerging patterns and research gaps. Ecosphere 6:art103-art103CrossRefGoogle Scholar
  63. Spiegel O, Nathan R (2012) Empirical evaluation of directed dispersal and density-dependent effects across successive recruitment phases. J Ecol 100:392–404CrossRefGoogle Scholar
  64. Stanton-Geddes J, Tiffin P, Shaw RG (2012) Role of climate and competitors in limiting fitness across range edges of an annual plant. Ecology 93:1604–1613CrossRefPubMedGoogle Scholar
  65. Sthultz CM, Gehring CA, Whitham TG (2007) Shifts from competition to facilitation between a foundation tree and a pioneer shrub across spatial and temporal scales in a semiarid woodland. New Phytol 173:135–145CrossRefPubMedGoogle Scholar
  66. Tielbörger K, Bilton MC, Metz J, Kigel J, Holzapfel C, Lebrija-Trejos E, Konsens I, Parag HA, Sternberg M (2014) Middle-Eastern plant communities tolerate 9 years of drought in a multi-site climate manipulation experiment. Nat Commun 5:5102CrossRefPubMedPubMedCentralGoogle Scholar
  67. Walker LR, Vitousek PM (1991) An invaded alters germination and growth of a native dominant tree in Hawaii. Ecology 72:1449–1455CrossRefGoogle Scholar
  68. Wilson WG, Nisbet RM (1997) Cooperation and competition along smooth environmental gradients. Ecology 78:2994–3017Google Scholar
  69. Wyszomirski T, Weiner J (2009) Variation in local density results in a positive correlation between plant neighbor sizes. Am Nat 173:705–708CrossRefPubMedGoogle Scholar
  70. Xiao S, Michalet R (2013) Do indirect interactions always contribute to net indirect facilitation? Ecol Model 268:1–8CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Christopher J. Lortie
    • 1
    • 2
    Email author
  • Alessandro Filazzola
    • 2
  • Clive Welham
    • 1
  • Roy Turkington
    • 1
  1. 1.Department of BotanyUniversity of British ColumbiaVancouverCanada
  2. 2.Department of BiologyYork UniversityTorontoCanada

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