Intraguild mutualism

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This presentation is the result of a one-week student group work during the Southerm-Summer School on Mathematical-Biology, held in São Paulo, BR, in January 2012, http://www.ictp-saifr.org/mathbio . As a follow-up of the subject pat of the group together with F. Lutscher (Univ. Ottawa) and R.M Coutinho (IFT-UNESP, Brazil) published a paper on ecological complexity on this subject, available at http://www.sciencedirect.com/science/article/pii/S1476945X12000773

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Intraguild mutualism

  1. 1. Intraguild mutualism Carlos H. Mantilla Fabio Daura-Jorge Maria Florencia Assaneo Marina Magalh˜es da Cunha a Murilo Dantas de Miranda Yangchen Lin January 22, 2012Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 1 / 19
  2. 2. Background Guild: species with common resource Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 2 / 19
  3. 3. Background Guild: species with common resource Focus on competition/predation Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 2 / 19
  4. 4. Background Guild: species with common resource Focus on competition/predation Intraguild mutualism (Crowley & Cox 2011 Trends Ecol. Evol. 26:627–633) Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 2 / 19
  5. 5. Background Guild: species with common resource Focus on competition/predation Intraguild mutualism (Crowley & Cox 2011 Trends Ecol. Evol. 26:627–633) Consequences for biodiversity and stability e.g. Gross 2008 Ecol. Lett. 11:929–936 Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 2 / 19
  6. 6. Intraguild mutualism Crowley & Cox 2011 Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 3 / 19
  7. 7. Groupers and moray eelsBshary et al. 2006 PLoS Biol. 4:e431 deardivebuddy.com Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 4 / 19
  8. 8. Objectives Does intraguild mutualism promote consumer coexistence? Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 5 / 19
  9. 9. Objectives Does intraguild mutualism promote consumer coexistence? General dynamical model (any mutualistic functional form) Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 5 / 19
  10. 10. Objectives Does intraguild mutualism promote consumer coexistence? General dynamical model (any mutualistic functional form) Stability analysis and simulation Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 5 / 19
  11. 11. Particular model 1 ˙ X = X(a21 Y Z + a1 Z − d1 ) ˙ Y = Y (a12 XZ + a2 Z − d2 ) ˙ Z = r(S − Z) − (e1 Y Z + e2 XZ + e12 Y ZX) Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 6 / 19
  12. 12. Simulation Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 7 / 19
  13. 13. Particular model 2 ˙ X = X(a12 Y Z + a1 Z − d1 ) ˙ Y = Y (a21 XZ + a2 Z − d2 ) ˙ Z = Z(r − e1 X − e2 Y − e12 Y X) Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 8 / 19
  14. 14. General model ˙ X = X [Zf (Y, α1 ) − d1 ] ˙ Y = Y [Zf (X, α2 ) − d2 ] ˙ Z = Z [r − e1 Xf (Y, α1 ) − e2 Y f (X, α2 )] Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 9 / 19
  15. 15. General model ˙ X = X [Zf (Y, α1 ) − d1 ] ˙ Y = Y [Zf (X, α2 ) − d2 ] ˙ Z = Z [r − e1 Xf (Y, α1 ) − e2 Y f (X, α2 )] Conditions for mutualism ∂f = g(X, α2 ) > 0 ∂X ∂f = g(Y, α1 ) > 0 ∂Y Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 9 / 19
  16. 16. Fixed points Z ∗ f (Y ∗ , α1 ) − d1 = 0 Z ∗ f (X ∗ , α2 ) − d2 = 0 e1 X ∗ f (Y ∗ , α1 ) + e2 Y ∗ f (X ∗ , α2 ) = r Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 10 / 19
  17. 17. Fixed points Z ∗ f (Y ∗ , α1 ) − d1 = 0 Z ∗ f (X ∗ , α2 ) − d2 = 0 e1 X ∗ f (Y ∗ , α1 ) + e2 Y ∗ f (X ∗ , α2 ) = r (0, 0, 0) (0, Y ∗ , Z ∗ ) (X ∗ , 0, Z ∗ ) (X ∗ , Y ∗ , Z ∗ ) Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 10 / 19
  18. 18. Fixed point (X ∗ , Y ∗ , Z ∗ ) X ∗ Z ∗ g(Y ∗ , α1 ) X ∗ f (Y ∗ , α1 )  0   Y ∗ Z ∗ g(X ∗ , α ) 0 Y ∗ f (X ∗ , α2 )  2    ∗ Z [−e1 f (Y ∗ , α1 )− Z ∗ [−e1 X ∗ g(Y ∗ , α1 )− 0   e2 Y ∗ g(X ∗ , α2 )] e2 f (X ∗ , α2 )] Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 11 / 19
  19. 19. Fixed point (X ∗ , Y ∗ , Z ∗ ) X ∗ Z ∗ g(Y ∗ , α1 ) X ∗ f (Y ∗ , α1 )  0   Y ∗ Z ∗ g(X ∗ , α ) 0 Y ∗ f (X ∗ , α2 )  2    ∗ Z [−e1 f (Y ∗ , α1 )− Z ∗ [−e1 X ∗ g(Y ∗ , α1 )− 0   e2 Y ∗ g(X ∗ , α2 )] e2 f (X ∗ , α2 )] −λ3 = mλ − b λ0 < 0 ⇒ R(λ1 ) = R(λ2 ) > 0 Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 11 / 19
  20. 20. Fixed point (X ∗ , 0, Z ∗ ) X ∗ d1   0 X ∗ Z ∗ g(0, α1 )   Z       0 Z ∗ f (X ∗ , α2 ) − d2 0        −Z ∗ e1 f (0, α1 ) −e1 Z ∗ X ∗ g(0, α1 )− 0    e2 Z ∗ f (X ∗ , α2 ) Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 12 / 19
  21. 21. Fixed point (X ∗ , 0, Z ∗ ) X ∗ d1   0 X ∗ Z ∗ g(0, α1 )   Z       0 Z ∗ f (X ∗ , α2 ) − d2 0        −Z ∗ e1 f (0, α1 ) −e1 Z ∗ X ∗ g(0, α1 )− 0    e2 Z ∗ f (X ∗ , α2 ) λ = Z ∗ f (X ∗ , α2 ) − d2 f (X ∗ , α2 ) f (0, α1 ) > d2 d1 f (Y ∗ , α1 ) f (0, α2 ) Fixed point (0, Y ∗ , Z ∗ ) > d1 d2 Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 12 / 19
  22. 22. Stability characteristics λ1 > 0 ∧ λ2 > 0 ⇒ coexistence λ1 < 0 ∧ λ2 > 0 ⇒ competitive exclusion λ1 < 0 ∧ λ2 < 0 ⇒ bistability Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 13 / 19
  23. 23. Simulations f (Y ∗ , α1 ) = α12 Y + α1 f (X ∗ , α2 ) = α21 X + α2 Parameter Value r 0.5 d1 0.1 d2 0.08 e1 1.002 e2 1.001 α1 0.01 α2 0.02 α12 0.0009 α21 0.00026 Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 14 / 19
  24. 24. Simulations Resource Consumer 1 Consumer 2 Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 15 / 19
  25. 25. Behaviour Mutualism Strenght 0.10 0.08 0.06 0.04 0.02 r 0.0 0.2 0.4 0.6 0.8 1.0 Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 16 / 19
  26. 26. Conclusion Parameters exist for mutualistic coexistence Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 17 / 19
  27. 27. Conclusion Parameters exist for mutualistic coexistence Resultant dynamics are oscillatory Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 17 / 19
  28. 28. Conclusion Parameters exist for mutualistic coexistence Resultant dynamics are oscillatory Works for any mutualistic functional form Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 17 / 19
  29. 29. Conclusion Parameters exist for mutualistic coexistence Resultant dynamics are oscillatory Works for any mutualistic functional form Intraguild mutualism may enhance stability Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 17 / 19
  30. 30. Directions Empirical data More species Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 18 / 19
  31. 31. Directions Empirical data More species Realistic network structure Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 18 / 19
  32. 32. Directions Empirical data More species Realistic network structure Stochasticity Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 18 / 19
  33. 33. Acknowledgements Roberto Andr´ Kraenkel e Paulo In´cio Prado a Ayana de Brito Martins Gabriel Andreguetto Maciel Renato Mendes Coutinho Funded by FAPESP and ICTP-SAIFR Group 3 (ICTP-SAIFR) Intraguild mutualism January 22, 2012 19 / 19

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