andersen et al. 2004: stoichiometry and dynamics

Stoichiometry and Population Dynamics

Andersen et al. 2004 Ecology LettersLauren Yamane

1Tuesday, November 13, 12

Food quality is important not just quantity

• Preference for high quality food (high nutrient: C ratio) in terrestrial studies (White 1993, Sterner & Elser 2002)


Problem: Consumers require relatively constant nutrient

ratio from low nutrient autotrophs

• Autotroph nutrient: C ratio often highly variable

• Variability due to physiological plasticity under varying conditions


Constraints in growth and population dynamics due to

food quality

• Link: Threshold Elemental Ratio (TER)

• TER = critical C: nutrient ratio

• Above TER get nutrient limitation

• Transfer efficiency decreases

• Below TER get C (Energy) limitation


Herbivores can have both negative and positive density dependent effects on

plant nutrient composition

• Negative: Herbivores remove the good stuff (traditional; Turchin 2003)

• Positive: Herbivores reduce biomass but nutrient input remains same + recycle nutrients Nutrient: C


Experiments with stoichiometry and facilitation

based on chemostat

x yD*NT

Total nutrientDilution rate

Autotroph Herbivore

D*x

D*y

Washout

(P)


Daphnia increase P:C Daphnia increase

P:C increase**Dilution rate (D) cannot be too low

Eventually C limitation sets in


Stoichiometry alters parameters in Lotka-Volterra

predator-prey model

• Modeling autotroph (A), herbivore (H) dynamics

• Like chemostat model

• (constant) Dilution rate sets nutrient input and washout of 2 species

Autotroph growth rate Herbivore function response

Herbivore numerical response


Functional responses (f.r.) reflect ingestion and handling

time constraintsHolling’s Type I

Holling’s Type 2 (handling time)


Traditional Lotka-Volterra models

Density independent growth (k1), Type I (I1)

Density independent growth (k1), Type II

(I2)

Density dependent growth (k2), Type I (I1)

Density dependent growth (k2), Type II

(I2)

Rosenzweig-MacArthur model

-Neutral stability -Asymptotic instability

y nullcline moves R

-Asymptotic stability

-Hopf bifurcation from stable focus to limit cycle Autotroph biomass (x)

Herbivore biomass (y)


Adding stoichiometry

Unrealistic: dynamics fall outside of NT


(I2)

Rosenzweig-MacArthur model

(Shaded gray is NT)

Stoichiometric density dependent growth

(k3), Type II (I2), energetic constraints

only on y (g1)

-Asymptotically stable focus


(I2), energetic & stoichiometric

constraints on y (g2)-Asymptotically stable focus

Stoichiometric density dependent growth (k3), Type II (I2), energetic &

stoichiometric constraints on y

(g2)-Asymptotically stable focus -Could develop into Hopf bifurcation from stable focus to limit cycle if K increased

Energetic constraintsNutrient constraints

Autotroph biomass (x)



Stability and persistence with stoichiometry depend on

nutrient level and D


Autotroph biomass (x)

Low NT, Low D

Low NT, High D

High NT, High D

*High NT, Low D


Stability and persistence with stoichiometry depend on

nutrient level and D

*


Time series of full stoichiometric model

Autotroph

Herbivore

Nutrient limited

Nutrient sufficient Nutrient limited

Energy limited


Conclusions

• Stoichiometry can have stabilizing effects on predator-prey dynamics

• Must include stoichiometric effects in both autotroph growth rate and herbivore numerical response for realistic dynamics

• Future directions: additional work on stoichiometry changes due to ontogeny and effects on pop dynamics


Questions

• Would functional response ever have stoichiometric constraints? Alter satiation in parameter?

• Stoichiometry important beyond nutrient-limited autotroph herbivore model?


andersen et al. 2004: stoichiometry and dynamics

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