Supporting Information Notes S1 & S2, Figs S1–S4, Tables S1 & S2
Notes S1 GAME THEORETIC MODEL DESCRIPTION:
To model the evolution of rhizosphere priming, a simple evolutionary bimatrix game was
developed to discern which plant and microbe strategies will be able to co-evolve. Let Ru
represent a pool of unavailable resources that may be mobilized by rhizosphere
microorganisms. Let E represent the plant costs associated with producing exudates, and let
Cr represent the costs to a microbe for mobilizing soil resources (e.g. cost of Soil Organic
Matter mineralization). The model then assumes that there might or might not be some sort of
closer association between cooperating microbes and priming plants compared to the other
strategies. Thus, let a represent the probability that cooperating microbes capture root
exudates relative to defecting microbes where 0≤a≤1. Similarly, let s, represent the
probability that resources released by cooperating microbes primed by a focal plant are
actually captured by that focal plant (0≤s≤1). The parameters s and a, can be thought of as
representing the security of the compound transaction between plants and microbes. Finally,
let p represent the proportion of priming plants in the population (the proportion of
non-priming plants is 1-p) and let q represent the proportion of cooperating microbes (the
proportion of defecting microbes is 1-q). With this model construct the success of each plant
or microbe strategy is dependent upon four factors: (1) the frequency of plant and microbe
strategies in each population, (2) the potential resources gained by plants or microbes, (3) the
costs invested by plants or soil microbes, and (4) the closeness of the association between
plant and microbe. These simple variables may be combined into an evolutionary game that
describes the coevolution of plant and microbe strategies. This game takes the form of a more
general game of cooperation (e.g. Brown & Vincent, 2008), but has been tuned to fit the
problem of a hypothesized mutualism behind rhizosphere priming effects (Kuzyakov, 2002).
Fitness outcomes for plants, microorganisms and the plant-soil interactions can be assessed as
follows:
Plant fitness outcomes
In population of pure non-priming plants (NP vs NP), individuals cannot access the
unavailable resource pool of resources and the net payoff from priming activities will clearly
be equal to 0 (Fig. S1). In a population of pure priming plants (P vs P), a focal plant receives
their own share of the unavailable resources that are released by cooperating microbes less
the costs of root exudates [qsRu-E], and they also receive a share of unavailable nutrients
released by their neighbor’s priming activities [(1-s)qRu] (Fig. S1). In a mixed population,
priming plants receive unavailable nutrients with probability sq, less the costs of root
exudates (sqRu -E), and non-priming plants receive a share of the nutrients that are lost from
the priming plants (1-s)qRu (Fig. S1). These four mean fitness outcomes are summarized in
the plant payoff matrix (Fig. S1).
Microbe fitness outcomes
It is also possible that microbes may evolve in response to root exudates produced by
plants with two distinct strategies: cooperate or defect with the plants. In a population of pure
cooperating microbes (C vs C), exudates are gained and resources are mobilized at some cost
such that the average per-capita fitness is pE-Cr (Fig. S2). In a population of defecting
microbes (D vs D) nothing is shared with plants and thus exudates are simply taken in
proportion to pE. In a mixed population cooperating microbes obtain exudates in proportion
to the frequency of priming plants, and their competitive ability, less the cost of releasing
resources for plants, paE-Cr (Fig. S2). Alternatively, the defecting microbes obtain exudates
in proportion to their competitive ability but share nothing with plants, p(1-a)E. These fitness
outcomes are summarized in a microbe payoff matrix (Fig. S2).
Plant–microbe coevolution
Which plant and microbe strategies will coevolve?
An evolutionarily stable strategy
(ESS) is one that cannot be invaded by a rare mutant using the other strategy (Smith & Price,
1973; Smith & Parker, 1976; Riechert & Hammerstein, 1983). Thus, for the plants, priming is
an ESS if it is resistant to invasion by the non-priming strategy. This occurs when individual
plants receive higher fitness in a population of pure priming plants compared to an invading
non-priming plant (i.e. P vs P > NP vs P). Comparing the appropriate cells from the plant
payoff matrix, (Fig. S1), this occurs when,
q[sRu+(1-s)Ru] -E > (1-s)qRu
(1a)
Inequality (1a) simplifies to:
sqRu>E
(1b)
Similarly, non-priming is an ESS if it is resistant to invasion by the priming strategy.
This occurs when individuals receive higher fitness in a population of pure non-priming
plants compared to an invading priming plant versus a resident non-priming plant (i.e. NP vs
NP > P vs NP). Comparing the appropriate cells from the payoff matrix (Fig. S1), this occurs
when:
0 > sqRu-E
(2a)
Inequality (2a) simplifies to:
sqRu<E
(2b)
Inequalities (1b) and (2b) suggest that there can be no stable coexistence between
priming and non-priming plants under this formulation. Resources gained (sqRu) must either
be less than (priming is an ESS) or greater than (non-priming is an ESS) the costs of root
exudates (E), with no parameter space in-between. Thus the proportion (p) of priming plants
must either be 0 or 1.
Following similar logic for microbial evolution, the cooperate strategy is an ESS if it
is resistant to invasion by the defecting strategy. From the payoff matrix (Fig. S2) this occurs
when,
pE-Ru > p(1-a)E
(3a)
Inequality (3a) simplifies to:
paE > Ru
(3b)
Alternatively, the defecting strategy is an ESS when,
pE > paE-Ru
(4a)
Inequality (4a) simplifies to:
p(a-1)E < Ru
(4b)
Since p is either 0 or 1, microbe evolution strongly depends on the plant strategies.
Defecting is always an ESS when p=0 (i.e. there is nothing for a microbe to gain from
attempting to cooperate with non-priming plants). However, when p=1, inequalities (4a) and
(4b) show that there is a region of parameter space where both cooperating and defecting are
simultaneously an ESS. However, coexistence of the two strategies is not possible (Fig. S2).
Thus, in this region of parameter space, the model predicts alternate stable states where the
microbe’s ESS will depend on initial starting conditions. Thus, for microbes q is also always
either 0 or 1.
Competing strategy
Priming
Priming
qRu -E
Non-priming
qsRu-E
Focal strategy
Non-priming
q(1-s)Ru
Fig. S1 Plant payoff matrix
0
The payoff matrix for priming plants versus non-priming plants showing average per-capita
fitness across the plant population. The model is symmetric, so only the payoffs of the focal
strategy are shown. Ru represents unavailable nutrients that are made available by microbes
primed with exudates at a cost to the plant represented by E. The transaction between plants
and free living soil microbes is more or less secure based on the parameter s, where 0≤s≤1. q
represents the proportion of microbes that cooperate with plants which is either 0 or 1.
Competing strategy
Cooperate
Defect
Cooperate
pE-Cr
paE-Cr
Defect
p(1-a)E
pE
Focal strategy
Fig. S2 Microbe payoff matrix
The payoff matrix showing average per-capita fitness across the microbe population for
microbes that cooperate or defect with plants. The model is symmetric, so only the payoffs of
the focal strategy are shown. E represents the amount of exudates received from plants, and Cr
represents the cost to the microbes of releasing unavailable resource for plant use. a represents
the competitive ability of the cooperating strategy relative to the defecting strategy for
capturing plant exudates. p represents the proportion of priming plants which is either 1 or 0.
References
Brown JS, Vincent TL. 2008. Evolution of cooperation with shared costs and benefits.
Proceedings of the Royal Society B-Biological Sciences 275: 1985-1994.
Kuzyakov Y. 2002. Review: Factors affecting rhizosphere priming effects. Journal of Plant
Nutrition and Soil Science-Zeitschrift Fur Pflanzenernahrung Und Bodenkunde 165:
382-396.
Riechert SE, Hammerstein P. 1983. GAME-THEORY IN THE ECOLOGICAL
CONTEXT. Annual Review of Ecology and Systematics 14: 377-409.
Smith JM, Parker GA. 1976. Logic of Asymmetric Contests. Animal Behaviour 24:
159-175.
Smith JM, Price GR. 1973. Logic of Animal Conflict. Nature 246: 15-18.
Notes S2 MICROBIAL PHYSIOLOGY MODEL DESCRIPTION:
Core Model
The core of the model is based upon the Allison et al. (2010) model. Here, we focus on
describing the main features of the model and the processes and parameters we modified (see
supporting information in Allison et al. 2010 for complete model description). This model
predicts SOM decomposition using Michaelis-Menten kinetics with the Vmax (maximum
velocity) and Km (half-saturation constant) of both microbial C and N uptake and enzyme
mediated decomposition modeled as a function of temperature following:
(1) Vmaxt = Vmaxo * exp (-Ea / gasconst * (temp+273))
(2) Kmt = Kmslope * temp + Kmo
The temperature sensitivity of Vmax is modeled using the Arrhenius function (Eq. 1). The
parameters, Ea and gasconst are the activation energy and ideal gas constant, respectively.
The response of Km to temperature is modeled as a linear function of soil temperature (Eq. 2).
In addition, the temperature sensitivity of carbon use efficiency (CUE) of soil microbes is
modeled in the same manner.
(3) CUE = CUEslope * temp + CUEo
To incorporate N dynamics into the core model structure, we followed the framework of
Drake et al. (2012). The main assumption is that the decomposition and uptake of N
follows C and can be modeled using the C to N ratio of the four main C pools: (1) SOC, (2)
DOM, (3) microbial biomass, and (4) enzyme (Table S1).
In this framework, if microbial N
demand is met than N is mineralized and released into soil solution, whereas if microbial N
demand is not met than N is immobilized.
Modifications
The two modifications that we made to the core model structure were the inclusion of a
seasonal time course of soil temperature (Fig. S3) and variation in the timing of inputs into
the C and N fractions of the SOM and DOM pools.
In the Allison et al., (2010) model,
inputs to SOM and DOM are of the same magnitude and occur at a constant rate for each
time step.
To mimic a seasonal litterfall pulse into SOM, we modified the SOM inputs to
add the same overall amount of C as the core model, but these inputs occurred at a higher rate
at the end of the growing season from day of year (DOY) 275-300 in each year (Table S1).
To mimic root exudation, we modified the timing of DOM inputs to occur only during the
growing season (DOY 100-275). Further, the total DOM input each year was assumed to be
half of the total SOM input (Table S1). These shifts in the timing of the SOM and DOM
inputs results in seasonal dynamics in SOC.
each year.
Litter inputs drive higher SOC in the fall of
Higher temperatures and root exudates lead to declines in SOC during the
growing season (Fig. S4).
Scenarios
To model how changes in root exudation and microbial physiology impact the size of the
SOC pool and rates of N mineralization, we simulated three scenarios: (1) 20% increase in
exudation with no change in physiology, (2) 20% increase in exudation coupled with a 20%
increase in the conversion of microbial necromass to SOC, and (3) 20% increase in exudation
coupled with a 10% increase in the rate of microbial turnover.
The changes in these
parameters are presented in Table S2. For the baseline model and each scenario, we ran the
model for 90 years to ensure equilibrium in SOC pools and N mineralization rates.
Table S1 Baseline model parameters modified from Allison et al., (2010)
Baseline Model
Parameter
Units
initSOC
mg cm-3
initDOC
-3
-3
mg cm
initBiomass
mg cm
initENZ
mg cm-3
inputSOC (DOY 275-300)
0.00068549
initial DOC pool
2.2274
initial Microbial Biomass pool
initial Enzyme pool
0.007
input to SOC
-3
-1
0
input to SOC
0.0005
input to DOC
0
input to DOC
0.0002
microbial turnover
0.00005
enzyme production
0.001
enzyme loss
0.5
necromass to SOC
0.63
carbon use efficiency
inputDOC (DOY 100-275)
mg cm-3 hr-1
-3
inputDOC (DOY 1-99; 276-365)
mg cm hr
rdeath
mg mg-3
-1
-1
hr-1
initial SOC pool
0.0109579
mg cm hr
rEnzLoss
173.7383
-1
inputSOC (DOY 1-274; 301-365)
hr
Description
-3
mg cm hr
rEnzProd
Parameters
-1
MIC to SOC
hr
CUEo
mg mg-3
rate of change in CUE with
CUEslope
degree
-1
-0.016
-3
mg SOC cm (mg
Vmaxo
-3 -1
-1
Enz cm ) h
maximum velocity of
100000000
-3
mg DOC cm (mg
Vmaxuptake o
biomass cm-3)-1 h-1
temperature
decomposition
maximun velocity of DOC
100000000
uptake
half saturation constant of
Kmo
-3
mg cm
500
decomposition
half saturation constant of DOC
Kmuptake o
-3
mg cm
0.1
uptake
rate of change in Kmo with
Kmslope
-3
mg cm degree
-1
-3
-1
5
temperature
rate of change in Kmuptakeo with
Kmuptake slope
mg cm degree
Ea
kJ mol-1
0.001
temperature
activation energy of
47
decomposition
activation energy of DOC
Ea uptake
kJ mol
gasconst
-1
47
uptake
kJ mol-1 degree-1
0.008314
ideal gas constant
CNs
unitless
16
C to N ratio of SOC
CNm
unitless
7
C to N ratio of microbes
CNe
unitless
3
C to N ratio of enzymes
CNDOC
unitless
2
C to N ratio of DOC
Table S2 Parameter modifications from the baseline model for the three scenarios
inputDOC
MIC to
Scenario
(DOY 100-275)
rdeath
SOC
1
0.0006
0.0002
0.5
2
0.0006
0.0002
0.6
3
0.0006
0.00022
0.5
Fig. S3 Seasonal variation in soil temperature at 5cm depth for 2011 at the Morgan Monroe
State Forest AmeriFlux site in IN, USA.
Soil Temperature at 5cm depth
(oC)
30
25
20
15
10
5
0
0
100
200
300
Day of Year
Fig. S4 Seasonal fluctuation in the size of the SOC pool for the first 30 years of the baseline
model simulation.