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Resource availability determines stability for mutualist–pathogen–host interactions

Abstract

Traditional explorations of interspecific interactions have generated extensive bodies of theory on mutualism and disease independently, but few studies have considered the interaction between them. We developed a model exploring the interactions among a fungal mutualist, a viral pathogen, and their shared plant host. Both microbes were assumed to alter the uptake and use of nutrients by the plant. We found that the productivity of the system and the strength of the plant–fungal mutualism influenced community dynamics. In particular, at low productivity, the pathogen may depend on the presence of the fungal mutualist for persistence. Furthermore, under some conditions, both the productivity of the system and the strength of the plant–fungal mutualism may simultaneously cause the mutualist to go extinct. We note the presence of cyclic plant–pathogen population dynamics only in the presence of the mutualist. As found in other models of consumer–resource interactions, cyclic dynamics were driven by high productivity, but, in contrast to simpler systems, high pathogen effectiveness did not consistently lead to cyclic dynamics. In total, association with mutualists can alter host–pathogen interactions, and the reverse is also true in that pathogens may alter host–mutualist interactions.

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Acknowledgments

We would like to the Mitchell Lab, Jason Hoeksema, Bridget Piculell, and Ann Rasmussen for discussions. We thank Shuijin Hu at North Carolina State University for mycorrhizal inoculum. This research was partially supported by a National Science Foundation (NSF) Graduate Research Fellowship to M.A.R. and a NSF Postdoctoral Research Fellowship in Biology under Grant No. DBI-12-02676 to M.A.R.

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Correspondence to Megan A. Rúa.

Appendix 1: Greenhouse experimental design and treatments

Appendix 1: Greenhouse experimental design and treatments

In January 2008, a 5-month experiment was conducted factorially manipulating arbuscular mycorrhizal fungi (mycorrhizal and no-mycorrhizal) and virus (infected and uninfected). For this experiment, we used the Eurasian annual host plant Avena fatua. This host plant was chosen because it is colonized by mycorrhizal fungi (Hu et al. 2005; Rillig 2006) and is a host for B/CYDVs (Malmstrom et al. 2005b). Experimental seed was hand-collected in Oregon.

Individual plants were grown in D60 Deeppots (Steuwe and Sons Inc., Oregon, USA). Each plant received 600 g of steam sterilized soil in a mixture of one part soil (Metromix 400) with two parts of pure sand (by mass). To inoculate plants with mycorrhizal fungi, we added 50 g of active mycorrhizal spore inoculum per pot. Mycorrhizal inoculum was obtained from a field at the Center for Environmental Farming Systems, North Carolina State University, near Goldsboro, NC, USA. We used inoculum which consists of spores from the mycorrhizal fungal species Glomus intraradices, Gigaspora margarita, and Scutellospora heterogama. To control for potential changes in nutrient content due to the inoculum, control plants received 50 g of autoclave sterilized inoculum. All pots received 50 mL of microbial filtrate solution filtrated by Whatman No. 1 filter paper from 10.0 g AM inoculum (in which mycorrhizal spores were removed) to correct for possible differences in the microbial community and mineral content between mycorrhizal and no mycorrhizal treatments.

To infect plants with virus, we used an isolate of barley yellow dwarf virus (PAV) obtained from a naturally infected Bromus vulgaris and maintained in Avena sativa cultivar Coast black oats. Virus inoculations occurred approximately 2 weeks after germination. Uninfected aphids of the species Rhopalosiphum padi (L.) were fed in petri dishes for 72 h on infected plant tissue. Five infected aphids were then transferred to each experimental plant, at which time the plants were capped to prevent the spread of aphids. Aphids were allowed to feed on each experimental plant for 48 h. Plants were then sprayed with a horticultural oil solution (SAF-T-SIDE, ClawEl Specialty Products, Pleasant Plains, IL) to kill the aphids. Mock-inoculated plants received the same treatment, but uninfected aphids were fed on uninfected tissue prior to being transferred to experimental plants. To test the plants for BYDV-PAV infection and to quantify relative viral titer concentration, a compound indirect double-antibody sandwich enzyme-linked immunosorbent assay (ELISA; Agdia Inc., Elkhart, IN, USA) was used on aboveground tissue from experimental plants (Cronin et al. 2010).

Plants were allowed to grow for 5 months and then harvested. Each week, the longest leaf was measured. We measured photosynthetic capacity (A max, micromoles CO2 square meter per second) on the youngest, fully mature leaf of a ramet using a CIRAS-2 gas exchange analyzer fitted with a rice cuvette (PP Systems, MA, USA). At harvest, plants were separated into above- and belowground portions. Both above- and belowground biomass was placed in a drying oven. Plants were dried at 60 °C for a minimum of 72 h to obtain dry biomass values. Soils were frozen and stored at −20 °C until they could be processed. The belowground fraction was washed to separate roots from soil. A subset of the roots from each individual were collected before drying, stained with trypan blue following the methods outlined in (Koske and Gemma 1989) and scored for intraradical AM colonization using the magnified gridline intersect method (McGonigle et al. 1990). Using this method, the percentage of root length colonized by intraradical hyphae was measured using a compound microscope (×200–400).

Appendix 2. Analytical solutions to various model outcomes

Stability of host–pathogen submodel

Here, we demonstrate the stability of host-pathogen submodel, i.e., Eqs. 2a and 2b, when mutualists are held at a constant (including zero) density, denoted as M *. Equilibria of host–pathogen submodel are determined by setting differential Eqs. 1a and 1b equal to zero and solving for densities. Three solutions exist: the trivial solution (\( \overline{H}=0,\kern0.5em \overline{P}=0 \)), a host only solution (\( \overline{H}=n-\frac{f}{\left(1+k\cdot M*\right)},\kern0.5em P=0 \) , and the non-trivial solution (\( \left.\overline{H}=\frac{d}{\left(s-b\cdot d\right)},\kern0.5em \overline{P}=\frac{\left(1+k\cdot M\right)}{f}\left(n-\frac{d}{c-d\cdot d}\right)\right) \). In this section, we are only concerned about the local stability of the non-trivial solution. This can be determined by examining the Jacobian of the equations linearized about the non-trivial solution. For these equations, the Jacobian can be written as:

$$ j=\left[\begin{array}{ll}-\frac{\overline{Hi\left(1+k\cdot M*\right)}}{1+\overline{P}}\hfill & -\frac{fi\left(1+k\cdot M*\right)}{1+\overline{P}}\hfill \\ {}\frac{c\overline{P}}{{\left(1+n\overline{H}\right)}^2}\hfill & 0\hfill \end{array}\right] $$

Since all equilibria and parameters are positive, it is easy to show that the determinant of J is positive and the trace is negative and therefore satisfy qualitative conditions for being locally stable as long as a positive equilibrium exists.

Solutions for parameter boundaries of qualitative model behavior

Here, we describe how boundaries for changes in qualitative model behavior were derived as shown in Fig. 4. Important parameter combinations that represent the ability of different organisms to invade when rare are derived first, and then various combinations of these that describe qualitatively different model behaviors are then described. First, the plant density that allows for invasion of the mutualist is condition where growth rate of mutualist (Eq. 1c) is positive. This is easily derived to occur when:

$$ H>1 $$
(2)

The natural enemy invasion criterion is derived similarly where its growth rate (Eq. 1b) is positive:

$$ H>\frac{1}{\left(\frac{c}{d}-b\right)} $$
(3)

Finally, we have three different potential equilibrium values of the host in relation to different mutualist conditions, i.e., where the growth rate of Eq. 1b is zero. In each of these equilibria, we assume the pathogen density is zero. The first equilibrium is when mutualist densities are zero.

$$ H=n-f $$
(4)

The next two represent the two solutions to the quadratic equation that represents where the mutualist nullcline crosses the host nullcline.

$$ H=\frac{k\left(1+n\right)-1+\sqrt{{\left(1-k\left(1+n\right)\right)}^2+4k\left(n\left(1-k\right)-f\right)}}{2k} $$
(5)
$$ H=\frac{k\left(1+n\right)-1-\sqrt{{\left(1-k\left(1+n\right)\right)}^2+4k\left(n\left(1-k\right)-f\right)}}{2k} $$
(6)

The boundary between enemy absent and enemy requires the mutualist to be present can be determined by substituting the value of H from Eq. 5 into Eq. 3 and solving for c so that

$$ c>\frac{2kd}{k\left(1+n\right)-1+\sqrt{{\left(1-k\left(1+n\right)\right)}^2+4k\left(n\left(1-k\right)-f\right)}}+bd $$

The boundary between where the enemy requires the mutualist to be present and where the enemy persists without the mutualist can be defined where Eqs. 4 and 3 are true:

$$ c>\frac{d}{\left(n-f\right)}+bd $$

Since enemies will drive hosts to their threshold at equilibrium, we can also determine the impact of enemies on mutualists. If the enemy equilibrium value (change the greater than in Eq. 3 to an equality) is less than the level that allows for the invasion of the mutualist, i.e., the maximum of Eqs. 2 and 6, than the enemy will drive the mutualist extinct. This will occur when:

$$ c>\frac{d}{max\left(1,\kern0.5em \frac{k\left(1+n\right)-1-\sqrt{{\left(1-k\left(1+n\right)\right)}^2+4k\left(n\left(1-k\right)-f\right)}}{2k}\right)}+bd $$

Finally, we determined the region of three species cycles using AUTO (Doedel et al. 1997). An initial equilibrium was found, and we used AUTO to map out the Hopf bifurcation as a combination of parameters n and c.

Fig. 6
figure6

Nullclines for the enemy graphed on the plant–mutualist nullcline space, varying k. Nullclines for the enemy graphed on the plant–mutualist nullcline space when the strength of the plant–mutualist relationship (k) and nutrient input (N) are altered. Panels ac represent nullclines of increasing nutrient inputs at a low fungal effective rate (k = 0.7) and panels df represent nullclines of increasing nutrient inputs at high fungal effect rates (k = 1.2). Black solid lines indicate fungal nullclines; gray lines indicate plant nullclines, and dashed black lines indicate enemy nullclines. Pathogen efficiency c = 4

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Rúa, M.A., Umbanhowar, J. Resource availability determines stability for mutualist–pathogen–host interactions. Theor Ecol 8, 133–148 (2015). https://doi.org/10.1007/s12080-014-0237-5

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Keywords

  • Viruses
  • Population dynamics
  • Mutualism
  • Arbuscular mycorrhizae