Source: PURDUE UNIVERSITY submitted to NRP
THE GAMES PLANTS PLAY: DEVELOPING AND TESTING GENERAL MODELS OF PLANT GROWTH AND ALLOCATION
Sponsoring Institution
National Institute of Food and Agriculture
Project Status
COMPLETE
Funding Source
HATCH
Reporting Frequency
Annual
Accession No.
1010722
Grant No.
(N/A)
Cumulative Award Amt.
(N/A)
Proposal No.
(N/A)
Multistate No.
(N/A)
Project Start Date
Oct 1, 2016
Project End Date
Sep 30, 2021
Grant Year
(N/A)
Program Code
[(N/A)]- (N/A)
Recipient Organization
PURDUE UNIVERSITY
(N/A)
WEST LAFAYETTE,IN 47907
Performing Department
Botany & Plant Pathology
Non Technical Summary
The production of biomass by plants is one of the most important processes on earth. For example, primary production by plants forms the basis for all life on earth, the majority of human calories depend directly on plant production, and the Earth climate system is controlled in part by the annual flux of 123 petagrams of CO2 out of the atmosphere caused by plant photosynthesis (Beer et al. 2010). At the base of the pursuit of plant science is a need for a general theoretical understanding of that allows us to predict the amounts of tissues like seeds, leaves, stems and roots produced by plants. This might seem like a trivial problem that has surely been solved, but plants have always posed special problems for mathematical models. This is because the mathematics of plant size (i.e. the amounts of leaves, stems and roots) is a surprisingly mathematical problem complicated. All else equal, plants adjust their allocation to organs like roots and leaves to optimize resource harvest. For example, when carbon is limiting they preferentially grow leaves, and when nutrients are limiting they preferentially grow roots (de Kroon et al. 2009). This means that the size of the plant, and the amounts of different tissues will depend on the resource environment in highly dynamical ways. This problem is further complicated by biotic interactions, which also change the size and shape of plants in complex ways. Competition changes resource uptake, and generally reduces plant size. Herbivory removes tissues, making plants smaller, but plants also respond to herbivores by adjusting growth. Mutualistic associations create positive feedbacks that generally enhance plant growth and reproduction, again changing their size. My research seeks general mathematical solutions to these problems that are general in the sense that they can be applied to all plants, (and even moss McNickle et al 2016). A key novel innovation is the application of evolutionary game theory to the process. In a game like checkers for example, the outcome of the game depends on the strategies of both players. Game theory is the mathematical language that describes games, where we can only predict outcomes by considering one player's strategy against the other player's strategy, and vice versa (Vincent et al. 1993, Vincent and Brown 2005). Biotic interactions take on the essential features of a game, where the strategy of a plant (here, the amount of leaves, stems or roots produced) depends on the strategies used by other organisms (here, neighbouring plants, herbivores, mutualistic partners). This provides a surprisingly powerful and novel predictive-framework that is, generating novel predictions for the long standing mathematical problem of predicting plant growth and allocation.Predicting plant growth and allocation has three important implications for the study of plant science. First, from an ecological point of view, plants form the base of the food chain and the basis for the number and diversity of species of organisms in any ecosystem. Second, agriculture depends on plant production. An understanding of the mathematics of plant growth can allow for targeted breeding for plants that maximize the production of agriculturally important tissues (e.g. fruit, seeds) and minimize the over-allocation to certain biotic interactions. Finally, climate models that seek to forecast future climate scenarios rely on mathematical models of plant growth because plant photosynthesis removes massive amounts of CO2 from the atmosphere each year. Currently, plant production remains the largest point of uncertainty in these models and my work can enhance the ability for governments and scientists to understand future climate scenarios by providing climate modelers with more realistic mathematical representations of plant growth.
Animal Health Component
(N/A)
Research Effort Categories
Basic
100%
Applied
(N/A)
Developmental
(N/A)
Classification

Knowledge Area (KA)Subject of Investigation (SOI)Field of Science (FOS)Percent
2062499107040%
2062499208060%
Knowledge Area
206 - Basic Plant Biology;

Subject Of Investigation
2499 - Plant research, general;

Field Of Science
1070 - Ecology; 2080 - Mathematics and computer sciences;
Goals / Objectives
Objective 1: Develop general game theoretic mathematical models of plant-biotic interactionsPlant-biotic interactions pose special problems for traditional models: the growth strategy of a plant depends on the strategies of associate biota (and vice versa). This means that plant-biotic interactions take on all the essential features of a game. General models of plant-plant competition have become common in recent years (McNickle and Dybzinski 2013). However, general game theoretic models for plant-herbivore interaction and plant-mutualism interaction simply do not exist. This project will develop general mathematical models that can form the basis for future theoretical understanding of these plant-biotic interactions.Objective 2: Experimentally Determine the mechanisms involved in neighbor recognition in soil.One of the game theoretic growth responses that plants use when they face plant-plant competition is that they increase the allocation to roots or shoots in order to pre-empt the resource supply of neighbors. For example, plants that compete for light will grow taller, and increase leaf production relative to plants that grow alone (Givnish 1982). Similarly, plants that compete for nutrients can over-proliferate roots relative to plants that grow alone (Gersani et al. 2001). Observing these growth responses is as straightforward as growing plants either alone or with neighbours and measuring tissue growth. However, elucidating the mechanism of neighbor recognition has been challenging, and the mechanism of neighbor recognition in soil remains unknown. A variety of candidate mechanisms have been proposed, including: a) chemicals exuded by roots (Semchenko et al. 2014); b) electrical oscillations from action potentials (Falik et al. 2003) and; c) depletion of the nutrients themselves (McNickle and Brown 2012). Mechanisms a) and b) have been explored experimentally and are not supported, but mechanism c) has received no attention. This project will experimentally test the nutrient depletion mechanism of neighbor recognition using greenhouse experiments.
Project Methods
O1: Develop general game theoretic mathematical models of plant-biotic interactionsGeneral approach: Continuous evolutionary game theory allows the mathematical prediction of quantitative traits (strategies) of organisms where their strategy depends on the strategies used by other organisms (i.e. players). This is achieved by making fitness (G) a mathematical function of: focal plant strategy v; the vector of other organism strategies u and; a vector of environmental variables y, into a G-function, G(v, u, y) (Vincent et al. 1993). The G-function is decomposed into two functions: 1) benefits that accrue from focal player strategy, opponent strategies and the environment, B(v,u,y) and; 2) costs that accrue from the strategy adopted by the focal player, C(v). Fitness in such a model is simply benefits minus costs: G(v,u,y)=B(v,u,y)-C(v). The solution is an evolutionarily stable strategy that maximizes reproductive output as a function of all biotic interactions and environmental variables included in the game (Apaloo et al. 2014). This general G-function approach will be the mathematical approach used throughout O1. Developing and identifying general equations for benefits and costs associated with different biotic interactions is the research goal of O1.O1.1) Develop a mathematical model of plant growth and allocation under herbivory. Herbivores forage on plant tissues and plants often respond to herbivore attack by increasing their growth in a response called over-compensation. I hypothesize that a game theoretic model of this interaction will help predict this phenomenon. By extending a general mathematical model of plant growth and allocation to roots and shoots that I previously developed (Lynch et al. In review, McNickle et al. In Review), I will develop a game theoretic model where herbivores may attack roots or shoots. This becomes a two player game between an herbivore and plant. Following the general G-function approach, plant benefits accrue from the harvest of carbon by photosynthesis and the uptake of nitrogen by roots and the costs are the carbon required to build and maintain tissues, as well as the nitrogen required to build tissues. The herbivore obtains benefits by consuming plant tissues, and costs accrue from expending effort searching for and consuming plant tissues. Since the herbivore removes plant tissues, the foraging of the herbivore feeds back on the benefits and costs of the plant, and the growth of the plant feeds back on the benefits and costs of the herbivore. By analysing the mathematical model I will ask: How are herbivores mathematically predicted allocate effort to plant attack based on plant size, and condition? How is a foliar herbivore or a root herbivore mathematically predicted to influence the production of shoots and roots in an attacked plant? What are the mathematically predicted implications of herbivore attack and compensatory growth for reproductive yield in plants?O1.2) Extend the mathematical herbivory model to include plant herbivore defence. The model in O1.1 seeks to simply to develop predictions about the compensatory growth response, but there are no plant defences included in that model. However, many plants possess active defences that deter attack from herbivores. Defence can be introduced as an additional plant strategy in the mathematical model that influences plant and herbivore benefits and costs in the general G-function approach to allow me to develop mathematical predictions about this aspect of plant biology. By analyzing the mathematical model I will ask: How are plants mathematically predicted to allocate to defence strategies compared to tolerance strategies? How is the type of herbivore (above- or below-ground) mathematically predicted to alter these strategies?O1.3) Develop a mathematical model of plant growth and allocation under a mycorrhizal association. Plants associate with a large number of mutualistic partners that essentially cooperate with each other to mutual benefit. One of the most common of these is an association with soil fungi known as mycorrhizae. In this association, fungi grow into or around the roots of plants and plants trade carbohydrates to the fungal partner in exchange for nutrients like phosphorus and nitrogen. The fungi are more efficient at acquiring nutrients, and the plants are more efficient at acquiring carbon. This naturally sets up a bargaining game between the fungus and the plant, which shapes benefits and costs. Here I will extend the plant model previously developed and described in O1.1, but instead of adding an herbivore I will add mycorrhizal fungus that trades with the plant to influence their benefits and costs. By analysing mathematical model I will ask: How is the presence of a fungal partner mathematically predicted to adjust the growth and allocation by plants to roots, or shoots? How is the mycorrhizal fungus mathematically predicted to adjust growth depending on the plant's allocation?O2: Determine the mechanisms involved in neighbor recognition in soil:General approach: For all O2 experiments I will use pea (Pisum sativum var. little marvel) in the greenhouse. Pea is ideal because it has a short life cycle (60 days) and exhibits over-proliferation of roots in response to plant-plant competition (O'Brien et al. 2005). Growth conditions in O2 will be natural sun supplemented with 16 hours of artificial light. Pots will be 15x15cm 50cm deep filled with SunGrow Propagation mix and watered with 1L of distilled water every two weeks. On watering 2 and 3 they will be watered with 1 L of 0.25g/L nutrient solution (Miracle Grow water soluble all-purpose plant food). After 60 days, pods, leaves, stems and roots will be harvested separately, dried and weighed. All experiments will be organized in a randomized block design, and the data analyzed using generalized linear mixed effects models.O2.1) Does the mechanism of neighbour recognition require cues from both above and below ground? I have preliminary data that leads me to hypothesize that plants require signals from neighbours both above and below ground in order to initiate the over-proliferation root response to competition. Experiment O2.1 will grow plants with or without root and shoot competition in a factorial design and test the hypothesis that the neighbor recognition response will only be observed when both root and shoot competition are present. Root and shoot competition will be excluded by building partitions above and below ground and placing plants on the same or opposite sides of the partition to include or exclude interactions as required. Increased root production in the root and shoot competition treatment relative to the shoot competition only treatment will indicate support for the hypothesis.O2.2) Is nutrient depletion by neighbours the mechanism of neighbour recognition below-ground? One proposed mechanism of neighbor recognition is that plants track nutrient depletion, however this mechanism has received no experimental attention. In experiment O2.2, I will grow peas in competition with different amounts of ion-exchange resin. Ion-exchange resins absorb nutrients from soil, and have been shown to compete with the roots of plants for available nutrients by depleting them over time just as a neighbouring plant would (Binkley 1984). The experiment will include a gradient of 10 different amounts of ion exchange resin, a plant-plant competition control, and a zero competition control (i.e. a plant grown alone). I hypothesize that along the gradient of increasing ion exchange resin the plants will gradually increase their root over-proliferation as predicted by game theoretic mathematical models. If nutrient depletion is not the cue, plants will grow the same as the zero-competition control along the entire ion exchange resin gradient. Nutrients will be extracted from resins to verify the effectiveness of the resins in absorbing nutrients.

Progress 10/01/16 to 09/30/21

Outputs
Target Audience:The audience is plant scientists and mathematical biologists, though these will come from a diversity of fields. For example, the vegetative growth and allocation of crop plants have important implications for agricultural yield, and potentially for breeders that seek to identify traits that may optimize yields. Additionally, plant-biotic interactions are important for understanding ecological communities in nature and a development of basic growth and allocation models will aide in the development of ecological understanding. Furthermore, there has been an ongoing debate about the importance of the plant-plant competition games in the ecological literature that largely has centered on the fact that a mechanism of neighbor recognition has not been identified and my work will contribute to this ongoing debate. Game theory is a growing field in biology and the general mathematics will be of interest to math biologists. Finally, identification of the mechanisms of neighbor recognition will be of interest to molecular biologists that study the molecular basis of biotic interactions among plants. Thus, scientists involved in crop breeding, ecology, mathematical biology and molecular biology will be the audience of this research. Changes/Problems:The changes and problems were discussed in the section about progress on the objectives. Briefly, I encountered two challenges, and made one change. First, models about plant cooperation turn out to be mathematically complicated. Cooperation is a positive-positive relationship, and such feedbacks are inherently unstable. Second, published results in the literature showed that pea was a good model system for understanding the mechanisms of neighbour recognition in plant. Unfortunately, the published results were probably a type-1 statistical error, and after five experiments during the course of this project I learnt that the previous results could not be replicated and peas were not a good model system. The change was that I switched to soybean as a model system. Unfortunately, switching systems, and switching to a much longer lived species, slowed progress. What opportunities for training and professional development has the project provided?Hatch projects do not provide direct support for graduate students or postdocs. Thus, I made progress on the objectives by collaborating with undergraduate researchers. In the Department of Botany and Plant Pathology plant science majors are required to take three research credits. I try to give these students their own mini-project as a mini-graduate research experience. Since 2016, 21 undergraduate researchers, and two highschool students have been involved in these efforts. Students are trained to search and read the primary literature, grow and care for plants, develop, execute an experiment, analyse data, and communicate results. Many students go on to graduate research or industry research following graduation. How have the results been disseminated to communities of interest?Results have been disseminated in the publications I have reported annually, and at annual meetings of the Ecological Society of America, the Canadian Society for Ecology and Evolution and the International Society for Dynamical Games. What do you plan to do during the next reporting period to accomplish the goals? Nothing Reported

Impacts
What was accomplished under these goals? The final year of this project was a difficult one for scientific progress due to the SARS-CoV2 pandemic.Since this is the final report on the project, I will summarise the total progress over the course of the project. Objective 1)This objective was to develop models for plant-biotic interactions. There are three primary modes of biotic interaction: competition, enemy attack and cooperation. Prior to this project, myself, and many others had developed a number of models of competition. Thus, I sought to understand models of enemy attack (e.g. herbivory, pathogens) and cooperation (e.g. microbial symbionts, pollination). Enemy attack turned out to be straightforward. In 2016 and 2017 I both developed a model of enemy attack, and in collaboration with an undergraduate researcher, empirically validated the model. This was published as McNickle and Evans (2018) as previously reported. Models of cooperation turned out to be more troublesome. Enemy attack has a natural stabilising effect because it is a positive for the enemy and negative for the plant. This positive-negative feedback is naturally stabilising. Cooperation however is positive for both individuals, and this positive-positive feedback can sometimes be incredibly unstable. With other researchers, I explored at least 5 different model formulations. Like many things in science, we learnt what did not work, but did not solve the problem. None the less, I made some small empirical progress. For example, Ritzi et al. (2019) as previously reported, discovered a novel mutualism in trees. I also made progress with a model system of mutant pea (Pisum sativum) that cannot form microbial symbioses. I expect we are close to a more complete understanding. Objective 2) This objective was about understanding the mechanism of neighbour recognition in soil when plants exhibit a response to competition. Here, progress was made with the experiments described in Mobley et al. (2021) as previously reported. The literature had converged on pea as a model species for plant competition studies. From 2016-2019 we performed 5 studies on pea. Indeed, these formed the basis for Mobley's MSc thesis which was completed under my supervision in 2019. Unfortunately, we learnt that the prior results in the literature could not be reproduced, and pea did not in fact have any responses to neighbours. My researched turned its attention to soybean (Glycine max) as a new model species. We began experiments using 20 genotypes from the the Soybean Nested Association Mapping population (SoyNAM). This work (not yet submitted) showed that there was a genetic basis for the neighbour recognition response. This sets my group up for future work that can use molecular analysis to identify the mechanism of neighbour recognition. I am writing an NSF grant to finish this work.

Publications


    Progress 10/01/19 to 09/30/20

    Outputs
    Target Audience:The target audience is other scientists. However, i have also participated in outreach events, where the general public is a target audience. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Through the activities described above, I contributed to the training and professional development of three undergraduate researchers. How have the results been disseminated to communities of interest?Through publication in scientific journals, posting of results to preprint servers, and presentations at national and international scientific meetings. What do you plan to do during the next reporting period to accomplish the goals?I believe we have accomplished the objectives of developing models for herbivory with McNickle and Evans (2018). The mutualism models continue to be difficult to solve.I have recruited an NSF postdoctoral fellow who will actively work on the mutualism problem from a theoretical mathematical perspective. We will examine experimental results from this past year (with Yufan Zhou) and continue to develop these models. For plant neighbour recognition, I have begun to examine how wavelengths of light alter neighbour recognition. I anticipate these studies will be complete in 2021.

    Impacts
    What was accomplished under these goals? Objective 1) This objective was about plant-biotic interactions and developing models to predict these interactions. In previous years McNickle and Evans (2018) effectively solved a model for plant-herbivore interactions under this project and I have not done further work on herbivory. Plant-mutualism interactions continue to be mathematically troublesome to solve, the models tend to suggest mutualism is highly unstable, yet this doesn't match experimental evidence. I have worked with an undergraduate researcher (Yufan Zhou) to develop experiments to gain more information about how to develop models. These experiments use mycorrhizae, a plant-fungus symbiosis in soil as a model system. I anticipate the experimental results will be published in 2021. Objective 2) In the 2019-2020 period covered by this progress report, I made progress on understanding neighbour recognition in plant roots. This includes McNickle (2020), a paper published that sought to better explore how soil factors influence the ability of plants to recognize and respond to neighbours in plant-plant competition. It also includes Mobley et al. (In Review) which sought to understand how above and below ground plant interactions combine to shape the neighbour responses of plant roots. The two coauthors (Mobley and Kruse) were both undergraduate researchers.

    Publications

    • Type: Journal Articles Status: Published Year Published: 2020 Citation: Gordon G. McNickle 2020. Interpreting plant root responses to nutrients, neighbours and pot volume depends on researchers assumptions . Functional Ecology. 34(10): 2199-2209
    • Type: Journal Articles Status: Under Review Year Published: 2021 Citation: Mariah L. Mobley, Audrey S Kruse, and Gordon G. McNickle In Review. Pisum sativum has no competitive responses to neighbours: a case study in reproducible ecology. Functional Ecology. Preprint: https://doi.org/10.1101/2020.09.29.318550
    • Type: Journal Articles Status: Under Review Year Published: 2021 Citation: Mina Rostamza and Gordon G. McNickle. In Review. A global database of photosynthesis model parameters, and phylogenetically controlled analysis of photosynthetic responses from every major terrestrial plant clade. Global Ecology and Biogeography. Preprint: https://doi.org/10.1101/2020.10.06.328682


    Progress 10/01/18 to 09/30/19

    Outputs
    Target Audience:The target audience is other scientists. However, i have also participated in outreach events, where the general public is a target audience. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Through the activities described above, I contributed to the training and professional development of two undergraduate researchers, and two post-doctoral fellows. How have the results been disseminated to communities of interest?Yes. See published paper. What do you plan to do during the next reporting period to accomplish the goals?We are actively working on mathematical models of mycorhhizae. These envision a trading system. We are also starting to design experiments that will test the models. These experiments will begin in spring 2020.

    Impacts
    What was accomplished under these goals? For Objective 1, I have been actively working towards mathematical models of (a) plant-herbivore interaction and (b) plant-mycorrhizae interaction, and developing experiments to test the mathematical models.In previous years I focused on herbivory, and published a paper in 2019 that described a model and experiment (McNickle and Evans 2018). The mathematics of plant-herbivore interaction are relatively straightforward, and so I have turned my attention to models of plant-mutualism. Most terrestrial plants form a mutualistic association with beneficial soil fungi called mycorrhizae. These mycorrhizae trade nutrients to the plant in exchange for sugars, and can dramatically enhance crop yields. I am actively developing game theoretic models for this mutualism. The model is still being developed and analysed. We will continue model development through 2020. However, we have developed the model to the point where we will also begin experiments in 2020 designed to test the model. Objective 2)Plants in agricultural fields face competition, both from members of their own species, and from weeds. This competition reduces yields in two ways: first competitors take away resources, and second, plants actually adjust their growth to maximize competitive ability. The mathematics of this competition as an evolutionary game are well described, however, we still do not know the mechanism by which plants recognize the roots of other plants in soil. With a series ofundergraduate researchers, I have performed four experiments using common peas (Pisum sativum,var Little Marvel). In all four experiments, partitions were constructed so that peas were grown in four experimental treatments: 1) with above ground competition only; 2) with below ground competition only; 3) with no competition at all, or; 4) with both above- and below ground competition together.This work is being prepared for publication. I have also examined competition within a quantitative trait locus (QTL) population of soybeans. This work is also still being analysed, but has the potential to identify genetic regions responsible for competition.

    Publications

    • Type: Journal Articles Status: Accepted Year Published: 2019 Citation: Ritzi, Morgan V., Stephen D. Russell, M. Catherine Aime, and Gordon G. McNickle 2019. First Report of Ectomycorrhizal Fungus, Laccaria ochropurpurea, Associated with Castanea dentata (American Chestnut) Roots in a Mixed-Species Plantation Plant Health Progress. 20: 140-141. https://doi.org/10.1094/PHP-01-19-0008-BR


    Progress 10/01/17 to 09/30/18

    Outputs
    Target Audience:I participated in an extension field day at Martell forest that reached 30 foresters and land managers. I also published one scientific paper, that reached an audience of scientists. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Through the activities described above, I contributed to the training and professional development of four undergraduate researchers (2 in 2018), and one post-doctoral fellow. One of the undergraduates has gone on to graduate school, and the other took a job at a government agency. The post-doctoral fellow also has taken a job in industry as a result of this training and professional development. How have the results been disseminated to communities of interest?Through publication, extension and conference proceedings. What do you plan to do during the next reporting period to accomplish the goals?The final experiment on pea competition has just been completed, and I will analyze the data in 2019 and write the paper. Thework on leaf physiology and competitionwe began in 2018 will continue. I will continue development of the mycorrhizae models.

    Impacts
    What was accomplished under these goals? ?Objective 1)I have been actively working towards mathematical models of (a) plant-herbivore interaction and (b) plant-mycorrhizae interaction, and developing experiments to test the mathematical models. undergraduate researcher, I have also tested a major prediction of this model. We grew wheat (Triticum spp., variety 9774-N2) in the greenhouse from Sept - Nov 2016. Herbivory was simulated by clipping a percentage of each leaf by length once it was fully expanded using sharp scissors. The damage treatments were 0%, 15%, 30%, 45% and 60% of the length of each fully expanded leaf clipped. After 90 days, fruits were fully developed, and plant senescence had begun. At this time, fruits and shoots were clipped, dried at 60°C, and weighed. Soil and roots were stored until they could be washed by freezing at -20°C. Thawed soil was washed on a 2mm sieve to collect roots which were dried at 60°C and weighed. Pisum sativum,var Little Marvel). In all four experiments, partitions were constructed so that peas were grown in four experimental treatments: 1) with above ground competition only; 2) with below ground competition only; 3) with no competition at all, or; 4) with both above- and below ground competition together.

    Publications

    • Type: Journal Articles Status: Accepted Year Published: 2018 Citation: McNickle, G.G., and Evans, W., 2018. Toleration games: Compensatory growth by plants in response to enemy attack is an evolutionarily stable strategy. AoB Plants. ply035. DOI: 10.1093/aobpla/ply035


    Progress 10/01/16 to 09/30/17

    Outputs
    Target Audience:I participated in an extension field day at Throckmorton/Meigs farm in summer of 2017 that reached 50 farmers and stakeholders. I described how competition alters crop yields, and discussed how mathematical models can be used for crop improvement. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Through the activities described above, I contributed to the training and professional development of two undergraduate researchers, and one post-doctoral fellow. One of the undergraduates has gone on to graduate school, and the other took a job at a government agency. The post-doctoral fellow also has taken a job in industry as a result of this training and professional development. How have the results been disseminated to communities of interest?I have participated in extension field days to disseminate some of my findings about plant-plant competition to 50 farmers and other landowners. This took the form of a poster, a presentation and a question and answer session. I am working on a manuscript which will disseminate results from the herbivory model and experiment to scientists in my field. What do you plan to do during the next reporting period to accomplish the goals? Nothing Reported

    Impacts
    What was accomplished under these goals? This work has the potential to have a large impact on crop breeding and production. There are really only three classes of biotic interactions: competition, mutualism and enemy attack from herbivores and pathogens. Each of these biotic interactions has enormous impacts on crop yields. For example, nutrient competition between plants in a field can reduce soybean yields by 30%, mutualism with nitrogen fixing bacteria can increase soybean yields by 38% and crop yields lost to herbivore pests are estimated at 15% even with pesticide inputs. By understanding the nature of these interactions from first principles, I will be able to gain novel insights that can help mitigate any costs associated with biotic interactions, and improve any benefits associated with biotic interactions. Below I expand upon my progress towards each objective. Objective 1) I have been actively working towards mathematical models of (a) plant-herbivore interaction and (b) plant-mutualism interaction, and developing experiments to test the mathematical models. 1a) First, logically, there are two basic classes of strategies that plants can employ as ways to resist damage from enemies: avoidance and tolerance. For sessile plants, avoidance primarily involves either defensive strategies (e.g. mechanical and chemical defence), or strategies that let plants escape the notice of enemies. Tolerance involves the degree to which plant fitness is altered by damage relative to an undamaged state, and a perfectly tolerant plant would equal obtain equal production when damaged or undamaged. For example, many plants are able to exhibit compensatory responses that minimize the fitness costs of a damaged plant compared to an undamaged plant. These commonly include tissue regrowth strategies. I have developed a game theoretic model of plant growth when damaged by herbivores that predicts these regrowth strategies as an evolutionarily stable strategy. Models are only useful if they can predict actual yields. With an undergraduate researcher, I have also tested a major prediction of this model. We grew wheat (Triticum spp., variety 9774-N2) in the greenhouse from Sept - Nov 2016. Herbivory was simulated by clipping a percentage of each leaf by length once it was fully expanded using sharp scissors. The damage treatments were 0%, 15%, 30%, 45% and 60% of the length of each fully expanded leaf clipped. After 90 days, fruits were fully developed, and plant senescence had begun. At this time, fruits and shoots were clipped, dried at 60°C, and weighed. Soil and roots were stored until they could be washed by freezing at -20°C. Thawed soil was washed on a 2mm sieve to collect roots which were dried at 60°C and weighed. We found that the plants exhibited compensatory growth that could be predicted by our mathematical models. Specifically, wheat increased its leaf production following damage such that damaged plants were actually larger than they should have been. By growing extra leaf tissue, the wheat plants were able to maintain the same amount of seed production even with 15% damage to their leaves. This suggests that herbivory rates of 15% or less, have no impact on farmer crop yields, because wheat possesses strategies to minimize these costs. We are now able to mathematically predict this strategy. I am currently writing the manuscript describing the model and the experiment in collaboration with the undergraduate researcher. 1b) Second, most terrestrial plants form a mutualistic association with beneficial soil fungi called mycorrhizae. These mycorrhizae trade nutrients to the plant in exchange for sugars, and can dramatically enhance crop yields. I am actively developing game theoretic models for this mutualism. With a post-doctoral researcher we have been actively developing a game theoretic model to predict how much nutrient and sugar should be traded. The model is still being developed and analyzed. We will continue model development through 2018. Objective 2) Plants in agricultural fields face competition, both from members of their own species, and from weeds. This competition reduces yields in two ways: first competitors take away resources, and second, plants actually adjust their growth to maximize competitive ability. The mathematics of this competition as an evolutionary game are well described, however, we still do not know the mechanism by which plants recognize the roots of other plants in soil. With an undergraduate researcher, I have performed two experiments using common peas (Pisum sativum, var Little Marvel). In both experiments, partitions were constructed so that peas were grown in four experimental treatments: 1) with above ground competition only; 2) with below ground competition only; 3) with no competition at all, or; 4) with both above- and below ground competition together. In the first experiment, we supplied the plants with high amounts of nutrients. Here, we were unable to detect any effect of competition, demonstrating how high levels of fertilization can potentially mitigate the negative effects of plant-plant competition. In the second experiment, plants were supplied with very low levels of nutrients. These results were inconclusive, and we are currently repeating the experiment.

    Publications