vol. 193, no. 2 the american naturalist february 2019

Priority Effects and Nonhierarchical Shape Composition in a Complex

Lawrence H. Uricchio,* S. Caroline Daws, Erin R. Spear,† and Erin A. Mordecai*

Department of Biology, Stanford University, Stanford, California 94305 Submitted June 27, 2018; Accepted September 19, 2018; Electronically published January 10, 2019 Online enhancements: appendix.

abstract: Niche and fitness differences control the outcome of measuring outcomes empirically is often infeasible when competition, but determining their relative importance in invaded dynamics proceed slowly relative to the timescale of exper- communities—which may be far from equilibrium—remains a press- iments. Theoretical coexistence models based on species ing concern. Moreover, it is unclear whether classic approaches for differences offer a powerful alternative for predicting com- studying competition, which were developed predominantly for pairs petitive outcomes (Burdon and Chilvers 1974; Tilman of interacting species, will fully capture dynamics in complex species 1980; Holt et al. 1994). However, linking models to real eco- assemblages. We parameterized a population-dynamic model using logical communities is challenging because realistic param- competition experiments of two native and three exotic species from a grassland community. We found evidence for minimal fitness differ- eter estimates are rarely available for species interacting ences or niche differences between the , leading to slow within a single ecological context. Moreover, existing theo- replacement dynamics and priority effects, but large fitness advantages retical approaches often make simplifying assumptions— allowed exotics to unconditionally invade natives. Priority effects driven such as reducing analyses to pairs of interacting species by strong interspecific competition between exotic species drove single- rather than considering the full dynamics of the assem- species by one of two exotic species in 80% of model out- blage—that may affect the inferred outcomes. As a result, comes, while a complex mixture of nonhierarchical competition and co- considerable uncertainty remains about the relative impor- existence between native and exotic species occurred in the remaining tance of different proposed diversity-maintenance mecha- 20%. Fungal infection, a commonly hypothesized coexistence mecha- fi nism, had weak fitness effects and is unlikely to substantially affect coex- nisms, and the outcome of competition can be dif cult to istence. In contrast to previous work on pairwise outcomes in largely predict. native-dominated communities, our work supports a role for nearly neu- Among several existing theoretical frameworks for spe- tral dynamics and priority effects as drivers of species composition in in- cies interactions, modern clarifies the vaded communities. mechanisms through which species differences affect the Keywords: competition, invasion, coexistence, communities, disease outcome of competition via their effects on niche differ- . ences and fitness differences (Chesson 2000). Niche differ- ences are the differences between species in use, natural enemies, requirements, or other factors that Introduction force per capita impacts of competition within species to Understanding the long-term outcome of competition in exceed those between species (Chesson 2000). These niche diverse species assemblages is a major goal of ecology, but differences cause population growth to be negatively fre- quency dependent because species achieve their highest per capita growth rates when they are rare and interact with mostly heterospecific competitors, while per capita growth * Corresponding authors; email: [email protected], [email protected]. † Present address: Biology Department, Regis University, Denver, Colorado declines as species become common and interact with many 80221. conspecific competitors. By contrast, in this framework, fit- ORCIDs: Uricchio, https://orcid.org/0000-0001-9514-8945; Daws, http://orcid ness differences are those differences between species that .org/0000-0001-5559-5206; Mordecai, http://orcid.org/0000-0002-4402-5547. determine per capita growth rates independent of relative Am. Nat. 2019. Vol. 193, pp. 213–226. q 2019 by The University of Chicago. , often including differences in fecundity, resource 0003-0147/2019/19302-58576$15.00. All rights reserved. This work is licensed acquisition, or survival. Coexistence occurs when niche dif- under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), which permits non-commercial reuse of the work with ferences, which generate negative frequency-dependent pop- attribution. For commercial use, contact [email protected]. ulation growth or stabilization, are strong enough to over- DOI: 10.1086/701434 come fitness differences between species (Chesson 2000). 214 The American Naturalist

Alternatively, priority effects can occur when population We hypothesized that complex multispecies dynamics growth is positively frequency dependent, allowing any spe- would be likely to emerge in recently invaded systems, in cies that is initially more common to exclude others but which competing species have not had long coevolutionary preventing species from invading when rare in the presence histories and hence may not have had sufficient time to of competitors (Mordecai 2011; Fukami et al. 2016). While evolve into distinct niches (MacDougall et al. 2009). Such assessing competitive outcomes in pairs of species with systems may be far from equilibrium and may represent known parameter values is straightforward in this frame- an opportunity to study complex multispecies dynamics work, predicting multispecies outcomes remains a chal- in the absence of strong stabilizing mechanisms driven by lenge (Saavedra et al. 2017; Barabás et al. 2018). . Moreover, predicting competitive out- Modern coexistence theory has motivated a suite of stud- comes in recently invaded systems is a pressing concern for ies that empirically measure the strength of niche differ- conservation, and understanding the processes that have ences and fitness differences—and, ultimately, the outcome the largest impact on the persistence of native species could of competition—in natural plant or algal communities. Many help preserve endemic . In this study, we investi- of these studies have emphasized the influence of stabilizing gated competitive outcomes in California , one of niche differences on species coexistence (Turnbull et al. the most ecologically important and widespread 2005; Adler et al. 2006, 2010; Levine and HilleRisLambers in the Western United States and a key reservoir of endemic 2009; Narwani et al. 2013; Godoy et al. 2014, 2017; Kraft biodiversity (Myers et al. 2000). Simultaneously, California et al. 2015). However, almost all empirical applications of grasslands are heavily invaded and human impacted since modern coexistence theory use pairwise growth rates when the nineteenth century (Mack 1989); exotic annual grasses rare to assess community-wide outcomes (e.g., Adler et al. now dominate, while native perennial bunchgrasses and an- 2007, 2010; Levine and HilleRisLambers 2009; HilleRis- nual forbs have declined to very low density throughout Lambers et al. 2012; Mordecai 2013; Godoy et al. 2014; Kraft much of their extent. In the long term, it is not clear whether et al. 2015; Mordecai et al. 2015). A growing body of theory the exotic annual grasses will competitively exclude native pe- shows that outcomes of competition may depart from pair- rennial grasses, whether native grasses will stably persist (at wise predictions when all species are analyzed simultaneously reduced densities), or whether priority effects will determine (e.g., Case 1995; Allesina and Levine 2011; Mayfield and whether native or exotic grasses dominate at a local scale. Stouffer 2017; Saavedra et al. 2017) and that even two-species Here we combine field experiments with mathematical models can depart from the predictions of invasion analyses models to predict the outcome of competition in a commu- in some settings (Barabás et al. 2018). Deviations from pair- nity of five co-occurring native and exotic grasses in a grass- wise predictions may originate from indirect effects on com- land . We develop and empirically parameterize petitor density; nonhierarchical interactions, in which compet- population-dynamic models for the species in this complex itive impacts are intransitive; or higher-order interactions, in community. The models incorporate a suite of demographic which the per capita impact of one species on another is me- rates experimentally measured for three different exotic an- diated by interactions with a third species. In complex com- nual grasses and two native perennial grasses at a single munities, it is theoretically possible to observe priority effects Northern California grassland site and include the impact within groups of species with high niche overlap and fitness of fungal pathogens on those demographic rates, which may similarity, which occur alongside deterministic coexistence affect competitive outcomes by altering fitness differences or competitive exclusion between groups of species with larger or by inducing negative frequency dependence of growth niche differences and fitness differences. Despite these theo- rates (Mordecai 2011, 2013). We estimate parameters of retical developments, there are few empirical examples of the model statistically from field observations of seed out- communities in which multispecies outcomes depart from put, germination, establishment, seed infection, and adult two-species predictions (but see Godoy et al. 2017; Mayfield survival for each of five competing species of exotic annual and Stouffer 2017), although alternative stable states have and native perennial grasses. Using the parameterized model, been empirically documented outside the coexistence litera- we study the multispecies outcome of competition, with and ture (Fukami et al. 2005; Carpenter et al. 2011; Staver et al. without pathogens. Specifically, we ask the following ques- 2011). It is unknown whether departures between pairwise tions: (1) How strong are intra- and interspecific competi- and multispecies predictions are a common biological phe- tion between native and exotic grass species? (2) What is the nomenon or a quirk of mathematical models. Moreover, it predicted outcome of competition? (3) Do complex out- is not clear how ecological contexts—such as the coevolution- comes, including priority effects and/or intransitive competi- ary history of the competing species and the level of distur- tion, emerge from the dynamics of the full multispecies as- bance—may influence the likelihood of complex multispecies semblage? (4) How strongly do foliar and seed pathogen dynamics as compared to negative frequency-dependent impacts on demographic rates influence the outcome of stabilization (Ocampo-Ariza et al. 2018). competition? Multispecies Outcome of Competition 215

Methods We also measured the impacts of competition on seed production in six transects that naturally varied in plant Empirical Data Collection and Parameter Estimation composition. Each transect varied in grass composition from Study System. We chose five focal species that are highly native perennial dominated at one end to exotic annual dom- abundant and widespread in California grasslands: exotic an- inated at the other, with five 1-m2 plots spanning each tran- nual grasses Avena barbata, Bromus diandrus,andBromus sect spaced approximately 5–10 m apart. For each focal plant hordeaceus and native perennial bunchgrasses Stipa pulchra in the transects, we estimated seed output in both the 2015 and Elymus glaucus. For each species, we measured a full and 2016 growing seasons (see appendix). complement of demographic rates that determine popula- To assess pathogen damage and its relationship with seed tion growth: seed germination, seedling establishment, the production and competitor density, we visually estimated impact of competition on per capita seed production, and leaf area damaged by fungal infection on a subset of leaves over-summer survival (for both seedling and adult perennial on each focal plant in both the transects and experimental bunchgrasses). We also assessed seed infection and survival plots. We used these data to quantify the impact of foliar fun- with a common fungal pathogen that causes a disease called gal infection on seed output, as well as the impact of plant spe- black fingers of death, which can kill native and exotic grass cies’ local relative abundance on pathogen damage. We note seeds (Beckstead et al. 2010). All experimental work was that this approach could underestimate the impact of fungal conducted in Jasper Ridge Biological Preserve, located in infection if resistance is generally costly, and most surveyed San Mateo County, California (377240N, 12271303000W; 66– plants were actively fighting infections. 207 m). This 485-hectare biological preserve is managed Our attempt to manipulate competitor densities in the by Stanford University and has a Mediterranean , experimental plots was only partially successful because of re- with cool, wet winters and warm, dry summers (mean an- cruitment from the seed bank. As a result, we combined all nual precipitation p 622:5 mm; Ackerly et al. 2002). All focal plants into a single data set of seed outputs and observed demographic rates (except the perennial seedling-to-adult- competitor densities (rather than using the target densities transition probability; see below) were measured in winter for the experimental plots). Our final data set included 439 2015 to spring 2016 (the 2016 growing season), an average A. barbata,399B. hordeaceus,319B. diandrus,387S. pulchra, rainfall year with 601 mm total precipitation distributed over and 234 E. glaucus individuals (see appendix for further de- 20 precipitation events. tails). We used Markov chain Monte Carlo (MCMC) to infer Competition Experiment and Transect Sampling. Seed out- parameters relevant to seed output (l), competition (a), put is an important component of plant reproduction and and foliar infection (b) from our competition experiment is strongly impacted by competitor density for many plants data (see “Population-Dynamic Model” and table 1 for pa- (Mordecai 2013; Mordecai et al. 2015). We measured seed rameter definitions) and performed simulation-based vali- output as a function of competitor density by varying the dation of our estimation procedure. Full details of this esti- density of each plant species in monoculture and in mixed- mation procedure and its validation are provided in the species plots and measuring per capita impact on seed pro- appendix, along with a more detailed description of the ex- duction for each competitor species (Levine and HilleRis- perimental design. We repeated the parameter inference Lambers 2009; Mordecai 2013). The 1-m2 competition plots procedures on subsets of the data that included either only were randomly assigned to five competitor density treat- the experimental plots or only the transects and found that ments, ranging from 10% to 100% of each species’ estimated parameter values were of similar magnitude and with over- natural density in monoculture, for each of the seven back- lapping posterior distributions (see fig. A7 and appendix; ground species groups (respective seedlings of A. barbata, figs. A1–A8 are available online). B. diandrus, B. hordeaceus,andE. glaucus; E. glaucus adults; S. pulchra seedlings; and S. pulchra adults). We also cleared Germination Data. We planted marked seeds of each focal 4-m2 plots of competitors to measure seed output on indi- species to track germination and seedling establishment in viduals of each species at low competitor density (though 30 plots of 25 individuals of each species in November 2015. natural from the seed bank meant that these We recorded their status weekly for 4 weeks in January and plots were not completely clear of competition). We used February as missing (M), alive (A), or alive with 150% of leaf weed matting, weeding, and seed addition to manipulate area with pathogen damage (P). We used a Markov model to competitor densities. At the end of the 2016 growing sea- estimate the probability of establishing, surviving, and be- son, we measured seed output from up to three focal plants coming heavily infected for each species by calculating weekly per species per plot (as available). See the appendix, avail- transition probabilities between these three states by plant able online, for a complete description of the competition species and then using the matrix to project forward 4 weeks experiment. to estimate the overall probability of germinating and estab- 216 The American Naturalist

Table 1: Descriptions of parameters and variables relevant to our population- dynamic model Parameters/variables Description

ajl Per capita competition impact of species l on species j b j Impact of foliar fungal infection per unit area infected

Aj Mean leaf area infected

lj Mean seed output in the absence of infection and competition

fj(t) Compound impact of competition and infection on seed output

Sj Seed output after accounting for competition and infection

gj Germination fraction

gj Seed survival rate in presence of BFOD pathogen

nj Seedling survival rate I fj Establishment probability for infected seedlings U fj Establishment probability for uninfected seedlings 2 Dl Density of competitor species l per m 0 nj Seedling transition rate in the absence of competition

nj(t) Seedling transition rate after accounting for competition

as Impact of seedlings on seedling-adult transition

aa Impact of perennials on seedling-adult transition

an Impact of exotic annuals on seedling-adult transition 2 Ds Density of seedlings per m 2 Da Density of exotic annuals per m 2 Dn Density of perennials per m I Pj Proportion of seedlings infected during seedling-adult transition

yj Rate of perennial adult over-summer survival a nj (t) No. annual seeds at time t p nj (t) No. perennial seeds at time t

aj(t) No. perennial adults at time t Note: Where not otherwise specified, the subscript j refers to species j. BFOD p black fingers of death. lishing. We repeated this calculation both with pathogens Adult Survival Data. To assess the survival of S. pulchra and present and with pathogens removed (i.e., as if all individuals E. glaucus, we marked 200 adult perennial bunchgrasses with experienced the establishment rates of uninfected individu- flags in June 2015 at four sites for each species and revisited als) in order to understand the impact of pathogens on seed- prior to senescence in June 2016. We recovered 167 S. pulchra fi fl ling establishment ( g. A1 shows inferred germination gj and and 170 E. glaucus ags on the second visit and recorded U I establishment fj and fj for uninfected and infected individ- them alive or dead based on observing green tissue and/or uals, respectively, for each species j). new fruiting stalks. We fit binomially distributed models of survival probability for each species using beta-distributed a p b p fi Seed Survival and Infection Data. Seeds that remain dor- priors with parameters 1and 1( g. A3). mant in the seed bank may contribute to population growth when they germinate in future years. To assess survival of nongerminating seeds between years, we buried 30 mesh Perennial Transition from Seedling to Adult. We modeled seed bags containing five sewn compartments of 100 seeds perennial seedling over-summer survival as a function of of each focal plant species 2–5 inches deep from November competitor density and per capita competitive effects using data and fitted parameters from previously published work 2015 through July 2016. We retrieved all intact seeds and fl scored them for black fingers of death (BFOD) pathogen (Mordecai et al. 2015). Brie y, we modeled perennial seed- damage (Beckstead et al. 2010; Mordecai 2013), which is ling over-summer survival as a beta-binomially distributed likely caused by one of the numerous Pyrenophora species process where for each observation k, the number of surviv- that are common in these sites (Spear and Mordecai 2018). ing seedlings maturing into adulthood was We tested all intact, nongerminated seeds for viability using germinatino, gibberellic acid, and cut tests, as in previous d(1 2 m ) work (Mordecai 2012). We parameterize the fraction of seeds Y ∼ beta binomial d, k , n , ð1Þ fi k k killed from BFOD infection as gj for species j ( g. A2). mk Multispecies Outcome of Competition 217 P p = 1 fi where mk n 1 kajDkj is the expected value over all subject to competition in their survival over their rst sum- competitor species j. Here n is the per capita survival prob- mer. Perennial seedlings survive at rate vj(t), given by ability in the absence of competition, a is the per capita j n0 competitive effects of individuals of species j, and D is the p j ð Þ kj nj(t) 1 1 1 , 4 number of individuals of species j in observation k. In the 1 asDs(t) aaDa(t) anDn(t) beta-binomial distribution, d affects the mean and variance, where D is the density of competitors; the subscripts s, a, and nk is the number of trials in observation k. The equation and n represent perennial seedlings, perennial adults, and m 0 for Yk is parameterized so that its mean is equal to k. Since annuals, respectively; and nj is the survival rate in the ab- we lacked the data to separately estimate aj for each individ- sence of competition. For this aspect of the model, we group ual species in our sample, we estimated an aj for perennial all annual and perennial plants together instead of comput- adults, perennial seedlings, and exotic annuals, respectively. ing each species competitive effect separately because we lacked the data necessary to infer the parameters for each species individually. Perennial seedlings that survive the Population-Dynamic Model summer then become adults in the following year. Perennial adults are also subject to over-summer mortality at rate (1 2

Model Structure. We developed a dynamic model that yj), modeled as competition independent because deaths of captures the effects of competition and fungal infection on adult bunchgrasses are relatively rare (fig. A3). growth rates for each grass species in our system, which is We model germination rate Gj after accounting for in- structurally similar to models developed in previous work fection and establishment (see “Seed Survival and Infec- (Mordecai 2013; Mordecai et al. 2015). All parameters and tion Data”)with variables in the population-dynamic model are listed in ta- p 2 U 2 I 1 I I : ð Þ ble 1. To model the effects of competition on the population Gj gj(1 gj)(fj (1 Pj ) fj Pj ) 5 growth of each species, we suppose that each plant of species Additionally, we suppose that the proportion of seeds re- j has a seed output of lj in the absence of competition and maining in the seed bank after germination and infection Bj that competition and infection reduce seed output by is given by p 2 2 : ð Þ 1 Bj (1 gj)(1 gj) 6 p P ð Þ f j(t) 1 1 b , 2 1 l ajlDl(t) Aj j At each time step, for each species j,wetrackthenumber a p of seeds nj (t) for exotic annuals or the number of seeds nj (t) where Dl(t) is the density of competitor species l per square and adults aj(t) for perennials. Combining across seed pro- meter at time t and Aj is the mean leaf area that was infected duction, competition, foliar fungal infection, fungal seed in- on individuals of species j. The expected seed output of a sin- fection, germination, establishment, and over-summer sur- gle individual Sj(t) is then vival, the full population growth equations are

p : ð Þ a 1 p a 1 ð Þ Sj(t) lj f j(t) 3 nj (t 1) nj (t)(Gjlj f j(t) Bj), 7

In the absence of transmission information, we do not ex- p 1 p 1 p ð Þ nj (t 1) aj(t)lj f j(t) nj (t)Bj, 8 plicitly model transmission of fungal pathogens but simply 1 p 1 p : ð Þ assume that each individual is infected at the mean level of aj(t 1) aj(t)yj nj (t)Gjnj(t) 9 observed foliar fungal infection for species j.

For each species j, we suppose that a fraction gj of the The germination, adult survival, seed infection, and seed- seeds germinate, and among these a fraction gj are infected ling transition parameters were estimated as described in with a fungal seed pathogen (BFOD). Seeds that germinate the previous sections. The competition (a), seed output and are not infected may then establish or may be eliminated (l), and foliar infection burden (b) were estimated using before they ever produce seeds. We supposed that the prob- custom MCMC software, as described in the appendix. Sim- ability of establishment depends on foliar fungal infection sta- ulations of each species in monoculture show a strong posi- tus and separately estimated the probability of establishment tive correlation with observed monoculture densities in the I U fi fi for infected (fj ) and uninfected (fj ) seedlings for each spe- eld ( g. A6), suggesting that our model parameterization cies j. The proportion of seedlings that are infected during the with independently measured demographic rates accurately I transition is given by P j . describes the system. Perennial seedlings are presumed to be weak competitors and are not included in the competition model and produce Separating Infectious Processes from Competition. Initially, no seeds in the first year of life (Mordecai et al. 2015) but are we considered three broad classes of models that (1) did 218 The American Naturalist not include the impacts of infection, (2) included only foliar Last, we performed invasion experiments to better un- infection, and (3) included both foliar infection and BFOD derstand the dynamics underlying some of the coexistence pathogen. Since foliar infection had a negligible impact on outcomes that were predicted under our model. In these dynamics and competitive outcomes, we compare models experiments, we compared the ability of E. glaucus to in- that include only foliar fungal infection to models that in- vade established S. pulchra plots with and without the pres- clude both foliar infection and BFOD. The foliar infection ence of an exotic annual competitor. We considered only model includes both the parameters relevant to infection the subset of posterior parameter estimates in which S. of perennial seedlings during their transition to adults and pulchra was predicted to coexist with B. diandrus, exclud- infection of leaves of adult perennials and exotic annuals. ing all replicates in which single species dominance was predicted. We simulated 100 years of S. pulchra growth Inferring the Outcome of Competition. We used the param- in the absence of competitors to allow it to establish. Sub- eterized models to investigate the outcome of competition sequently, at time t p 100, we either invaded B. diandrus using both pairwise and multispecies approaches to assess or allowed S. pulchra to continue in the absence of com- any differences in the outcome across approaches and to petitors for another 100 years, and finally we introduced understand potentially complex outcomes more mechanis- asingleE. glaucus individual at time t p 200. We summa- tically. First, we used the posterior parameter estimates and rized these experiments by calculating the proportion of the population-dynamic model to compute growth rate posterior samples in which S. pulchra is able to prevent when rare (GRWR) for each pair of species. If in a pair E. glaucus from invading after 600 simulated years post- of species each has GRWR 1 1 (i.e., log(GRWR) 1 0, where invasion. We sampled one set of parameters randomly from log is the natural logarithm), then stable coexistence is among the posterior estimates to display this invasion ex- predicted because the rarer species is expected to increase periment, but note that we vary the timing of the invasions in prevalence, preventing either species from being excluded for the purpose of visualization (fig. 4). (Turelli 1978; but see Case 1995). Pairwise competition cal- culations were performed in the presence of fungal infection (i.e., including all model parameters pertinent to foliar or Results seed fungal infection). Evidence for Strong Interspecies Competition To calculate GRWR for each species pair, we sampled the relevant demographic rate parameters from their pos- We calculated the pairwise log(GRWR), where zero is the terior distributions and simulated one species forward to threshold for invasion, of each species invading a monocul- its stable monoculture density; from there, we computed ture of each other species to assess the pairwise outcomes of the growth rate of an invader of another species. For pe- competition (fig. 1A). We also calculated the proportional rennials, we computed GRWR as the dominant eigenvalue decrease in GRWR relative to the growth rate in the absence of the 2#2 matrix describing the rate of transition be- of competition to assess the overall impact of competition tween seed and adult stages, which accounts for their on population growth (pdGRWR; fig. 1B). The values plot- stage-structured life history (Mordecai 2013). For exotic ted in figure 1 represent the mean over 250 independent annuals, we calculated GRWR by simulating the addition samples of the parameters from their posterior distribution. of a single individual to the monoculture species and cal- If there were strong niche differences between all pairs of culating the growth rate in the second generation. We also species, each species would strongly constrain its own growth calculated percent difference in GRWR (pdGRWR) as rate but have a relatively weak competitive impact on other 100(1 2 A=B), where B is the GRWR in an empty plot species. By contrast, we observed high niche overlap in this and A is the GRWR under invasion conditions. system, in which interspecific competition constrains inva- Second, we investigated competitive outcomes for the full sion growth rates as much or more than intraspecificcom- species assemblage using simulations. Because outcomes petition (fig. 1A). Along the diagonal, where each species could be initial condition dependent, we initialized our sim- competes with itself at its stable monoculture density, the ulations at a range of observed densities from the transects. log(GRWR) was always very near zero (fig. 1A). When the We simulated 600 years and report results of species native perennial species (Elymus glaucus and Stipa pulchra) mixtures at this time point (Mordecai 2013). For species were the invaders, they were constrained to log growth rates that were not present in a sampled transect, we introduced close to zero by all competitors except Avena barbata,which a pseudo-count of one individual so that each species is ini- is unable to constrain either species. By contrast, neither pe- tially present in each simulation. We consider species with rennial species reduced the log(GRWR) of any of the annual population sizes exceeding one individual at the end of the species to below zero. Bromus hordeaceus and Bromus dian- simulation to have persisted, while species with less than drus tightly constrained each others’ growth rates but were one individual are excluded. not strongly constrained by the perennial competitors. Avena Multispecies Outcome of Competition 219

A B SP SP

EG log(GRWR) EG pdGRWR 2.0 −0.4 1.5 −0.6 BH 1.0 BH 0.5 −0.8 BD 0.0 BD Invader species Invader species Invader AB AB

SP EG BH BD AB SP EG BH BD AB Resident species Resident species

Figure 1: Strength of pairwise competition inferred from the growth rates of invaders introduced at low density to established monocultures of residents. A, Log of growth rate when rare (GRWR) 2 log(GRWR) 1 0 is the invasion criterion. Larger positive values (darker yellow/or- ange) represent high niche overlap, while darker purple represents less overlap. B, The proportional difference in each species growth rate in the presence of the resident species as compared to its growth rate in the absence of competition. Perennial native species: Stipa pulchra (SP), Elymus glaucus (EG); annual exotic species: Bromus hordeaceus (BH), Bromus diandrus (BD), Avena barbata (AB).

barbata was a poor competitor in this community and only Based on our two-species competition observations (fig. 1), constrained itself while being tightly constrained by both of we expected that either B. hordeaceus or B. diandrus would its annual competitors. persist in most simulations because they have large growth These results are not driven solely by some species hav- rates even when invading a monoculture of native perennial ing low overall (competition-independent) growth rates, competitors. Since this species pair displayed large interspe- because competition reduced GRWR for nearly all species cific competition coefficients, we also expected that they pairs (fig. 1B). The strongest impacts of competition were would rarely coexist. The pairwise invasion analysis also sug- of B. diandrus and B. hordeaceus on each other, resulting gests that A. barbata should rarely persist given its low growth in growth rates reduced by 95%296.4% relative to the ab- rate in the presence of its competitors and that the native sence of competition. Elymus glaucus and S. pulchra were perennials S. pulchra and E. glaucus would sometimes persist, also subject to competition with each other, reducing S. given that their mean replacement rates were typically near pulchra’s growth rate 49.3%251% and E. glaucus’s growth one (fig. 1A). Consistent with these expectations, either B. rate by 72.7%–73.6% relative to growth rates in absence of hordeaceus or B. diandrus persisted in 99.7% of simulation competition. The impacts of B. diandrus and B. hordeaceus replicates (fig. 2A), while the two species almost never co- on the perennials were of similar magnitude to the observed existed with each other (0.32% of replicates). Avena barbata perennial-perennial impacts. was nearly always excluded. Native perennials persisted in 22.0% of replicates, usually by coexisting with either B. hor- deaceus or B. diandrus, but rarely coexisting with each other (0.39% of replicates). Predicted Community Composition The wide range of possible outcomes could reflect either Is Exotic Annual Dominated uncertainty in the parameter estimates or dependence on We next sought to investigate competitive outcomes when all the initial conditions of our simulations. To differentiate five species compete simultaneously. Although it would be between these possibilities, we investigated persistence as possible to perform a multispecies invasion analysis, such a function of initial competitor densities (fig. 3). If each spe- analyses can provide misleading results because GRWR ex- cies’ success is strongly dependent on initial conditions, this ceeding 1 does not necessarily imply stable persistence when suggests that priority effects play a much larger role in de- more than two species are included (Case 1995; Dormann termining community composition than uncertainty in pa- and Roxburgh 2005; Saavedra et al. 2017). Instead, we exam- rameter estimates, and vice versa. We observed that the pe- ined the outcomes of competition by directly assessing the fi- rennial species’ persistence in multispecies competition was nal simulated community composition across a range of em- weakly dependent on initial community composition: the pirically observed densities as initial conditions. For this probability of S. pulchra persistence increased modestly analysis (fig. 2A), we included the impact of foliar fungal in- with its initial density. By contrast, the annual species B. fection on demographic rates but not the pathogen BFOD. hordeaceus and B. diandrus showed striking priority effects 220 The American Naturalist

0.8 A 0.8 B species) species) s s 0.6 0.6 species BD BH 0.4 0.4 BH−AB EG−BD EG−BH SP−BD 0.2 0.2 all others (Proportion of outcomes with (Proportion of outcomes with s 0.0 s 0.0 P P 12345 12345 s (number of species persisting at t= 600) s (number of species persisting at t= 600)

Figure 2: Proportion of outcomes in which a given species or species combination persisted after 600 generations in the population-dynamic model. Each replicate represents a single sample from the posterior distribution of the model parameters and initial competitor densities from a randomly sampled transect from among the set of transects that we measured. The X-axis corresponds to the number of species (s) that persisted over 600 simulated years, while the Y-axis corresponds to the proportion of replicates (Ps) that resulted in this outcome. Each bar is subdivided into the specific set of species that were observed to have log of growth rate when rare greater than 0 for a particular pa- rameter set and transect sample. All compositions that occurred in under 1% of replicates are grouped into a single color. A, Results from a model that includes foliar fungal infection but not the black fingers of death (BFOD). B, Results from the model that includes both foliar fungal infection and BFOD. Perennial native species: Elymus glaucus (EG), Stipa pulchra (SP); annual exotic species: Bromus diandrus (BD), Bromus hordeaceus (BH), Avena barbata (AB).

driven by strong interspecific competition across the densi- priority effects when the native perennial species com- ties of all competitors except A. barbata, which had only peted directly (fig. 4A). When S. pulchra was introduced first, modest effects on any species. 36.4% of simulation replicates resulted in dominance by S. pulchra, whereas 99.9% of replicates in which E. glaucus was introduced first resulted in dominance by E. glaucus. The two perennial species coexisted in only 0.1% of rep- Nonhierarchical Competition between Natives and Exotics licates. Notably, the two native perennial species were not equally We next tested how the invasion of exotic annuals might likely to coexist with each of the dominant exotic annuals: alter competition outcomes between the two perennial spe- S. pulchra was much more likely to coexist with B. diandrus cies. When B. diandrus invaded simulated monocultures of than B. hordeaceus. To better understand the dynamics S. pulchra, the priority effect preventing E. glaucus from in- driving these outcomes, we compared invasion simulations vading was substantially stronger. Among replicates in which that included only the native perennials to simulations in S. pulchra and B. diandrus coexisted, E. glaucus was able to which an exotic annual invader preceded the native peren- invade in only 4.5% (as compared to 52.9% of these same pa- nial invader. rameter sets when B. diandrus was not included in the simu- When the native perennials competed in the absence of lation). Hence, when coexistence was predicted between S. exotic annuals, their dynamics are nearly neutral, as indi- pulchra and B. diandrus, the presence of the exotic annual cated by the near equality of intraspecificandinterspecific B. diandrus increased the likelihood of persistence for S. pul- competition strength (fig. 1A). Although neutral dynamics chra at the expense of E. glaucus (fig. 4). These results suggest cannot result in long-term stable coexistence, they are a strong impact of nonhierarchical competition on outcomes expected to result in relatively slow loss of one of the spe- in this system, in which no single species can dominate and cies (Adler et al. 2007). Nearly neutral dynamics could re- coexistence is only possible given specific arrival orders. sult in priority effects if interspecific competition is slightly These dynamics result in deterministic competitive exclusion stronger than intraspecific competition. Consistent with these or coexistence mediated by priority effects that make the final expectations, we observed slow replacement dynamics and composition dependent on stochastic arrival order. Multispecies Outcome of Competition 221

1.00 A B 1.00 C 0.75 0.75 0.75 v r 0.50 0.50 u surv s surv 0.50 P P P 0.25 0.25 0.25

0.00 0.00 0.00 0 500 1000150020002500 0 200 400 600 0 100 200 300 BH density BD density AB density

D 1.00 E 1.5 species 0.75 1.0 SP v r EG

surv 0.50 su 0.5 BH P P BD 0.25 0.0 AB 0.00 −0.5 5101520 0 5 10 15 20 SP density EG density

Figure 3: Effect of initial conditions on the outcome of competition. Estimated probability of persistence (Psurv) of each species (colored points and lines) as a function of initial density of each species in the simulation (X-axis). Points represent the proportion of simulations resulting in persistence that were initialized at the corresponding density, while loess curves (and gray uncertainty envelopes) were fitwith the function geom_smooth in ggplot. Perennial native species: Stipa pulchra (SP), Elymus glaucus (EG); annual exotic species: Bromus hordeaceus (BH), Bromus diandrus (BD), Avena barbata (AB). Priority effects occur when the probability of persistence depends strongly on initial density.

Seed Infection Hampers a Weak Competitor, A. barbata of niche differences versus fitness differences (Levine and HilleRisLambers 2009; Adler et al. 2010; Narwani et al. While the simulation and invasion results suggest that exotic 2013; Godoy and Levine 2014; Godoy et al. 2014; Kraft annuals will dominate perennials and either competitively ex- et al. 2015). By contrast, we found a large degree of niche clude them or reduce their population sizes, pathogens could overlap in an empirically parameterized model of an invaded reduce this effect if exotic annuals incur a higher fitness cost California grassland (fig. 1A). The model suggests that com- than perennials from infection. We repeated the simulation petition in multispecies assemblages can lead to complex experiments in the previous section with the impact of fungal outcomes that mix deterministic competitive exclusion or infection by BFOD included (fig. 2B). BFOD decreased the coexistence with stochastic priority effects that determine overall success of A. barbata, which was already the weakest the identity of persisting species. Although a previous model annual competitor. Avena barbata persisted in 1.98% of predicted exotic annual dominance over native perennials, replicates that excluded BFOD but almost never persisted with a small probability of native coexistence with exotics, it in its presence (0.12% of replicates). Species other than A. did not predict priority effects among pairs of exotic or na- barbata were only minimally affected by BFOD, consistent tive species because it relied solely on a pairwise approach with low rates of infection that we observed empirically and composite parameter estimates from a range of species (fig. A2). (Mordecai et al. 2015). Our work supports the results from a growing body of theoretical studies suggesting that compet- itive outcomes in complex communities can depart from pre- Discussion dictions from pairwise species comparisons (Case 1995; Alle- The long-term outcome of competition is difficult to ob- sina and Levine 2011; Mayfield and Stouffer 2017; Saavedra serve directly in nature, so empirically parameterized math- et al. 2017) and provides evidence that slowly occurring, ematical models are critical for predicting when competi- nearly neutral dynamics may play an important role in com- tive exclusion, coexistence, or priority effects are most likely. petitive outcomes (Adler et al. 2007). The results suggest that To date, most studies have focused on pairwise outcomes in methods for assessing the outcome of competition in multi- multispecies communities, emphasizing the relative strength species assemblages that move beyond invasion analyses A B C 1.00 1.00 1.00 species 0.75 0.75 0.75 SP 0.50 0.50 0.50 EG BH (scaled size) (scaled size) 0.25 (scaled size) 0.25 0.25 K K K BD N N 0.00 N 0.00 0.00 0 200 400 600 0 200 400 600 0 200 400 600 t (years) t (years) t (years)

Figure 4: Effect of exotic annuals on invasion dynamics. Panels A–C correspond to a single set of parameter estimates sampled from the posterior distribution. A, Elymus glaucus (EG) invades at t p 100 and is able to establish and eventually replace Stipa pulchra (SP). B, EG invades at t p 100 and is able to establish and gradually replace SP. Bromus diandrus (BD) invades at t p 220 and coexists with SP, reversing the invasion of EG and preventing EG and Bromus hordeaceus (BH) from invading in the future. C, EG invades at t p 100 and is able to establish and gradually replace SP. BH invades at t p 220 and outcompetes both perennials. BD cannot invade due to the priority effect between BD and BH. Units on the Y-axis correspond to population sizes relative to monoculture density Perennial native species: S. pulchra, E. glaucus; annual exotic species: B. hordeaceus, B. diandrus. Priority effects occur when the probability of persistence depends strongly on initial density. Multispecies Outcome of Competition 223 are an important avenue for theoretical and empirical de- the a priori expectation of strong stabilization within co- velopment (Saavedra et al. 2017; Barabás et al. 2018). evolved communities, our study did not identify substantial We found that the population growth model parameterized niche differences between the two native species or the two with field estimates of demographic rates accurately predicted exotic Bromus species with an overlapping European home species densities in monoculture (fig. A6), suggesting that it range. Instead, the results suggest that nearly neutral dynam- can realistically capture equilibrium outcomes. In this five- ics determine competitive outcomes in some pairs of species species assemblage, we found species pairs with high niche with long coevolutionary histories. overlap—exotic annuals Bromus diandrus and Bromus hor- Among the mechanisms that may maintain diversity in deaceus; and native perennials Elymus glaucus and Stipa complex communities, intransitive competition has received pulchra—and nonhierarchical competition such that no a great deal of interest (Laird and Schamp 2006; Allesina and single species was dominant over all others (fig. 1). This Levine 2011; Soliveres et al. 2015; Matías et al. 2018; Stouffer results in a complex posterior distribution of competitive et al. 2018). However, a recent study using empirically param- outcomes that includes competitive exclusion of all other eterized population-dynamic models found that intransitive species by either B. diandrus or B. hordeaceus or coexistence competition was uncommon and not likely to promote coex- of one of these exotic annuals with one native perennial, ei- istence among a set of 18 competing annual grass species ther E. glaucus or S. pulchra (fig. 2). The outcome of com- (Godoy et al. 2017). In our study, although we found evidence petition between the two congeneric exotic annuals was for nonhierarchical competition, simulations suggested that it driven by strong interspecific competition, resulting in pri- was unlikely to promote coexistence of more than two spe- ority effects (fig. 3). Among the subset of outcomes in which cies. However, this does not imply that nonhierarchical com- coexistence was predicted between S. pulchra and B. diandrus, petition has no role in diversity maintenance. Priority effects, the presence of B. diandrus usually prevented the subsequent like those reported here, could lead to a spatial patchwork of invasion of E. glaucus, augmenting the priority effect exerted competitors, with and stochastic recolonization by S. pulchra on its native perennial competitor through non- determining the distribution of competing species. hierarchical competition. Hence, invasion by an exotic species Previous empirical work on the outcome of competition with moderate niche overlap may increase resilience to inva- in invaded California grasslands has suggested a wide range sion by native competitors with high niche overlap. Since of possible outcomes and coexistence mechanisms, includ- the two native species are predicted to compete nearly neu- ing (1) the requirement for previous disturbance to explain trally in the model, almost all predicted outcomes precluded the invasion of exotics in perennial-dominated plots (Strom- their long-term stable coexistence, meaning that S. pulchra berg and Griffin 1996; Seabloom et al. 2003; Corbin and may indirectly benefitfrominvasionbyB. diandrus via its D’Antonio 2004), (2) competitive dominance of exotic an- negative effect on E. glaucus (fig. 4). nuals over S. pulchra (Dyer and Rice 1997), and (3) spatial Studies applying modern coexistence theory have often variation in outcomes determined by seed dispersal (Di- documented substantial niche differences between species Vittorio et al. 2007) and habitat (Everard et al. 2009). A lim- pairs, while variation in the magnitude of fitness difference itation of most previous work considering more than two determines the potential for coexistence or competitive ex- competing species is that the empirical results were not clusion. However, these studies typically explore commu- linked to a dynamic model, making it difficult to project nities in which species have long coevolutionary histories dynamics over long timescales. Our parameterized model and belong to similar functional guilds (e.g., native annual is inconsistent with prediction 1 because it predicts that ex- forbs; Levine and HilleRisLambers 2009; Adler et al. 2010; otic species can invade undisturbed perennial plots and con- Narwani et al. 2013; Godoy et al. 2014; Kraft et al. 2015; sistent with prediction 2 because a portion of predicted out- but see Godoy and Levine 2014). In such systems, we might comes led to unconditional exotic dominance, as predicted expect that co-occurrence over long timescales has led spe- in a previous two-species model (Mordecai et al. 2015). In- cies to minimize their fitness differences, maximize their terestingly, our model projections are broadly consistent niche differences, or both, leading to long-term stable coex- with co-occurrence observations made in the field—despite istence. In invaded systems, exotic species must have fitness having only a few observations of each species within our advantages, niche differences, or both with respect to the transects, we found a modest anticorrelation between the native species in order to have successfully invaded (Mac- two Bromus species (r p 20:22), as would be predicted by Dougall et al. 2009). Our study found support for large fitness our model. Our qualitative field observations also suggest that advantages of invading species and modest niche overlap that these species exist predominantly in separate patches within was potentially small enough to promote coexistence (20% Jasper Ridge. posterior probability). This is consistent with the possibility While our study did not attempt to assess environmen- that competitive exclusion and priority effects may be com- tal and spatial variation in competitive outcomes (i.e., pre- mon long-term outcomes in invaded communities. Despite diction 3 above), coexistence mechanisms occurring over 224 The American Naturalist broad temporal and spatial scales may be an important species, suggesting that coexistence is not substantially af- contributor to observed species distributions. The five fo- fected by fungal infection (Spear and Mordecai 2018). cal species in our system have co-occurred at the study site However, because the two native perennial species compete and other California grassland sites for more than a hun- almost neutrally in our model, even modest pathogen im- dred years, implying that co-occurrence may be driven by pacts could have a substantial effect; because their fitness nonequilibrium dynamics that play out over long time- differences are small, our study may have been underpow- scales or that stabilizing processes occur over larger spatial ered to investigate this specific outcome. or temporal scales. Although soil moisture and nutrient Though the outcome of competition in invaded systems is availability vary spatially at both neighborhood and regional often poorly understood, our work shows that stabilizing scales across California grasslands and precipitation varies niche differences, and particularly the role of pathogens in several-fold between years, demographic studies of species in- that stabilization, are not ubiquitous at local scales in nature, teractions are regularly conducted at small spatial and tem- especially in systems with short coevolutionary histories be- poral scales, as in the present study (Seabloom et al. 2003; tween species. Assessing the strength of stabilization and the Corbin and D’Antonio 2004; DiVittorio et al. 2007). Envi- outcome of competition is important not only for fundamen- ronmental variation combined with the long life spans of tal ecological understanding but also for maintaining resilient perennial bunchgrasses and the high seed production of an- ecosystems as they respond to global change. Future work in nual grasses could provide ample opportunity for environ- other systems that are potentially far from equilibrium, such mental fluctuations to promote coexistence over space or time as invaded ecosystems, is necessary to test the generality of (Warner and Chesson 1985; Cáceres 1997; Chesson 2000; our results and to predict the long-term outcome of competi- Chesson et al. 2005; Usinowicz et al. 2017; Li and Chesson tion in nature. 2018). An alternative to larger-scale stabilizing processes is that priority effects occur at small spatial scales, while the turnover and random colonization of sites allows patches of different species composition to persist in a matrix of mu- Acknowledgments tually noninvasible patches (Vannette and Fukami 2014). We thank our editors and anonymous reviewers at The Amer- Our results are consistent with this priority effect mechanism ican Naturalist for comments that improved the quality of the and do not preclude the possibility of coexistence mecha- manuscript. We acknowledge generous support and assis- nisms occurring over larger scales. A major challenge for fu- tance from Teri Barry, Nona Chiariello, Phillippe Cohen, ture work in systems with large and variable geographic ranges Joe Sertich, Reuben Brandt, Johannah Farner, Steve Gomez, is to incorporate multiscale spatial and temporal variation Bill Gomez, Stuart Koretz, Cary Tronson, Divya Ramani, that may contribute to patterns of co-occurrence. Ryan Tabibi, Esther Liu, Sandya Kalavacherla, Vidya Ragh- In addition to the outcome of competition, identifying vendra, Jason Zhou, Virginia Parra, Claudia Amadeo-Luyt, explanatory mechanisms is paramount for understanding Gaurika Duvar, Elizabeth Wallace, the Jasper Ridge Kennedy the assembly of ecological communities and their potential endowment fund, the Stanford University Vice Provost for to respond to species invasions. Pathogens are widely hy- Undergraduate Education summer research fellowship for pothesized to promote by specializing on undergraduates, and the Stanford University Raising Interest common host species, causing a demographic disadvantage in Science and Engineering (RISE) summer internship pro- to common species and an advantage to rare species (Aug- gram. We thank members of the Fukami, Peay, and Mordecai spurger 1983; Augspurger and Kelly 1984; Gilbert et al. 1994; labs for helpful comments on the project and Rodrigo R. Petermann et al. 2008; Mordecai 2011, 2013; Bagchi et al. Granjel, Ignasi Bartomeus, Oscar Godoy, and members of 2014). As with strong niche differences more generally, this the Biotic Interactions and Global Change group for their Janzen-Connell effect has been demonstrated mostly in peer review of our manuscript. L.H.U. was supported by native-dominated plant communities (Augspurger 1983, 1984; the National Institutes of Health Institutional Research and Augspurger and Kelly 1984; Gilbert et al. 1994; Petermann Academic Career Development Awards fellowship (NIGMS et al. 2008; Bagchi et al. 2014). By contrast, pathogen impacts grant K12GM088033). E.A.M. was supported by a grant from in this invaded grassland community differ in two important the National Science Foundation (DEB 1518681). ways. First, the foliar fungal pathogens in this community typically infect multiple grass hosts, including native and exotic species (Spear and Mordecai 2018). Second, the demo- graphic impacts were mostly minimal, except the negative impact exerted by the BFOD pathogen on A. barbata Literature Cited (fig. 2B). Another study in this system found no evidence Ackerly, D., C. Knight, S. Weiss, K. Barton, and K. Starmer. 2002. that pathogen load or impacts increased on locally common Leaf size, specific leaf area and microhabitat distribution of chap- Multispecies Outcome of Competition 225

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The bunchgrass Stipa pulchra, the state grass of California, is found in patches in Jasper Ridge Biological Preserve. The authors studied the eco- logical processes that determine the success or failure of native grasses and found that the order of arrival of invasive European grass species has a major impact on plant community composition. Photo credit: Reuben Brandt.