Cyclic population dynamics and density‐dependent intransitivity as pathways to coexistence between co‐occurring annual plants

Recent studies have brought renewed attention to the importance of complex species interactions—notably intransitive interactions—to patterns of plant community diversity. One underappreciated avenue through which intransitivity can occur is through cyclic population dynamics. Although such cyclic intransitive relationships have been extensively studied in predator–prey systems, evidence of their importance in competitive communities, notably plant communities, is more limited. Most studies of coexistence in plant communities assume fixed-point coexistence even while utilising models that allow for cyclic population dynamics. In this paper, we explore the potential for density-dependent, cyclic population dynamics and intransitivity in a model for annual plants. We then examine how these density-dependent cycles impact mutual invasibility and ultimately stable coexistence between plant species pairs. We do this using data collected from four co-occurring annual plant species living in natural wildflower communities in SW Western Australia. To maximise the number of biologically plausible pathways by which coexistence mediated by density-dependent cyclic intransitivity can occur, we use an annual plant model that allows for competitive direct interactions, facilitative direct interactions and higher-order interactions between species. Results from our empirically parameterised model suggest that monocultures of all four focal species can have cyclic solutions with periodicity <1 under sunny (“open”) or shaded field conditions. Cyclic patterns drive variation in annual abundance patterns, with stable solutions for persistent monocultures and invasibility potential (the capacity of one population to invade another) common. Mutual invasibility in the face of cyclic population dynamics was found for just one of six species pairs, only under open environmental conditions. Our results illustrate the potential for cyclic intransitivity to both drive and prevent stable coexistence in environmentally heterogeneous biological communities. Synthesis. We provide analytical and empirical evidence that coexistence in competitive communities (annual plants) can be achieved under non-equilibrium circumstances, through density-dependent cyclic intransitivity. Our results suggest that cyclic population dynamics may be common and important for coexistence dynamics in some types of communities. In such communities, the exploration of stable coexistence should, therefore, include consideration of cyclic as well as fixed-point equilibria for maximal accuracy.

[1]  B. Bolker,et al.  Spatial Moment Equations for Plant Competition: Understanding Spatial Strategies and the Advantages of Short Dispersal , 1999, The American Naturalist.

[2]  M. Gilpin.  Limit Cycles in Competition Communities , 1975, The American Naturalist.

[3]  M. Daws,et al.  Pre- and post-harvest influences on physiological dormancy alleviation of an Australian Asteraceae species: Actinobole uliginosum (A. Gray) H. Eichler , 2008, Seed Science Research.

[4]  Nathan J B Kraft,et al.  Intransitivity is infrequent and fails to promote annual plant coexistence without pairwise niche differences. , 2017, Ecology.

[5]  Werner Ulrich,et al.  Intransitive competition is widespread in plant communities and maintains their species richness. , 2015, Ecology letters.

[6]  Janneke HilleRisLambers,et al.  The importance of niches for the maintenance of species diversity , 2009, Nature.

[7]  C. Elton,et al.  The Ten-Year Cycle in Numbers of the Lynx in Canada , 1942 .

[8]  G. Gauze.  The struggle for existence, by G. F. Gause. , 1934 .

[9]  J. Huisman,et al.  Biodiversity of plankton by species oscillations and chaos , 1999, Nature.

[10]  Effects of exotic annual grass litter and local environmental gradients on annual plant community structure , 2017, Biological Invasions.

[11]  J. HilleRisLambers,et al.  Rethinking Community Assembly through the Lens of Coexistence Theory , 2012 .

[12]  Daniel S Maynard,et al.  Diversity begets diversity in competition for space , 2017, Nature Ecology &Evolution.

[13]  Yi Wang,et al.  mvabund– an R package for model‐based analysis of multivariate abundance data , 2012 .

[14]  Richard J Hobbs,et al.  Specific leaf area responses to environmental gradients through space and time. , 2014, Ecology.

[15]  A. Hastings,et al.  Stochastic Dynamics and Deterministic Skeletons: Population Behavior of Dungeness Crab , 1997 .

[16]  S. Prober,et al.  Resource heterogeneity and persistence of exotic annuals in long-ungrazed Mediterranean-climate woodlands , 2011, Biological Invasions.

[17]  Peter B Adler,et al.  A niche for neutrality. , 2007, Ecology letters.

[18]  Jacob Usinowicz,et al.  The spatial scales of species coexistence , 2017, Nature Ecology & Evolution.

[19]  V. Volterra.  Fluctuations in the Abundance of a Species considered Mathematically , 1926 .

[20]  V. Volterra.  Fluctuations in the Abundance of a Species considered Mathematically , 1926, Nature.

[21]  R. Hobbs,et al.  Climate moderates release from nutrient limitation in natural annual plant communities , 2015 .

[22]  Robert A. Laird,et al.  Competitive Intransitivity Promotes Species Coexistence , 2006, The American Naturalist.

[23]  Eyal Bairey,et al.  High-order species interactions shape ecosystem diversity , 2016, Nature Communications.

[24]  P. Herman,et al.  A Practical Guide to Ecological Modelling , 2009 .

[25]  M. Mayfield,et al.  Distinct invasion strategies operating within a natural annual plant system. , 2015, Ecology letters.

[26]  Oscar Godoy,et al.  Phenology effects on invasion success: insights from coupling field experiments to coexistence theory. , 2014, Ecology.

[27]  Stefano Allesina,et al.  Interaction rules affect species coexistence in intransitive networks. , 2011, Ecology.

[28]  J. Wootton,et al.  The Nature and Consequences of Indirect Effects in Ecological Communities , 1994 .

[29]  A. Hastings.  Transient dynamics and persistence of ecological systems , 2001 .

[30]  Nathan J B Kraft,et al.  Plant functional traits and the multidimensional nature of species coexistence , 2015, Proceedings of the National Academy of Sciences.

[31]  N. Stenseth,et al.  Population regulation in snowshoe hare and Canadian lynx: asymmetric food web configurations between hare and lynx. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Stefano Allesina,et al.  Beyond pairwise mechanisms of species coexistence in complex communities , 2017, Nature.

[33]  Daniel B. Stouffer,et al.  Higher-order interactions capture unexplained complexity in diverse communities , 2017, Nature Ecology &Evolution.

[34]  Nathan J B Kraft,et al.  Phylogenetic relatedness and the determinants of competitive outcomes. , 2014, Ecology letters.

[35]  David Tilman,et al.  Limiting Similarity in Mechanistic and Spatial Models of Plant Competition in Heterogeneous Environments , 1994, The American Naturalist.

[36]  R. May,et al.  Nonlinear Aspects of Competition Between Three Species , 1975 .

[37]  P. Chesson.  Mechanisms of Maintenance of Species Diversity , 2000 .

[38]  Stefano Allesina,et al.  A competitive network theory of species diversity , 2011, Proceedings of the National Academy of Sciences.