Competitive intransitivity, population interaction structure, and strategy coexistence

Sherpa Romeo green journal. Permission to archive accepted author manuscriptIntransitive competition occurs when competing strategies cannot be listed in a hierarchy, but rather form loops – as in the game Rock-Paper-Scissors. Due to its cyclic competitive replacement, competitive intransitivity promotes strategy coexistence, both in Rock-Paper-Scissors and in higher-richness communities. Previous work has shown that this intransitivity-mediated coexistence is strongly influenced by spatially explicit interactions, compared to when populations are well mixed. Here, we extend and broaden this line of research and examine the impact on coexistence of intransitive competition taking place on a continuum of small-world networks linking spatial lattices and regular random graphs. We use simulations to show that the positive effect of competitive intransitivity on strategy coexistence holds when competition occurs on networks toward the spatial end of the continuum. However, in networks that are sufficiently disordered, increasingly violent fluctuations in strategy frequencies can lead to extinctions and the prevalence of monocultures. We further show that the degree of disorder that leads to the transition between these two regimes is positively dependent on population size; indeed for very large populations, intransitivity-mediated strategy coexistence may even be possible in regular graphs with completely random connections. Our results emphasize the importance of interaction structure in determining strategy dynamics and diversity

TRY plant trait database – enhanced coverage and open access

Plant traits - the morphological, anatomical, physiological, biochemical and phenological characteristics of plants - determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits - almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Data from: Calculating competitive intransitivity: computational challenges

Intransitive, or 'rock-paper-scissors' competition is compelling because it promotes species coexistence and because recent work suggests it may be common in natural systems. One class of intransitivity indices works by considering s, the minimum number of competitive reversals to convert a given competitive community (i.e., a 'tournament') to a hierarchy. The most straightforward example of such 'reversal-based' indices is Petraitis' index, t = 1 - s/M, where M is the maximum s across all possible n-species tournaments. Using exhaustive searches, we prove that Petraitis' formula for M (and, therefore, t) does not hold for n ≥ 7. Furthermore, the determination of s for even moderate values of n may prove difficult, as the equivalent graph-theoretical problem is NP-hard; there is no known computationally feasible way to compute an exact answer for anything but small values of n, let alone a closed-form solution. Petraitis' t is a valuable index of intransitivity; however, at present its use is limited to relatively species-poor systems. More broadly, reversal-based indices, while intuitive, may be problematic because of this computability issue

find_M

A Matlab MEX function, written in C++, which, given n, provides a list of all n-species tournaments, gives the minimum number of reversals required to change them into their respective minimally distant hierarchies (s in Petraitis 1979), and also gives the maximum minimum number of reversals (M in Petraitis 1979)

find_s

A Matlab MEX function, written in C++, which finds the minimum number of competitive reversals required to change a given tournament to a hierarchy (s in Petraitis 1979)

Appendix B. Figures showing the raw data for the number of generations until the first extinction and final species richness.

Figures showing the raw data for the number of generations until the first extinction and final species richness

The Influence of Matrix Size on Statistical Properties of Co-Occurrence and Limiting Similarity Null Models.

Null models exploring species co-occurrence and trait-based limiting similarity are increasingly used to explore the influence of competition on community assembly; however, assessments of common models have not thoroughly explored the influence of variation in matrix size on error rates, in spite of the fact that studies have explored community matrices that vary considerably in size. To determine how smaller matrices, which are of greatest concern, perform statistically, we generated biologically realistic presence-absence matrices ranging in size from 3-50 species and sites, as well as associated trait matrices. We examined co-occurrence tests using the C-Score statistic and independent swap algorithm. For trait-based limiting similarity null models, we used the mean nearest neighbour trait distance (NN) and the standard deviation of nearest neighbour distances (SDNN) as test statistics, and considered two common randomization algorithms: abundance independent trait shuffling (AITS), and abundance weighted trait shuffling (AWTS). Matrices as small as three × three resulted in acceptable type I error rates (p ) was associated with increased type I error rates, particularly for matrices with fewer than eight species. Type I error rates increased for limiting similarity tests using the AWTS randomization scheme when community matrices contained more than 35 sites; a similar randomization used in null models of phylogenetic dispersion has previously been viewed as robust. Notwithstanding other potential deficiencies related to the use of small matrices to represent communities, the application of both classes of null model should be restricted to matrices with 10 or more species to avoid the possibility of type II errors. Additionally, researchers should restrict the use of the AWTS randomization to matrices with fewer than 35 sites to avoid type I errors when testing for trait-based limiting similarity. The AITS randomization scheme performed better in terms of type I error rates, and therefore may be more appropriate when considering systems for which traits are not clustered by abundance

Evidence of deterministic assembly according to flowering time in an old-field plant community

Summary 1. Theory has produced contrasting predictions related to flowering time overlap among coexisting plant species largely because of the diversity of potential influences on flowering time. In this study, we use a trait-based null modelling approach to test for evidence of deterministic assembly of species according to flowering time in an old-field plant community. 2. Plant species coexisting in one-metre-square plots overlapped in flowering time significantly more than expected. This flowering synchrony was more pronounced when analyses focused on bee-pollinated species. Flowering synchrony was also observed for wind-pollinated species, although for only one of our two null model tests, highlighting the sensitivity of some results to different randomization methods. In general, these patterns suggest that relationships between pollinators and plants can influence community assembly processes. 3. Because our study community is composed of approximately 43% native plant species and 57% exotic species, and because the arrival of new species may complicate plant-pollinator interactions, we tested whether flowering time overlap was altered by introduced species. Flowering synchrony was greater in plots with a higher proportion of introduced species. This pattern held for both null model tests, but was slightly stronger when analyses focused on beepollinated species. These results indicate that introduced species alter community flowering distributions and in so doing will inevitably affect pollinator-plant interactions. 4. Finally, we tested whether our results were influenced by variation among study plots in above-ground biomass production, which some theory predicts will be related to the importance of competition. Our results were not influenced by this variation, suggesting that resource variation among our plots did not contribute to observed patterns. 5. Synthesis: Our results provide support for predictions that coexisting species should display flowering synchrony, and provide no support for species coexistence via temporal niche partitioning at this scale in this study community. Our results also indicate that introduced species significantly alter the community assembly process such that flowering synchrony is more pronounced in plots with a greater proportion of introduced plant species

Appendix A. Movies of the lattice model depicting six-species competition, varying the localness of competition ("local" vs. "global") and the level of intransitivity ("hierarchical" vs. "intransitive").

Movies of the lattice model depicting six-species competition, varying the localness of competition ("local" vs. "global") and the level of intransitivity ("hierarchical" vs. "intransitive")

Effects of ‘Target’ Plant Species Body Size on Neighbourhood Species Richness and Composition in Old-Field Vegetation

<div><p>Competition is generally regarded as an important force in organizing the structure of vegetation, and evidence from several experimental studies of species mixtures suggests that larger mature plant size elicits a competitive advantage. However, these findings are at odds with the fact that large and small plant species generally coexist, and relatively smaller species are more common in virtually all plant communities. Here, we use replicates of ten relatively large old-field plant species to explore the competitive impact of target individual size on their surrounding neighbourhoods compared to nearby neighbourhoods of the same size that are not centred by a large target individual. While target individuals of the largest of our test species, <i>Centaurea jacea L.</i>, had a strong impact on neighbouring species, in general, target species size was a weak predictor of the number of other resident species growing within its immediate neighbourhood, as well as the number of resident species that were reproductive. Thus, the presence of a large competitor did not restrict the ability of neighbouring species to reproduce. Lastly, target species size did not have any impact on the species size structure of neighbouring species; i.e. they did not restrict smaller, supposedly poorer competitors, from growing and reproducing close by. Taken together, these results provide no support for a size-advantage in competition restricting local species richness or the ability of small species to coexist and successfully reproduce in the immediate neighbourhood of a large species.</p></div