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1.  The Influence of Matrix Size on Statistical Properties of Co-Occurrence and Limiting Similarity Null Models 
PLoS ONE  2016;11(3):e0151146.
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 < 0.05) for both the co-occurrence and trait-based limiting similarity null models when exclusive p-values were used. The commonly used inclusive p-value (≤ or ≥, as opposed to exclusive p-values; < or >) 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.
doi:10.1371/journal.pone.0151146
PMCID: PMC4778770  PMID: 26942941
2.  Patterns of Cross-Continental Variation in Tree Seed Mass in the Canadian Boreal Forest 
PLoS ONE  2013;8(4):e61060.
Seed mass is an adaptive trait affecting species distribution, population dynamics and community structure. In widely distributed species, variation in seed mass may reflect both genetic adaptation to local environments and adaptive phenotypic plasticity. Acknowledging the difficulty in separating these two aspects, we examined the causal relationships determining seed mass variation to better understand adaptability and/or plasticity of selected tree species to spatial/climatic variation. A total of 504, 481 and 454 seed collections of black spruce (Picea mariana (Mill.) B.S.P.), white spruce (Picea glauca (Moench) Voss) and jack pine (Pinus banksiana Lamb) across the Canadian Boreal Forest, respectively, were selected. Correlation analyses were used to determine how seed mass vary with latitude, longitude, and altitude. Structural Equation Modeling was used to examine how geographic and climatic variables influence seed mass. Climatic factors explained a large portion of the variation in seed mass (34, 14 and 29%, for black spruce, white spruce and jack pine, respectively), indicating species-specific adaptation to long term climate conditions. Higher annual mean temperature and winter precipitation caused greater seed mass in black spruce, but annual precipitation was the controlling factor for white spruce. The combination of factors such as growing season temperature and evapotranspiration, temperature seasonality and annual precipitation together determined seed mass of jack pine. Overall, sites with higher winter temperatures were correlated with larger seeds. Thus, long-term climatic conditions, at least in part, determined spatial variation in seed mass. Black spruce and Jack pine, species with relatively more specific habitat requirements and less plasticity, had more variation in seed mass explained by climate than did the more plastic species white spruce. As traits such as seed mass are related to seedling growth and survival, they potentially influence forest species composition in a changing climate and should be included in future modeling of vegetation shifts.
doi:10.1371/journal.pone.0061060
PMCID: PMC3623855  PMID: 23593392
3.  Cotyledon damage affects seed number through final plant size in the annual grassland species Medicago lupulina 
Annals of Botany  2010;107(3):437-442.
Background and Aims
The effects of cotyledon damage on seedling growth and survival are relatively well established, but little is known about the effects on aspects of plant fitness such as seed number and size. Here the direct and indirect mechanisms linking cotyledon damage and plant fitness in the annual species Medicago lupulina are examined.
Methods
Growth and reproductive traits, including mature plant size, time to first flowering, flower number, seed number and individual seed mass were monitored in M. lupulina plants when zero, one or two cotyledons were removed at 7 d old. Structural equation modelling (SEM) was used to examine the mechanisms linking cotyledon damage to seed number and seed mass.
Key Results
Cotyledon damage reduced seed number but not individual seed mass. The primary mechanism was a reduction in plant biomass with cotyledon damage that in turn reduced seed number primarily through a reduction in flower numbers. Although cotyledon damage delayed flower initiation, it had little effect on seed number. Individual seed mass was not affected by cotyledon removal, but there was a trade-off between seed number and seed mass.
Conclusions
It is shown how a network of indirect mechanisms link damage to cotyledons and fitness in M. lupulina. Cotyledon damage had strong direct effects on both plant size and flowering phenology, but an analysis of the causal relationships among plant traits and fitness components showed that a reduction in plant size associated with cotyledon damage was an important mechanism influencing fitness.
doi:10.1093/aob/mcq259
PMCID: PMC3043934  PMID: 21196450
Cotyledon damage; herbivory; fitness; Medicago lupulina L.; alpine grassland; structural equation modelling (SEM); plant growth; flowering phenology

Results 1-3 (3)