Ecological Archives E095-234-A1

Brittany J. Teller, Colin Campbell, Katriona Shea. 2014. Dispersal under duress: Can stress enhance the performance of a passively dispersed species?. Ecology 95:2694–2698. http://dx.doi.org/10.1890/14-0474.1

Appendix A. Detailed methods, statistical analysis, figures, and references.

Methods: To experimentally test our hypothesis that biological traits are correlated with combinations of traits that improve dispersal distance in the mechanistic WALD model, we imposed drought conditions on Carduus nutans (Asteraceae) individuals that had been planted in pots in a high tunnel at The Pennsylvania State University's agricultural research farm near State College, Pennsylvania. Seed source was grouped by maternal line from each of three different field populations occurring at least 25 kilometers apart and maternal information was masked from practitioners using random ID assignment. Seedlings were started in the greenhouse, and transplanted to a common garden to overwinter in 2009. Pre-reproductive individuals, 36 in each treatment, were then transplanted into individual pots and divided evenly into 9 blocks just before plant reproduction commenced (i.e., plants bolted) in the spring of 2010. After a week-long acclimation period, drought was imposed on all randomly assigned treatment plants on the same day in May 2010, and relieved after 3, 6, 12, and 18 days with no watering. The control and post-drought plants were watered daily until they senesced. At least one, and up to two, primary capitula were taken from each experimental plant prior to seed release. Final capitulum height was recorded and mature capitula were stored before dissection. Terminal velocity was averaged over ten healthy seeds from each capitulum; the terminal velocity of each seed was determined by measuring its average falling time over multiple replicated drops through a chamber of still air of known length (seeds reach their terminal falling velocity almost instantly (Skarpaas and Shea 2007).

Statistical Analyses: Tests for statistical significance were conducted on raw data using linear mixed effects models in R (R Core Development Team 2014). Null hypothesis testing was the primary method of model selection because our a priori hypotheses and experimental design were clear (Bolker et al. 2009); however, where appropriate, the most parsimonious statistical models were selected based on lowest AIC criteria (Burnham and Anderson 2002). The best-fit statistical models all accounted for blocks and maternal lines as random effects, and treatment as a fixed effect. Models also accounted for imbalance caused by uneven capitulum replication among individuals, and for cases when data from more than one capitulum was used per plant. All results for 3, 6, and 12 days of drought were not statistically different from the control in any recorded measure; gypsum soil moisture availability readers show little water stress in these treatments. Thus, while these treatment groups were not excluded from the analysis, only the control and extreme drought groupings are discussed.

Figures 1, Appendix Fig. 2A–B, and Appendix Fig. 4A–B were created using generalized linear models and back-transformed 95% confidence intervals wherein points represent averaged capitulum values for individuals. Splines (Figure 1, and 2A–B) were generated by first grouping empirical data by similar terminal velocities: data were subdivided into 20 equal subintervals, from minimum to maximum observed values, and bins with <2 data points were then systematically combined with adjacent bins. The height and terminal velocity values for the data in each final (i.e., potentially aggregate) bin was averaged to produce a knot point for a cubic polynomial spline. Each knot point was weighted according to the quantity of data in the corresponding bin. This methodology produced high-fidelity splines that (a) are sensitive to the non-uniform distribution of data by preferentially weighting density-rich portions of the plane, and (b) avoid over-fitting to extreme data.

Median and maximum dispersal distances from the WALD model were calculated from 1,000 simulations for each combination of biological parameters present when all other parameters were held constant (to integrate over a season of wind speeds, Skarpaas and Shea 2007). Parameter estimates for abiotic factors such as wind speed and turbulence, and surrounding vegetation height were used with permission from Jongejans et al. 2008a, for the Pennsylvania, USA population.

 

FigA1

Fig. A1. Bulk treatment differences analyzed with linear mixed effect models shown with averages and 95% confidence intervals (±1.96*SE). (A) Seed release height (i.e., capitulum height) was significantly lower in the drought treatment (P < 0.05), but (B) terminal velocity did not differ significantly between treatments on average (P>0.05). Plants from the drought treatment did not differ in (C) average number of seeds per capitulum, but did exhibit (D) statistically significantly lighter seeds on average (P>0.05). (E) Treatments resulted in significantly different seed plume loading (P < 0.05).


 

FigA2

Fig. A2. (A) Number of healthy seeds per capitulum covaried positively (P < 0.05) with plant height but not differently between treatments. (B) Seed weight significantly covaries with plant height in the drought treatment (P < 0.05 in a one-tailed test). Unfilled portions of the bounding curves represent extrapolations and do not contain real data. The legend follows Fig. 1.


 

FigA3

Fig. A3. (A) Survival analysis shows that seeds collected from drought stressed plants (red open circles) germinated significantly later (P < 0.05), and less frequently (P < 0.05) than well-watered plants (blue closed circles), however (B) linear mixed effects models, which controlled for unbalanced design as a result of uneven survival, showed there were no significant effects of maternal-generation treatments on offspring height (P > 0.05).


 

FigA4

Fig. A4. WALD-predicted dispersal distance regressed on trait values with 95% CI. (A) Differences in terminal velocity between treatments (phenotypic plasticity in seed traits) contribute to differences in dispersal outcomes, but (B) height serves as a strong determinant of predicted dispersal distance for this species. Symbols and lines are as in Fig 1.


 

Literature cited

Bolker, B. M., et al. 2009. Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology and Evolution 24:127–135.

Burnham, K. P., and D. R. Anderson. 2002. Model Selection and Multi-model Inference: A Practical Information-theoretic Approach. Springer, New York, New York, USA.

R Development Core Team. 2014. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing.


[Back to E095-234]