Do Plants Optimize Their Floral Displays
A Study Using Patches of Solidago Canadensis
Introduction
There is a literature of moderate size that explores the relationship between plants and their pollinators with respect to the effect of floral display on the number and length of pollinator visits. This is part of a much larger literature on optimization in plant-pollinator interactions, much of which looks at the question from the perspective of the pollinator.
Optimization for the pollinator looks at how it (usually bees of various sorts) can maximize its energy gain per unit effort. There are two parts to the structure of floral displays that directly affect maximization: if plants occur at higher density (and therefore flowers, as well) then the high cost of movement between plants is reduced. Bees should choose patches of higher density if floral displays of individual plants are equal in size, condition, or other factors that may influence the availability of nectar and pollen. Pollinators should also choose plants with larger numbers of flowers. There is evidence to suggest this occurs in nature. The figure below shows data gathered by Paton (1982) for two species of plants, Correa schlectendalii and Eucalyptus cosmophylla, pollinated by the New Holland honeyeater (a bird).
These results demonstrate that honeyeaters visit more often, spend longer, and more of them visit individual plants that have a larger number of flowers.
From the perspective of the pollinator there is also optimization, movement between patches is also apparently a portion of the strategy to maximize energy intake per unit time or effort. Pollinators move from one patch to the one that encloses the largest visual angle, thus either to a smaller patch that is very near or an at least proportionally larger patch that is more distant (Pyke, G. et al. 1977).
For the goldenrod, Solidago canadensis, pollination is not usually due mostly to the activity of bees or bumblebees. Instead, the situation is described as “mess and soil” pollination. Various beetles, flies and other insects that visit the flowers seem to achieve the majority of successful pollinations. Thus, our experiment is mostly measuring optimization by bees, rather than benefit to the plants. We are using this easily accessible system to address a question that would in most plants, be addressing how they can optimize visitation and pollination rates.
Methods
Prior to the laboratory period the site to be used was identified. Within the large patch, approximately 30 x 15m, a random number table was used to locate a system of patches of three sizes: 1m, 1/2m and 1/4m in diameter. Three such sets of patches were marked, with the potential to mark additional patches, if necessary, at the time of the field exercise. The boundaries of these patches were marked with different colours of marking tape tied to plants along the boundaries to designate the sizes. A zone around each of these patches was cut, both to isolate the patches and make them separate areas for bees and to permit observation of bees from outside but adjacent to the patches.
In the field working groups of 3 students should find a patch that is experiencing visits from pollinating bees. One student should act as ‘recording secretary’, noting the total time if visits
for each if 10 bees visiting a patch. Visit patches of each size class, and record at least 10 visits for each size patch. Data should be reported electronically or on paper to permit the group data to be combined.
Analysis
The times reported for bee visits will be (have been) subjected to an ANOVA with time as the dependent variable and patch diameter as the independent variable Sokal and Rohlf 1995). An a posteriori test of ANOVA results will (did) indicate whether all patch sizes differed, or only some subset (e.g. all smaller patches might differ in visit times from the largest diameter).
Bibliography
Paton, D.C. (1982) The influence of honeyeaters on flowering strategies of Australian plants. In J.A. Armstrong, J.M. Powell, and A.J. Richards, eds. Pollination and Evolution. Royal Botanical Gardens, Sydney. Pp.95-108.
Pyke, G.H., Pulliam, H.R. and Charnov, E.L. 1977. Optimal foraging: a selective review of theory and tests. Quart. Rev. Biol. 52:137-154.
Pyke, G.H. (1978) Optimal foraging in bumblebees and coevolution with their plants. Oecologia36:281-293.
Sokal, R.R. and Rohlf, F.J. (1995) Biometry 3rd ed. W.H. Freeman, N.Y., N.Y.
Here are the means and other basic statistics for all the timing data. For statistical analysis, if this were to be intended for publication, we would need to perform some sort of transformation of the times, since the kurtosis for small and medium patches is quite high. That means the distribution of times, assumed to be normal, is not; the distribution is platykurtic (a wider and flatter top than a normal distribution).
The following results are for:
PATCHSIZE = 0.250
TIMEN of cases / 105
Minimum / 1.000
Maximum / 276.00
Mean / 39.838
Std. Error / 5.372
Standard Dev / 55.051
C.V. / 1.382
Skewness(G1) / 3.035
Kurtosis(G2) / 9.644
The following results are for:
PATCHSIZE = 0.500
TIMEN of cases / 97
Minimum / 2.000
Maximum / 474.00
Mean / 55.691
Std. Error / 7.961
Standard Dev / 78.403
C.V. / 1.408
Skewness(G1) / 3.686
Kurtosis(G2) / 16.196
The following results are for:
PATCHSIZE = 1.000
TIMEN of cases / 99
Minimum / 2.000
Maximum / 391.00
Mean / 85.758
Std. Error / 8.438
Standard Dev / 83.953
C.V. / 0.979
Skewness(G1) / 1.482
Kurtosis(G2) / 2.309
Here is the regression analysis for these data, done without the transformation. Note that the regression was done including a constant (a Y intercept) and it isn’t 0. That’s interesting; a different regression would have been obtained had the constant not been included. Also note that there are a number of cases (all the very long times) that are outliers. There are a number of available tools to remove or ‘fix’ outliers. One, called Winsorizing (note the spelling, it has nothing to do with our fair city), moves values down to the next smaller value, then recalculates statistics. Eventually, all outliers can be ‘fixed’. The outcome you see here: the effect of patch size on bee residence time is very highly significant (P < 0.001)
Dep Var: TIME N: 301 Multiple R: 0.254 Squared multiple R: 0.065
Adjusted squared multiple R: 0.061 Standard error of estimate: 73.061
Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT 24.788 8.831 0.000 . 2.807 0.005
PATCHSIZE 61.087 13.448 0.254 1.0 4.543 0.000
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
Regression 110146.061 1 110146.061 20.635 0.000
Residual 1596046.192 299 5337.947
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*** WARNING ***
Case 35 is an outlier (Studentized Residual = 4.318)
Case 67 is an outlier (Studentized Residual = 3.856)
Case 122 is an outlier (Studentized Residual = 3.856)
Case 159 is an outlier (Studentized Residual = 6.075)
Case 226 is an outlier (Studentized Residual = 6.075)
Durbin-Watson D Statistic 1.976
First Order Autocorrelation 0.009
Finally, here is the figure drawn from these data. As you saw in the earlier version using incomplete data, there is no sign of curvilinearity in these data. Look for the smaller tick mark on the right hand axis to see the standard error for 1m patches; the other two are evident.