Mating by outcrossing plants depends on the frequency and quality of interaction between pollen vectors and individual flowers. However, the historical focus of pollination biology on individual flowers (floricentrism) cannot produce a complete understanding of the role of pollination in plant mating, because mating is an aggregate process, which depends on the reproductive outcomes of all of a plant’s flowers. Simultaneous display of multiple flowers in an inflorescence increases a plant’s attractiveness to pollinators, which should generally enhance mating opportunities. However, whenever pollinators visit multiple flowers on an inflorescence, self-pollination among flowers can reduce the pollen available for export to other plants (pollen discounting) and increase the incidence of inbreeding depression for embryos and offspring. Therefore, the size of floral displays that maximizes mating frequency and quality generally balances the benefits of attractiveness against the costs of self-pollination. This balance can shift considerably if different flowers serve female and male functions at one time (sexual segregation) and flowers are arranged in inflorescences so that pollinators visit female flowers before male flowers. However, the effectiveness of sexual segregation depends on the extent to which a particular inflorescence architecture induces consistent movement patterns by pollinators. In general, the consistency of pollinator movement patterns varies with inflorescence architecture and differs between pollinator types. Such variation creates many options for the evolution of the diverse inflorescence characteristics within angiosperms, which can be appreciated only by moving beyond a floricentric perspective of the role of pollination in plant mating.
Harder L.D., Jordan C.Y., Gross W.E. & Routley M.B., 2004, Beyond floricentrism: the pollination function of inflorescences. Plant Species Biol. 19: 137–148 [link][Floricentrism.pdf]
Clonality is very common in flowering plants, but its consequences for sexual reproduction have rarely been explored. While clonal growth can increase the number of flowers a plant produces it may also limit reproductive success through pollen discounting (reduction in pollen exported to adjacent clones) and pollen limitation (failure of outside pollen to reach the centre of a clone). Using clones of domestic apple (Malus x domestica) that ranged from 1 to 5 orchard rows wide, we found that the patterns of siring success were consistent with the presence of pollen discounting, but we failed to detect evidence for pollen limitation. The results suggest that paternal function may be more sensitive to the effects of clonality than female function.
Routley M.B., Kron P. & Husband B.C., 2004, The consequences of clone size for paternal and maternal success in domestic apple (Malus x domestica). Am. J. Bot. 91: 1326–1332 [link][PDF] AppleCloneSize.pdf
Dichogamy, the temporal separation of gender within a flower, is widespread throughout the angiosperms, occurring in over 250 families. There are two forms of dichogamy: protandry, in which male function precedes female function, and protogyny, the converse. Dichogamy has traditionally been interpreted as a mechanism to avoid inbreeding. However, recent evidence indicates that this inbreeding-avoidance hypothesis cannot completely explain the evolution of dichogamy. An alternate hypothesis is that dichogamy acts to reduce interference between gender functions. Interference can occur within a flower or between flowers on an inflorescence and result in substantial reductions in male and female reproductive success. To date there are very few tests of this interference-avoidance hypothesis or, in fact, investigations of the evolution of dichogamy in general. My Ph.D. thesis was a comprehensive evaluation of the evolutionary significance of dichogamy, including functional, genetic, comparative, and theoretical analyses of this important floral character.
This Claytonia species is protandrous. The flower on the left is in male phase with its anthers shedding pollen and the stigma closed and unreceptive. The flower on the right is approximately one day older and is in female phase. The stigma is open and receptive and the anthers have moved away to the side and are empty of pollen.
Functional analyses
As an evaluation of the fitness consequences of protandry, we tested the interference-avoidance hypothesis with enclosed, artificial populations of Chamerion angustifolium (Onagraceae) by experimentally manipulating protandry and inflorescence size and measuring pollinator visitation, seed set, female outcrossing-rate, and outcross siring-success. Protandrous plants had a marginally higher female outcrossing rate than adichogamous plants, but similar seed set and visitation rates. More importantly, protandrous plants (blue points) had, on average, a twofold siring advantage relative to adichogamous plants (red points). However, this siring advantage did not increase linearly with inflorescence size, suggesting that protandry acts to enhance siring success, but not exclusively by reducing between-flower interference.
To better understand the function of protandry, we analyzed single bee visits to pairs of C. angustifolium flowers in the field and the lab. The patterns of pollen removal and deposition revealed two major consequences of simultaneous hermaphroditism. First, the presence of anthers impeded pollinator’s access to the stigma. Second, pollinators spent more time foraging on hermaphroditic flowers, relative to female flowers. Protandry allows pollen to be exported in the absence of this within-flower interference and can enhance both male and female reproductive success through reductions in pollen discounting and facilitated selfing, respectively.
Genetic analysis
The genetic basis of dichogamy may have important implications for its evolution. Consequently, we conducted genetic analyses of protandry in C. angustifolium using a paternal half-sib design and an artificial selection experiment. We found moderate heritability (h^2^=0.27) for the duration of male phase. An analysis of plants from the artificial selection experiment showed no genetic correlation between male-phase duration and aspects of floral size. However, we estimated a positive genetic correlation between male-phase duration and floral display size. In addition, we detected a negative correlation between male- and female-phase durations which creates the opportunity for fitness trade-offs between male and female function.
Phylogenetic analysis
To gain a broader perspective on the evolution of dichogamy, we used a current, well resolved phylogeny of the angiosperms to conduct a comparative analysis of dichogamy and self-incompatibility. Using paired-comparisons and maximum-likelihood correlation analyses, we found that protandry is positively correlated with self-incompatibility and protogyny with self-compatibility. These results support a role for interference avoidance in the evolution of protandry and inbreeding avoidance in the evolution of protogyny, suggesting that the two forms of dichogamy provide different functions. In addition, dichogamy changes character states throughout the phylogeny, allowing rapid responses to changing ecological circumstance.
Theoretical analysis
We developed a conceptual model to synthesize the effects of male-phase duration, inflorescence size, and inbreeding depression on pollen import and export. The relative fitness of protandry is strongly affected by the combination of floral display size and inbreeding depression. Furthermore, the trade-off between male- and female-phase durations produced a fitness landscape much more favourable to the evolution of protandry.
Conclusions
Collectively, this research suggest that protandry enhances male fitness through reductions in both within- and between-flower interference, while protogyny reduces inbreeding. This work has revealed unexpected fitness benefits to protandry and helps to explain the wide taxonomic and ecological distribution of this trait in flowering plants.
Routley M.B. & Husband B.C., 2005, Does sexual segregation reduce within-flower interference? In preparation [draft]
Routley M.B. & Husband B.C., 2005, Responses to selection on male-phase duration in Chamerion angustifolium. J. Evol. Biol. J. Evol. Biol. 18:1050-1059 [link][pdf]
Routley M.B., Bertin R.I. & Husband B.C., 2004, Correlated evolution of dichogamy and self-incompatibility: a phylogenetic perspective. Int. J. Plant Sci 165: 983-993 [link][pdf]
Routley M.B. & Husband B.C., 2003, The effect of protandry on siring success in Chamerion angustifolium (Onagraceae) with different inflorescence sizes. Evolution 57: 240–248 [link][pdf]
The outcrossing rate is a fundamental attribute of plant populations that determines population genetic structure, individual plant fitness, and ultimately speciation rates. The outcrossing rate can be influenced by population size through reductions in both mate availability and pollinator service. We investigated the effect of population size on the outcrossing rate in 10 populations of Aquilegia canadensis in Southern Ontario, Canada.
Across a range of sizes from 32 to 750 reproductive individuals, we found that small populations (n < 35, red line) had a significantly lower outcrossing rate than large populations (n > 90, blue line).
Given the high estimate for inbreeding depression in this species (0.88 ± 0.14), small populations may experience a rapid decline in population-level fitness that can lead to local extirpation. The consequences of human-induced habitat fragmentation suggest that such local extinctions are common due to this demographic effect.
Routley M.B., Mavraganis K. & Eckert C.G., 1999, Effect of population size on the mating system in a self-compatible, autogamous plant, Aquilegia canadensis (Ranunculaceae). Heredity 82: 518–528 [link][PopulationSizeT.pdf]
As I use R for data analysis and simulations, I become more comfortable and proficient with the R/S syntax and style of programming. One important insight is the use of vector assignments in simulations. I have often read that using such assignments is the preferred method, but until recently I had not realised the importance of this statement. To illustrate the use of vector assignments and their advantages, consider two models of the style illustrated below:
Model 1:
value1List <- seq(1:10)
value2Function <- function (value1) {
ifelse(value1 < constant1, constant2, constant1)
}
tableDimension <- length(value1List)
outputTable <- NULL
outputTable <- data.frame(value1=numeric(tableDimension),
value2=numeric(tableDimension))
n <- 1
for (value1 in value1List) {
outputTable[n, ] <- c(value1, value2Function(value1))
n <- n + 1
}
Model 1 is how I originally approached R programming. It begins with declaration of a sequence for value1 and a function declaration to calculate value2 from each value1. I then declare a table to capture the output and fill it with zero values. The main loop of the program consists of replacing the rows of the output table with each value of value1 and the calculated value2. I use the variable n to keep track of the next row in the table. The function rbind() could also be used to generate the table, but it’s use for large datasets is quite inefficient.
Model 2 takes the approach of constructing each column of the output table in sequence. It begins by repeating the values of the value1List and then creates the value2 column through a vector assignment. No control structures or function calls are required in Model 2.
How is this important? Model 1 seems intuitive (at least to me) while the syntax of Model 2 is opaque at first glance. However, consider this figure:
On the x-axis is the number of data points in the output table on a log scale. The y-axis shows how long the model takes to calculate these values. Model 1 is the blue line. Model 2 is the red line. This illustrates two important points:
* Model 1 is always slower than Model 2.
* As the size of the dataset increases, Model 2 remains fast while Model 1 rapidly consumes all of the computer resources.
This is why vector assignments should be used when programming with R. Just to be clear, the models described here are simple abstractions of the types of models used to generate this figure.
A particular challenge with maintaining a weblog is the uploading and resizing of images. The process involves choosing the correct images, creating large & thumbnail sized versions, uploading these images to the webserver, and posting the appropriate code into the weblog post. In the spirit of my last few posts, image2web is an applescript I use to automate this process:
--user-specific variables
property theAlbum : "Marked"
--contains the images to be uploaded
property theBasePath : "the:path:to:the:local:images:" as alias
--the local path to the weblog
property tagBaseUrl : "[www.your.website.org/path/to//...](http://www.your.website.org/path/to//blog/images/)"
--the url to the weblog images
---declare globals
property htmlText : ""
--stores the image tags & is copied to the clipboard
tell application "Finder"
set theList to name of every folder of theBasePath
end tell
--choose which weblog category the images belong to
set theCategoryList to choose from list theList
with prompt "Choose the post's category:"
set theCategory to first item of theCategoryList
tell application "Finder"
set theCategoryFolder to folder theCategory of theBasePath
end tell
--I use a smart album that collects photos with the checkmark tag
tell application "iPhoto"
activate
select album theAlbum --so we can see which images are involved
set theImages to every photo of album theAlbum --collect the images
repeat with thisImage in theImages
set thisImage to get image path of thisImage
my processImage(thisImage, theCategoryFolder)
--resize & generate the thumbnail
set theResult to the result --avoid declaring more globals
set thePhotoName to item 1 of theResult
set theMainImagePath to item 2 of theResult
set theThumbnailImagePath to item 3 of theResult
my uploadImage(theMainImagePath, theThumbnailImagePath) --upload the image
my makeTag(theCategory, thePhotoName) --create the appropriate html
end repeat
set the clipboard to htmlText --pass the html code to the clipboard
end tell
on processImage(thisImage, theCategoryFolder)
set theResult to display dialog "Enter the name for " & thisImage & ":" default answer ""
set thePhotoName to text returned of theResult
tell application "Finder"
set theDestinationPath to POSIX path of (theCategoryFolder as string)
set theMainImagePath to (theDestinationPath & thePhotoName & ".jpg")
set theThumbnailImagePath to (theDestinationPath & thePhotoName & "-thumb.jpg")
do shell script "/usr/local/bin/convert -resize 640x480 +profile \" * \" " & "\""
& thisImage & "\"" & " " & theMainImagePath
---use extra quotes to protect against spaces in path names
do shell script "/usr/local/bin/convert -resize 240x240 +profile \" * \" " & "\""
& thisImage & "\"" & " " & theThumbnailImagePath
end tell
return {thePhotoName, theMainImagePath, theThumbnailImagePath}
end processImage
on uploadImage(theMainImagePath, theThumbnailImagePath)
set theMainImage to POSIX file theMainImagePath
set theThumbnailImage to POSIX file theThumbnailImagePath
tell application "Transmit"
open theMainImage
open theThumbnailImage
end tell
end uploadImage
on makeTag(theCategory, thePhotoName)
set htmlText to htmlText & ""
--show the thumbnail & link to the full-size image
end makeTag
The CBC has begun an experiment with podcasting. I’m impressed with the progressive approach to technology that the CBC has adopted and hope they expand the experiment to more of their programs.
Quirks & Quarks is the CBC’s excellent science program. I usually download the mp3 archives of the show on the weekends and listen while I walk Ceiligh.
Of course, loading up the Quirks & Quarks webpage, finding the archives, downloading the mp3s, and adding them to iTunes takes at least a few minutes. Computers are much better and handling such tedium.
The “Astronomy Picture of the Day” is a source of fantastic images. To take advantage of this resource, I went looking for a way to automatically set the current image as my Desktop background. A quick Google search turned up a perl script at www.haroldbakker.com. Although this was a great start, I wasn’t completely happy with the implementation of this script and decided to write my own.
The apod.pl script is written in perl and both sets the Desktop background and copies a description of the image to the Desktop as an html file. You can add the script to your Script menu and run it as appropriate. Even better, download the runApod.scptapplescript and have iCal set the Desktop at a convenient time. I’ve set up my computer to run the perl script early each morning so that I have a new Desktop background each day. Note that runApod.scpt expects apod.pl to be in “~/Library/Scripts/apod/”.
These data measured the genetic architecture of male-phase duration in Chamerion angustifolium. There are three files in the archive used to estimate genetic variances & covariances with VCE.
Format:
protandryHeritabilityData.dat: Contains the measured data for male- & female-phase duration, flower size, & display size
protandryHeritabilityPedigree.ped: Contains the pedigree information for the selection experiment
protandryHeritabilityVCE: Is the VCE file that configures the analysis
Citation:
Routley, M.B. & B.C. Husband. 2004. Responses to selection on male-phase duration in Chamerion angustifolium. J. Evol. Biol. in press Download paper: protandryHeritability.pdf
A recent column in the Globe & Mail reminded me of our Federal Government’s plan for reducing greenhouse gas emissions: the One Tonne Challenge.
This campaign challenges each Canadian to reduce their contribution to greenhouse gas emissions by one tonne. The first step is to calculate your emissions and then implement recommendations for reductions. According to the online calculator, Kelly & I combined emit 4.23 tonnes annually. Fortunately, this is below the national average of 5.5 tonnes per person and significantly better than Alberta’s average of 8 tonnes per person. Still, we could do better. However, the suggestions provided aren’t much help. They largely concern implementing energy savings to our home — which we rent and have little control over. Here are the suggestions I could implement:
Take a 5-minute shower instead of a bath.
Turn off lights when a room is not in use.
Use a cold water wash and rinse instead of warm or hot water to wash your clothes.
Replace standard light bulbs with compact fluorescent light bulbs where lights are on for three or more hours at a time.
The website has a variety of good suggestions. The trick is convincing Canadian’s to assume some responsibility for climate change. Monetary incentives seem like the best strategy, but those are not currently under consideration.
Yet another useful site from Google: Google Scholar. The site provides an interface for searching the scientific literature with typical Google ease. Some preliminary tests suggest that it is quite effective at finding relevant literature.
I’ve written a script that imports a JSTOR citation page into BibDesk. To use the script, I suggest adding it to your script menu. Then, with the JSTOR citation page as the active web page in Safari, run the script and the citation will be added to the active BibDesk file. I use the first author’s last name and last two digits of the year as a cite key (e.g. Darwin59), you may want to change this to suit your style.
The script is written in perl and bracketed by two Applescript commands: one to extract the html source from the JSTOR page and the other to add the citation to BibDesk. Unfortunately, JSTOR citation pages contain almost no semantic markup, so I am not convinced that the approach is entirely robust. However, so far it has worked well for me and might be useful to you. Any feedback is welcome.
An interesting read from Wired News – The Crusade Against Evolution. In addition, the Panda’s thumb has been following and carefully dissecting the recent controversy over an intelligent design paper being published in a peer-reviewed journal. The evolution-creation debate seems to be resurfacing after a short time off. The debate is important and the intelligent design supporters have to be countered, but their arguments have become hackneyed.
Plants are sessile and, consequently, many species rely on pollinators for mating opportunities. However, pollinators do not necessarily visit every individual in a population with equal frequency. Plant attributes, such as floral display and reward provisioning, can influence the frequency of pollinator visitation. Furthermore, aspects of population density and structure may also influence visitation patterns. One effect of this unequal distribution of pollinator activity is that pollinators create networks of connections between plants in which a few plant receive many visits and many plants receive few visits. Such networks are termed ‘scale-free’ and can be contrasted with random networks. Random networks follow a Poisson distribution of connection frequency and have the familiar bell shape characteristic of many biological patterns. Scale-free networks have power-law distributions with no peak, just a steady decline in the frequency of nodes with increasing number of connections. Technically, in a scale-free network the probability that any node is connected to k other nodes is proportional to 1/k^n^, where n is usually around 2.
Measuring networks
The hallmark of a scale-free network is a hub or node with a high number of connections. A relatively simple test for hubs is to plot a histogram of the number of connections between plants. This is illustrated in the following figures. On the left, many plants have a low frequency of connections, while a few plants have many connections. Those plants with many connections could be hubs. Contrast this with the right. The distribution of connections follows a bell shape with no plants having an excessive number of connections. There are no hub plants in this population.
Importance of scale-free networks
The analysis of scale-free networks has provided insights into fields as diverse as scientific-citation patterns, disease epidemics, world-wide-web structure, and cellular metabolism. Such power suggests that applying network thinking to pollination biology may be useful. These networks are produced through a process of growth and unequal creation of connections. Clearly plant populations experience changes in population size and pollinator behaviour often leads to 'traplining’ or enhanced visitation to particular phenotypes. Consequently, plant populations have some of the prerequisites for scale-free networks. Scale-free networks are very resilient to the random loss of nodes, because the vast majority of network function is provided by the hubs. In a plant population context, if a population can be characterised by a power-law distribution, population growth rates and persistence are likely driven by a small subset of the plants. Such an asymmetry would have important implications for evolutionary ecology and conservation questions.
An important first step is to determine if pollinator-visitation patterns follow a power-law distribution. Hub plants could then be identified and the mechanisms producing the pattern investigated. Are hubs spatially clustered? Do they have larger-than-average floral displays or brighter floral pigments? What are the demographic consequences of removing hubs from a plant population? All we need is data on pollinator visits to plant populations. The data I have access to are inconclusive, mostly because they have insufficient visit frequencies. Any other data sets would be appreciated.
There’s a powerful approach to modelling called dynamic state variable programming, covered in Dynamic State Variable Models In Ecology by Clark & Mangel. I’ll post more about the approach sometime, but for now I wanted to make an example from the book available. The first chapter of the book includes a guide through the creation of a patch foraging model. A fully implemented version is available in True BASIC, but I’ve decided to use R for all of my modelling and analyses. Consequently, I’ve implemented the patch selection model from Clark & Mangel in R. It is available from http://public.me.com/mroutley/patchSelection.txt for anyone interested.
Until recently, I was able to use journal abbreviations in all of my manuscripts. Consequently, my .bib file contains only abbreviations in the journal field. Now I need to produce some bibliographies with full journal names. With a .bib file you can use macros to handle changing abbreviated names to full names. However, BibDesk cannot use macros. Instead I wrote a perl script that searches through a .bib file and creates a new file with journal abbreviations changed to full names.
This script has been quite useful to me, so I decided to make it generally available here as longJournals. Feel free to modify it to suit your database. The important sections are near the top where the input and output files are declared and the substitution rules are listed. There are two types of substitution rules to handle some abbreviation conflicts (for example, Ecol. could be Ecology or Ecological). The first set of rules takes precedence over the second.
Rather than maintain two .bib files, I decided to use the abbreviated file as the main file and then periodically replace the long-journals file. The script could be improved to make it more flexible, but I only maintain one .bib file so it made sense to hardcode the file names and replacement arrays in the script. The copy linked to above has most of the substitution rules removed, since I assume they are not generally useful.
Suggestions are appreciated. Be sure to test out the script with a backup database first. Changes are not undoable.
I have been investigating issues of ovule and seed development recently. One question that has come up is: How much variation is there in seed size? I had analysed some seed set data for some earlier work with some image analysis software. Consequently I have a large data set of seed area and perimeter for Chamerion angustifolium. A rough look at the data is:
The data set is available as seedSizeData.txt.zip. Bewarned, the file contains over 100,000 lines – be sure to use an efficient text editor or stats package. All dimensions are in cm. The seed? column contains a 1 for seeds and 2 for objects smaller than seeds. See this for details.
