Local mating and heritability

Focus focus focus.  There have been lots of articles this week about how kin selection explains everything.  It is very tempting to go off on a heated rant about how it is time to move past 1964, and maybe start doing some science around social evolution.  Instead, I will maintain focus and continue to talk about measuring heritability in natural populations.

One of the sad things about being a theoretically oriented population geneticist is that when you do work with organisms they are inevitably boring weedy plants.  This is a double whammy bad because first, nobody cares unless your study is somehow revolutionary, but also since weeds are, well, weeds, they may not always be the best choice of organisms.  That was the case in a paper I wrote with Steve Tonsor (Tonsor and Goodnight 1997. Evolution 51, 1773).  In this study we examined the effects of mating structure; however, since it was a weed there was no population structure, and thus mating structure had no effect.  Still we can use it as a lesson in how heritability studies might be profitably done in a more structured system.

This study was done using Plantago lanceolata, which we chose because it is so exotic and has such a lovely little flower – Ok, it’s an ugly weed that was chosen because it was easy to work with.


Plantago lanceolata in its native habitat.  (from http://luirig.altervista.org/flora/taxa/index2.php?scientific-name=plantago+lanceolata)

 Actually, the real reason we chose it is that Steve Tonsor had done extensive work on gene flow in this plant, and we knew the pollen flow profile.

Pollen flow profile

(Tonsor and Goodnight 1997. Evolution 51, 1773)

 There are a number of gory details on these designs that you encounter when dealing with real data.  The main one was that we didn’t have enough plants or facilities to do a full half sib nested design.  Instead we ended up using a “pseudonested” breeding design.  I will ignore this detail but only bring it up to emphasize that reality often gets in the way of theory in the experiments.

In any case, we set up two parallel breeding designs.  The first was a standard half-sib design in which we randomly selected 100 pollen parents and mated each to 10 seed parents, with each producing three offspring.  Do the math, that is 100 X 10 X 3 = 3300 plants.  For this design the seed parents were randomly assigned to the pollen parents without regard to where they were physically located in the field.  The second design was identical, except that the seed parents were chosen based on their physical location in the field and, based on the pollen flow distance, the probability that they would have mated with the pollen parent in nature.  Now do the math:  that is now 6600 plants, or 2200 parents.  That is why we ran out of plants and needed to use a bit of statistical slight of hand.

The point is that these two breeding designs were identical, except in the choice of the seed parents.  In one they were chosen randomly using the standard methods such as you might find discussed in Falconer and MacKay  or Becker (If anybody wants to do a service to mankind they will find a way to get this on line because it is WAY out of print).  The second design mimics reality.  This is seen in the distribution of intermate distances.

seed parent distribtion

(Tonsor and Goodnight 1997. Evolution 51, 1773)

In this particular study we thought that population structure is what should be preserved, so we did that by choosing seed parents based on the pollen flow pattern.  The choice of seed parents was still random; however it was not chosen from a uniform random distribution, it was chosen from a distribution of the matings that might actually occur.

In any case these plants were planted out in a prepared field in random order and allowed to grow for one growing season.  At the end of the season they were measured for a number of traits, and the heritability measures for the two mating designs were compared.

Plantago Results

Results of the two breeding design.  “random” is the standard design, “localized” is a design where seed parents were chosen based on the pollen flow distribution.  (Tonsor and Goodnight 1997. Evolution 51, 1773)

The last column is the important one.  These are the estimated heritabilities for the two designs.  As I say, rather sadly, there are no significant differences between the two designs.  Grasping at straws, however, it is interesting that the heritabilities tend to be slightly higher for the localized mating design.

Although failing to get a discernible effect of breeding design was disappointing, but in retrospect not surprising.  I had postulated an increase in heritability for the localized mating design because the localized mating design would have preserved local gene associations.  In other words, the random design would have measured the additive genetic variance as defined by Fisher, whereas the localized mating design would have measured the effective additive genetic variance, that is the variance that was actually available to contribute to a response to selection in the population structure.

The fact that these two measures were not significant is not surprising because Plantago is a weed, and none of these fields are particularly old.  Thus, the plants we sampled were almost certainly relatively recent invaders.  As such it was probably too much to expect that they actually would have set up a significant population structure in that short time period.  We know that population structure is potentially important, thus I am tempted to conclude that it may not be important for outbreeding weedy species, but nevertheless may be important for species in more stable environments that have had time for population structure to develop.

My final thought is that this is actually something of a win-win situation.   On the one hand it does provide a nice experimental design for comparing the effects of localized mating on variance components.  On the other the lack of significance suggests that in many situations it may not be terribly necessary to use a more complicated localized mating design type of a study.

2 Responses to “Local mating and heritability”

  1. Andy;

    I helped Steve brainstorm about how to test pollen flow. He decided on building a low speed wind tunnel that pulled air (fan at the back pulling air out rather than at the front pushing air in). The reason for this is that it gave laminar flow. He then placed vaseline covered slides along the length of the wind tunnel. A potted flowering plant was placed a the front of the wind tunnel. From this it was the simple but time consuming task of counting pollen grains on slides.

    As I remember he decided it wasn’t the number of pollen grains, but the number of grain clumps that was important. This significantly changed the distribution. As I remember it the actual pollen flow was a lot less than you might expect.

  2. Andy Cairns PhD says:


    I am a semi retired Weed Science Professor. I live in Cape Town, South Africa. Some time ago I identified several glyphosate-resistant populations of Plantago lanceolata in the Western Cape(weedscience.org. As far as I know this is the only place in the world where this weed has developed resistance to any herbicide. I am interested in how far pollen can be carried as this factor will impact on the spread of the glyphosate-resistant biotypes. In some areas
    it appears to spread to spread very quickly and in others more slowly. Any ideas on this would be welcome.


    Andy Cairns

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