In my previous post I simulated binary morphological trait data to evaluate the prevalence of cryptic diversity for morphologically complex and simple organisms. Here I aim to do the same thing for measurable (continuous) traits, which are often more abundant in algae  (i.e., there are more measurable traits than discrete traits).

In addition, I want to look in more detail at how directional selection may influence the diagnosability of species. This is relevant because it is well known that habitat can have a profound effect on algal phenotypes. Finally, I will investigate how habitat-induced phenotypic plasticity affects species diagnosability. As before, I will tackle this problem with simulations of morphological trait evolution (see last week’s post).

Simulation 1: Effect of number of traits on species diagnosability

With the first set of simulations, I want to check if last week’s conclusion that more complex lineages have a lower prevalence of cryptic species is also valid for measurable (continuous) traits. To do this, I simulated the evolution of continuous morphological traits evolve along a species tree. The simulation protocol is as follows:

  1. Simulate a Yule species tree (pbtree from phytools package) and rescale to have root-to-tip length of 1.
  2. Simulate evolution of the desired number of traits along the tree. I simulated under a simple diffusion process (Brownian motion model, σ2 = 1.0) using OUwie.sim from the OUwie package for this. Seems like using a bazooka to kill a mosquito, but the choice for OUwie will become clear below.
  3. The result of the previous step is a set of trait values for each species.
  4. Loop through all species pairs and see how many can be distinguished from one another based on the trait values.

This overall procedure is similar to what I did for discrete traits, but there are a couple of important differences…

First, it’s no longer possible to count the number of distinct morphologies. Traits that vary along a continuous scale will never be exactly the same so the concept of “unique morphology” doesn’t make sense anymore.

Second, I needed to come up with a way to have a realistic amount of intraspecific variation of the continuous traits in the generated datasets. The simulations return only a single trait value for each species. To solve this, I looked at my Halimeda morphometric datasets and noticed that the standard deviation of traits is typically about 15% of the mean value for those traits. So, to get variation of intraspecific trait values, I used a normal distribution with the simulated trait value as the mean and 15% of this value as the standard deviation. Not a particularly elegant way of simulating phenotypic variance in populations, but good enough for the purpose…

Lastly, for step 4 of the procedure, we need to calculate the percentage of species that can be distinguished from one another. This is easy for discrete traits (the character combinations of the two species are either identical or different), but quite difficult for continuous traits. How different do two species need to be to call them morphologically distinguishable? I decided to sample 20 values from the distribution of each trait (i.e., the normal distribution explained in the previous paragraph). This is an attractive solution because it is equivalent to constructing a morphometric dataset by taking measurements of all traits on 20 randomly selected samples from each species. Then, I compared the two species trait by trait. If one (or more) of the traits had non-overlapping ranges, the species were considered as distinguishable. In fact, I used the range between the 2.5 and 97.5 percentile of the sampled trait values to allow for a tiny bit of overlap. If there was overlap between the ranges of all traits, the species were considered indistinguishable.

Now let’s get back to the simulations. I started by running a simulation for 10 traits and 20 traits to see if simple organisms are harder to distinguish from each other than complex organisms. The number of taxa in the simulated trees was varied between 10 and 100 and the outcome was summarized into a boxplot. Remember that we previously saw that the number of species does not affect the percentage of distinguishable species, so a boxplot suffices to summarize the results. Here are the results:


As expected, the percentage distinguishable species is higher for complex organisms (72.5 % for organisms with 20 characters) than for simpler organisms (54.2% for organisms with 10 characters). This is congruent with what we found for discrete characters.

Simulation 2: Effect of habitat-induced selection on the phenotype

The second thing I wanted to look at is how selection on morphological traits would influence how easy it is to do distinguish species based on morphological traits. In this second set of simulations, I followed this procedure:

  1. Simulate a Yule species tree (pbtree from phytools package) and rescale to have root-to-tip length of 1.
  2. Simulate in which of five possible habitats the species reside. This is done by “simulation mapping” of a discrete trait with 5 states (representing 5 habitats) using the sim.history function in phytools. The rate of the Markov process controlling habitat evolution was set at 0.3 and it was enforced that all habitats are occupied at the end of the simulation.
  3. Simulate evolution of the desired number of traits along the tree.
    1. Half of the traits were simulated as before (no selection, simple Brownian motion model, σ2 = 1.0).
    2. The other half of the traits were simulated under directional selection, with an Ornstein-Uhlenbeck model that evolves towards different optimal trait values depending on which habitat the lineage in question occupies. Parameter values were α = 0.5, σ2 = 1.0 and θ = [1, 3, 5, 7, 9]. In other words, if a lineage is in habitat #1, the trait will be pulled towards the optimal value of θ1 = 1 with a strength of α = 0.5. For habitat #4, this would become a pull towards θ4 = 7 of the same strength α. The state at the root of the tree (θ0) was set at 5 (i.e., the median of the θ vector).
    3. OUwie.sim from the OUwie package was used to carry out the simulations.
  4. As before, the result of the previous step is a set of trait values for each species.
  5. Loop through all species pairs and see how many can be distinguished from one another based on the trait values, again using the procedures described above.

Here’s what came out of this simulation:


Pretty cool. There’s an increase of how many species can be distinguished from each other in both cases. While the increase from 54.2 to 59.7 for the 10-character situation is obviously not significant, the increase from 72.5 to 85.8 for the more complex organisms certainly is. I had not expected this result. I had expected a decrease. After all, habitat selection drives morphological traits to certain “optimum values”, and such traits would thus not contribute to distinguishing between species that live in the same habitat.

The reasoning above is true, but incomplete. Only 50% of the characters are driven towards optimum values while the other 50% evolve free from selective forces. Selection subdivides the morphologies into five habitat-specific categories, thereby subdividing the species distinguishability problem into five smaller sub-problems (one for each habitat). These smaller subproblems are easier to solve with the remaining characters that are not under selection, leading to an overall increase of species distinguishability compared to the simulation without selection.

Simulation 3: Effect of phenotypic plasticity in response to habitat

Clearly, selection is only part of the story. So far, I have assumed that every species lives in a single habitat. In most organisms, and this is certainly true for algae, one also has species that live in multiple environments and feature adaptive morphological plasticity in response to those environments.

The effect of plasticity in response to habitat is harder to simulate using the type of approach I’ve chosen, but here’s the simulation design I came up with:

  1. Simulate a Yule species tree (pbtree from phytools package) and rescale to have root-to-tip length of 1.
  2. Simulate which of five habitats the species live in as in the previous simulation.
  3. Simulate a binary trait to create lineages with and without phenotypic plasticity.
    1. Perform “simulation mapping” of a binary trait along the tree, where one state denotes plastic and the other non-plastic. This was done with sim.history (phytools).
    2. For simplicity and to avoid difficulties associated with plastic species returning to non-plastic, I forced the root state to be non-plastic and only allowed changes from non-plastic to plastic. The latter was achieved by setting the plastic to non-plastic rate to 10–10. The non-plastic to plastic rate was 1.0.
    3. I also forced the fraction of plastic and non-plastic species to be similar (at least 1/3 plastic and at least 1/3 non-plastic) by repeating the simulation mapping until this condition was met.
  4. Simulate evolution of the desired number of traits along the tree.
    1. Half of the traits were simulated without selection (Brownian motion model, σ2 = 1.0).
    2. The other half of the traits were simulated under directional selection with an Ornstein-Uhlenbeck model as described above (simulation 2).
    3. The difference with the simulation above is that lineages that show phenotypic plasticity were assumed to occupy all five habitats. For these lineages, five separate evolutionary tracks were simulated, i.e. one towards the optimum of each habitat.
    4. OUwie.sim from the OUwie package was used to carry out the simulations.
  5. The result of the previous step is a set of trait values for each species.
  6. Loop through all species pairs and see how many can be distinguished from one another based on the trait values, again using the procedures described above.

What’s different from before is that instead of having one mean trait value per species, we now end up with five mean trait values for plastic species (because they were simulated along 5 evolutionary tracks towards different optima). So I sampled 4 values from each of the corresponding five distributions (normal, mean = simulation outcome, standard deviation = 15% of mean). This resulted in 20 trait measurements for comparison to other species in step 6.

Here are the results:


Neat. The species distinguishability clearly drops from the condition with selection and without plasticity (59.7 to 48.6% for the simpler organisms and 85.5 to 69.7% for the more complex organisms). In other words, plasticity has a strongly negative effect on the potential to recognize species based on their morphology. Any advantages brought about by habitat selection (i.e. subdivision of the species distinguishability problem into sub-problems) are completely wiped out by the presence of species that have distinctive morphologies in the different habitats they inhabit.

Wrapping up

That was an interesting set of experiments. Let me just recapitulate the most important results:

  1. Species from character-poor lineages are more difficult to distinguish from one another than species from character-rich lineages.
  2. Selection towards habitat-specific phenotypic optima increases rather than decreases our ability to distinguish between species.
  3. Habitat-determined phenotypic plasticity within species greatly reduces the likelihood that one can distinguish between species based on morphology, even in complex organisms.

Obviously, these are just a handful of simulations, and I don’t expect these results to be valid across a wider range of parameter settings. For example, I would expect that point 2 may not hold if a greater proportion of characters are under selection. I would also anticipate that the relative importance of the drift (σ2) and directional (α) components of the Ornstein-Uhlenbeck model may change things. Perhaps I will explore this further for another post. Or you could do it yourself.

You can download the code for these simulations from here.

These results are also presented in a paper that is about to appear in Journal of Phycology. [UPDATE: This paper is now out here. A PDF is available here]


I’ve just posted a presentation I gave at the Evolutionary Potential in Marine Populations at the AWI station in Sylt to SlideShare. The notes that go with the slides follow below.


Slide 1

  • different talk than most in this workshop
  • deeper back in time, coarser picture
  • many species and overall patterns

Slide 2

  • these folks did the hard work

Slide 3

  • title says adaptation to environmental change => focus is on temperature
  • this is how sea surface temperature evolved during the Cenozoic

Slide 4

  • instead of using fossils, our goal was to see if similar conclusions could be achieved using phylogenies
  • starting from phylogeny and values for sea surface temperature affinities at tips

Slide 5

  • inference about past using models of evolutionary change
  • this way we can study how evolution of thermal affinities relate to figure below
  • since the phylogeny includes speciation events (bifurcations) we can relate niche evolution to diversification

Slide 6

  • main goal is exploration of techniques
  • these are the specific questions we set out to answer

Slide 7

  • our two model systems

Slide 8

  • first question

Slide 9

  • evolutionary change in continuous character usually modeled using simple diffusion model
  • graph => several simulations under same rate
  • parameter => rate of change => sigma^2

Slide 10

  • bigger sigma^2
  • optimize the model => rate of change is quantified (estimated)

Slide 11

  • to answer question whether niches evolve faster when climate is changing
  • we subdivided the tree into upward, downward and stable trends in SST
  • optimize diffusion model with 3 different rates
  • how does sigma^2 compare between conditions

Slide 12

  • big difference between sigma^2 of stable vs the other two
  • more evolution in warming and cooling periods => looks promising
  • model is a substantially better fit than the null model with only one identical rate for the regimes
  • how accurate are these estimates => don’t know => simulations being done to find out

Slide 13

  • Codium is very different story
  • likelihood surface as flat as a pancake
  • not enough information to solve the parameter optimization problem

Slide 14

  • next question => adaptation

Slide 15

  • model derived from diffusion model
  • selection in addition to diffusion
  • rate of diffusion sigma^2
  • selective force (measured by alpha) towards an optimum value (in our case temperature optimum)

Slide 16

  • we’re going to try and find out whether optimum theta differs between warming, stable and cooling
  • sigma squared and alpha are kept constant at their ML estimates

Slide 17

  • model with selection does a better job at explaining evolution of SST preferences in both cases
  • Dictyota => very strange result => higher optimum for cooling periods than for warming periods
  • potential reasons: (1) flat likelihood surface with slightly better fit for this, (2) shaky molecular clock
  • Codium did optimize nicely this time
  • somewhat more reasonable order of values although 120º for stable condition is problematic

Slide 18

  • does the profile predict the adaptation optimum at a fine scale?
  • does this predict the pattern of SST evolution better than models in which there is no such association?

Slide 19

  • new procedure that permits testing these sorts of questions
  • skip the details (1) it is based on the same type of model as before, (2) not all parameters were automatically optimized, (3) SST optimum was varied through time following profile
  • I’ve been having some unanticipated problems with the matrix calculations involved in the optimization => work in progress

Slide 20

  • last question => are speciation-extinction dynamics influenced by niche evolution

Slide 21

  • work stems from my interest in diversity patterns
  • typical diversity patterns: well-characterized LDG
  • many possible explanations => focus here is on species turnover and how rates of diversification relate to the niche

Slide 22

  • seaweeds don’t follow general rules => bimodal diversity pattern
  • do same evolutionary processes hold or is diversification faster in temperate habitats?

Slide 23

  • Codium is suitable case study with similar diversity map

Slide 24

  • evolution of SST affinities traced along phylogeny
  • clade 3: almost half of all species in young clade, only 25 Ma
  • seems to be associated with move from temperate into tropics
  • logical question: is diversification faster in tropics

Slide 25

  • model of diversification dynamics in which diversification is function of SST

Slide 26

  • optimum value of beta => positive association between SST and diversification
  • higher rates in tropics
  • so process seems similar to other organisms and reasons for bimodal diversity pattern has to be sought elsewhere

Slide 27

  • that’s what we found for Codium

Slide 28

  • no such thing for Dictyota => constant diversification explains it better

Slide 29

  • previous test only checked for very simple relationship between SST and diversification
  • many other types of relationships you could imagine
  • for example one could expect that clades whose niches are more evolvable manage to diversify more rapidly
  • we do seem to find that in Dictyota
  • split phylogeny up in major clades
  • positive relationship between rate of SST evolution and diversification

Slide 30

  • slope very deviant from that simulated under null model

Slide 31

  • lineages with many allopatric sister species along latitudinal thermal gradient diversify more rapidly
  • we seem to have a situation where clades that some clades manage to speciate more often along the latitudinal thermal gradient than others
  • clades that do, diversify more rapidly, probably because their presence in both temperate and more tropical habitats permits further radiation in those habitats

Slide 32

  • there are definitely caveats to the approach proposed here

Slide 33

  • overview of some caveats

Slide 34

  • for me, three conclusions emerge from these experiments
  • results are very taxon specific => very little generality in what we find
  • lots of uncertainties and sometimes simply not enough data to even get the models to optimize => these techniques can be a piece of the puzzle but with them alone we’re never going to get a fly-on-the-wall perspective of what happened during evolutionary history
  • it’s going to take a lot of intimate face-to-face time with my computer to get a better understanding of how far we can take these methods