Ree et al. 2005/Ree and Smith 2008 rate matrices

I was wondering what information would be possible to incorporate in the transition matrix of Ree et al. 2005 constructed by simulation that would not be possible to incorporate in the rate matrix of Ree and Smith 2008. For example, in that paper the absence of a dispersal route between areas at certain times was apparently successfully modelled in the Hawaii example (by setting certain rates equal to 0?). I would think that if you had prior information about the relative probability of dispersal in different directions you could take that into account, for example either by constraining E->W dispersal to be a certain fraction of W <- E or estimating the two rates separately. What kinds of information would require a simulation approach to incorporate?

Ree & Smith 2008

Page 4: What does it mean to "condition on specific character states at internal nodes" and estimate the "ancestral state of any particular node without conditioning on other nodes in the tree"?

Also, thank you to the classmates who have patiently answered many of my questions. Your feedback has taught me a lot!

Ronquist 1997

How is a unit area defined? If vicariance is assumed, why do daughter species occur in the same area in figure 1a?

Alfaro et al. 2009 : Fostering Other Sorts of Diversity

Alfaro et al. point out that the PJ innovations could have been a 'key innovation' that allowed them to successfully colonize new environments or develop more functional/trophic diversity. I find these statements to be intriguing merely for suggesting that different diversity currencies (stealing a term from DJ) could be increased by key innovation, independent from each other. What could this mean for the Simpsonian ecological explanation of key innovations? Why would a key innovation increase speciation rate in some cases and not in others? (Never mind how to explain cases where key innovation affect extinction rates (as in insects...)

Really not quite certain why "establishing 'ecological' footholds" is less testable than allowing for a wider diversity of other trophic characters, as Alfaro et al. argue.

Variable Diversification on a Morphospace

So, let's talk bothersome things.

Everyone knows morphospace, right? Multivariate spaces of morphological traits, both continuous and discrete? Liow, a former CEB student, showed that extinction rate varies significantly across a morphospace in a series of papers. Specifically, in some clades, she found that morphologically extreme taxa showed markedly different extinction rates... and the pattern differed between clades. Taxa on the periphery are different from taxa in the middle. Ricklefs has also found a pattern in bird clades (Ricklefs, 2006).

So, what's so cool about that? This evidence shows that diversification systematically varies in a morphospace. Thus, we might expect that different areas of morphospaces may routinely have differing speciation and extinction rates. However, I am worried that our tools to explore this is limited. Maddison's asymmetry argument extends also to trying to pierce these patterns. Liow's extinction-morphospace data is based on the paleontological record, so is probably robust to the asymmetry pattern (she knows the trait value of the taxon and its longevity). But to what limit can we explore patterns of diversification on a morphospace? Given some sort of data about evolutionary rates and trait values, can we estimate the speciation or extinction rate surface in the morphospace? 

Hrm. I worry that reality might be very complicated but there is simply no way to have enough data to reconstruct reality. What model are we willing to compromise with?

Maddison et al. 2007

I think it is neat that this is the first paper to incorporate extinction rates into a model of character evolution and diversification (that I have read). Is this why Rick Ree said last week that models prior to 2007 should probably not be used??? If so, this paper seems to be an impressive step forward. I am wondering about delta t. What are the effects of increasing and decreasing the time slice? Why does the model shrink the time interval as it approaches the root? Do high degrees of homoplasy in characters alter the performance of the model? Also, I am wondering why the option of state change and speciation is not included in figures 2 and 3? Following last week's discussion of key innovations, that strikes me as an important combination.

(Collar et al., 2010) Averaging AICc values to take into account error?!

Recently while catching up on my PCM literature, I read the Collar et al. paper I brought up a few days ago. Their methods involve them fitting multi-rate BM models to their data, much like the Collar et al. paper we read. They have a lot of phylogenetic uncertainty and other sources of uncertainty (such as ancestral state reconstruction). To account for this, they fit models to their data, taking into account the posterior distributions of trees, and then reported and compared the mean AICc values for each model, fit to each trait. What do you guys think of this? Is this an accurate way to account for error, by fitting models to every permutation and taking the average AICc?

Response to previous LTT post

I'm having trouble commenting on Dave's LTT post (I keep getting an error message), so I thought I'd respond in post form.

Two questions:

1. Does anyone know if there is a molecular phylogeny of extant cockle genera? It would be interesting to add the 'ltt' produced by molecular data. I doubt it would reflect the fossil ltt of all genera, but how close does it come to approximating the fossil ltt of extant genera? 2. I wonder how closely a molecular 'ltt' based on genera would reflect a molecular 'ltt' based on species?

Comparing True Diversity Curves to LTT-esque Plots

Here is a plot that Dave Jablonski sent me of generic diversity
in cockles. One curve shows the 'true' diversity (based on fossil
appearances) and the other curve shows the diversity if you only found
the living genera (and thus approximates an extant lineage-through-time plot,
although not quite... but its close enough!). There was discussion
last week of what such a plot would look like, so there it is.

As you can see, the 'extant-only' fails to catch many of the details, particularly a pronounced mass extinction in the KT. The timing of the Cenozoic diversity increase is off by 10 million years. Finally, cockles have actually been decreasing in diversity recently, but the 'extant-only' plot shows only rapid recent increase.

A Plea for Multimodal Diversification Analyses

This isn't the topic I brought up last week, but it will sound like the same discussion.

So, it strikes me that despite all the extrinsic vs. intrinsic noise made by several of the papers we read this week, what we'd really like to do is test such hypotheses using a tree-painting approach, like in the multi-OU, multi-BM type models that we explored earlier in the class. Why can't we take a tree, paint a scenario of extrinsic increase of diversification (say, increase speciation due to the formation of a large island archipelago) with two clades having their own intrinsic key innovations that further boosts their diversification, use maximum likelihood to estimate the diversification factors and BANG get our AICc and AIC-W values and actually say to ourselves based on the best fitting model "Gee, looks like the breakup of Pangaea was pretty important (x1.5 speciation rate), but developing specialized leaves seems to have greatly decreased clade A's extinction rate (x0.001 extinction rate)."

Isn't that really what we should want?

Obviously, this would require a heck of tree, with a number of fossil lineages on it, particularly as I think we SHOULD ask questions about how speciation and extinction rate changes over time. But it seems like that's where the field will be heading now anyway.

Or maybe I'm obsessed with pipe dreams.

Is lability a heritable trait?

Rabosky and McCune (2009; one of the non-required readings) write that heritability of species traits across speciation events is one of the patterns that "immediately indicates the possibility of species selection" (p. 70). They define heritability as the "tendency of progeny species to resemble their 'parents' [ancestor lineages]." On p. 71 they discuss the radiation of Hawaiian honeycreepers, a classic adaptive radiation, and write that "their high rate of diversification has been attributed to evolutionary lability of feeding morphology." Although not stated outright, it is implicit based on the inclusion of this honeycreeper example in the paper that R&M are thinking of lability of feeding morphology as a possible trait that could have led to species selection in the honeycreeper radiation. Given the emphasis that traits must be heritable in order to be evidence for species selection, is this a legitimate example for species selection? Can proponents of species selection 'have their cake and eat it too' by demanding that traits must be heritable across speciation events in order to be considered evidence of species selection, but then proclaim 'heritability of lability' when faced with classic adaptive radiations that do not have obvious heritable key traits other than high inter-specific morphological or behavioral diversity? In other words, is lability itself a heritable trait, or do the diversity of feeding strategies and bill morphologies of Hawaiian honeycreepers simply indicate a total lack of heritability of these traits across speciation events?

Paradis 2005

Pg 6: "Considering the observed distributions of body mass in each clade of primates, the clade effect now explains the overall positive relationship between body mass and speciation rate." What exactly is meant by clade effect? How was it taken "into account" in this study to produce a negative relationship (pg 10)?

Pg 8:"It cannot be excluded that a likelihood function may be derived taking extinction into account, but this derivation still needs to be found." What are the major obstacles to incorporating extinction into a liklihood function?

Rabosky (2009) and Magallon/Castillo (2009)

Magallon and Castillo (2009) found that younger angiosperm clades had higher rates of diversification. In Rabosky (2009), he mentions how this trend could be due to density-dependence.

While Magallon and Castillo (2009) don't discuss density dependence per se, they do mention the following, which sounds awfully similar to density dependence:

"It could be argued that the increase in the rate of diversification rate through time represents the initial species accumulation of young clades during an exponential diversification process. However, the estimators used here are explicitly modeled as a stochastic birth-and-death process (Bailey, 1964) where the speciation rate and the extinction rate are constant through time and lead to exponentially increasing or decreasing diversity (Magallon & Sanderson 2001). The diversification rate of a clade going through the initial phase of explosive species accumulation in an exponential process should not be detected as a higher net diversification rate because the estimators are expected to account for the initial explosive phase." (my italics)

So...what gives? Are these two papers conflicting? Or I am I just misunderstanding something here (quite likely)?

Magallon, S. & A. Castillo. 2009. Angiosperm diversification through time. American Journal of Botany 96: 349-365.

[as an aside: Magallon and Castill0 (2009) also argue that this trend (younger clades with higher diversification rates), could not be due to the "pull of the present" as the "estimators of diversification rate used here account for the possibility of extinct, unobserved diversity, by being conditional on the survival of the clade to a given time after its origin (Magallon & Sanderson 2001), in this case, the present."]

Maybe its the psychedelic colors, but...

Figure I b in Box 2 of Ricklefs (2007) is really blowing my mind. Are the NA and SA clades just placed on top of each other, or is there some interaction there? I see that there's likelihood ratios in there, but thats about as far as I get...

What's your Model of Diversification?

In the two Rabosky papers we read, Rabosky outlines different complications and heterogeneties not taken into account by the more general birth-death models. In both, he argues that too much evidence (generally using evidence from the fossil record) argues that these complexities are common enough that they must be taken into consideration before the birth-death model can be applied. I made a similar point in a previous post that we don't have enough information to handwave phenotypic trends, considering that in some fossil groups they are ubiquitous (...such as graptolites), and that this may be problematic for using ancestral state reconstruction using only extant taxa.

So, what model of diversification do you think clades generally follow? And how would you go about testing it?

The birth-death model provides an obvious baseline: it is basically a statement that speciation and extinction control the actual level of diversity. The problem with the birth-death model (Rabosky, 2010) is that it considers diversification rates to be homogenous: speciation and extinction rates cannot evolve along branches or change with time. The obvious place to test these assumptions is the fossil record. Paleontologists have known since Newell's work in the fifties that mass extinction events occur where extinction rates increase; similar evidence for temporal differences in both speciation and extinction rates have been known for decades (Van Valen wrote an excellent paper on the Permo-Triassic's 'resetting' effect on diversification rate in the seventies). 'Horizontal' variation (i.e. across different branches, rather than 'vertical', or variation with time) was acknowledged by Stanley (1975) in his classic book Macroevolution, where he found that the diversification rates of different classes/phyla differed significantly along a linear relationship between speciation and extinction. Sepkoski confirmed this with his own database in 1997. More recently, Roy et al. (2009) showed in one of the few paleontological datasets where such could be tested that extinction was phylogenetically clustered (they didn't look at speciation at all). This leaves the nagging question: Which is greater: the between-lineages variation in diversification rates or the across-time variation? Do both need to be considered or does one swamp out the other? Do speciation and extinction vary similar across both scales?

Rabosky (2009) breathes life into the much maligned logistic diversification model of Sepkoski's. This throws a wrench into the classic macroevolutionary equation D=S-E (diversity = speciation minus extinction), by suggesting that clades at the regional and even global scale may have an effective carrying capacity due to some sort of poorly understood density dependence. As Rabosky points out, many case studies in the fossil record support some sort of 'stability level', although some would argue otherwise (Steve Stanley and Michael Benton have argued repeatedly for an exponential model).

But in that case, what does this imply for the temporal and between-lineage variability we accounted for above? Is the true, general process of diversification really a result of logistic carrying capacity AND speciation and extinction rates which vary both temporally and between-lineages? Are there any additional complexities we are willing to add to this already frightfully intricate model? I suppose time and more research will tell.

Finally:
Remaining mysteries of diversification that I don't think anyone understands. Except maybe Leigh Van Valen, but I don't understand him somtimes. Rabosky and McPeek also have their own answers.

1) Speciation and extinction are tightly correlated across clades in the fossil record. Extinct groups (like graptolites, trilobites and ammonites) have the fastest rates.

2) No correlation between clade age and richness. (Possibly untrue).

3) Extremely old groups with very poor species diversity.

4) Young groups with paradoxically low extinction rates in molecular phylogenies, as opposed to the high extinction rates of fossil lineages.

5) My own research on graptolites. During a global cooling event, four graptoloid families suffer tremendous extinction rates while one graptoloid family, which was the least abundant and diverse prior to the glaciation, experiences zero extinction and greatly increased speciation. Obviously there must be some sort of physiological cold-tolerance held by the fifth family, but could that alone explain such a raw pattern of differential diversification? I am not sure.

Nee 2006

Pg. 13: On a spindle diagram, why would a paraphyletic clade (intuitively) appear more bottom-heavy than it actually is?

Sanderson & Donoghue 1996

I like the fact that the authors provide a summary of the methods used for reconstructing diversification rates in Table 1. I understand that the sample size for a phylogeny with known branch times is the number of terminal taxa. For a phylogeny lacking time estimates the sample size is “now of the order of 2-10, the maximum number of clades that can be considered given available methods and computational constraints” (pg 19). What computational constraints limit the estimation of sample size in tree-based methods without time?

The concluding discussion of molecular clocks offers three options for non-clock-like behavior of which the second appears the most promising to me. With the current models of molecular evolution, and all of the sequence data available, why is it not possible to develop rate models for different genes? When a molecular clock is rejected, is there a way of measuring to what degree the data deviate from clock-like behavior? What is known about the causes of rate heterogeneity across sites and across time? Is it possible to break the tree down into rate partitions that are clock-like?