Fit simple models of trait evolution
fitSimple( y, model = c("GRW", "URW", "Stasis", "StrictStasis", "OU", "covTrack"), method = c("Joint", "AD"), pool = TRUE, z = NULL, hess = FALSE )
the model to be fit, one of
parameterization to use:
if TRUE, sample variances are substituted with their pooled estimate
a vector of a covariate, used only for the "covTrack" model
if TRUE, standard errors computed from the Hessian matrix are returned
This is a convenience function that calls the specific individual
functions for each model and parameterization, such as
opt.joint.GRW. The models that this function can fit are:
GRW: General Random Walk. Under this model, evolutionary
changes, or "steps" are drawn from a distribution with a mean of
and variance of
mstep determines directionality and
vstep determines volatility (Hunt, 2006).
Unbiased Random Walk. Same as GRW with
mstep = 0, and thus evolution
is non-directional. For a URW,
vstep is the rate parameter.
Stasis: This parameterization follows Sheets & Mitchell (2001), with
a constant mean
theta and variance
omega (equivalent to white
Strict Stasis: Same as Stasis with
omega = 0,
indicating no real evolutionary differences; all observed variation is
sampling error (Hunt et al. 2015).
model (Hunt et al. 2008). This model is that of a population ascending a
nearby peak in the adaptive landscape. The optimal trait value is
alpha indicates the strength of attraction to that peak (= strength of
stabilizing selection around
vstep measures the random walk component (from genetic drift) and
anc is the trait value
at the start of the sequence.
covTrack: Covariate-tracking (Hunt et al. 2010). The trait tracks
a covariate with slope
b1, consistent with an adaptive response.
evar is the
residual variance, and, under
method = "Joint",
b0 is the intercept of the
relationship between trait and covariate.
paleoTSfit object with the model fitting results
For the covariate-tracking model, z should be a vector of length
method = "Joint" and n - 1 when
"AD", where n is the number of samples in
"Joint" is a full likelihood approach, considering each time-series as
a joint sample from a multivariate normal distribution. Method =
is a REML approach that uses the differences between successive samples.
They perform similarly, but the Joint approach does better under some
circumstances (Hunt, 2008).
Hunt, G. 2006. Fitting and comparing models of phyletic
evolution: random walks and beyond. Paleobiology 32(4): 578-601.
Hunt, G. 2008. Evolutionary patterns within fossil lineages: model-based assessment of modes, rates, punctuations and process. p. 117-131 In From Evolution to Geobiology: Research Questions Driving Paleontology at the Start of a New Century. Bambach, R. and P. Kelley (Eds).
Hunt, G., M. A. Bell and M. P. Travis. 2008. Evolution toward a new adaptive optimum: phenotypic evolution in a fossil stickleback lineage. Evolution 62(3): 700-710.
Sheets, H. D., and C. Mitchell. 2010. Why the null matters: statistical tests, random walks and evolution. Genetica 112– 113:105–125.
y <- sim.Stasis(ns = 20, omega = 2) w1 <- fitSimple(y, model = "GRW") w2 <- fitSimple(y, model = "URW") w3 <- fitSimple(y, model = "Stasis") compareModels(w1, w2, w3)
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