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About 98 results
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/02%3A_Fitting_Statistical_Models_to_Data/2.01%3A_Introduction
    Evolution is the product of a thousand stories. Individual organisms are born, reproduce, and die. The net result of these individual life stories over broad spans of time is evolution. At first glanc...Evolution is the product of a thousand stories. Individual organisms are born, reproduce, and die. The net result of these individual life stories over broad spans of time is evolution. At first glance, it might seem impossible to model this process over more than one or two generations. And yet scientific progress relies on creating simple models and confronting them with data. How can we evaluate models that consider evolution over millions of generations?
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/07%3A_Models_of_Discrete_Character_Evolution
    This chapter describes the Mk model, which can be used to describe the evolution of discrete characters that have a set number of fixed states. We can also elaborate on the Mk model to allow more comp...This chapter describes the Mk model, which can be used to describe the evolution of discrete characters that have a set number of fixed states. We can also elaborate on the Mk model to allow more complex models of discrete character evolution (the extended-Mk model). These models can all be used to simulate the evolution of discrete characters on trees.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/09%3A_Beyond_the_Mk_Model
    The simple Mk model provides a useful foundation for a number of innovative methods. These methods capture evolutionary processes that are more complicated than the original model, including models th...The simple Mk model provides a useful foundation for a number of innovative methods. These methods capture evolutionary processes that are more complicated than the original model, including models that vary through time or across clades. Modeling more than one discrete character at a time allows us to test for the correlated evolution of discrete characters.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.05%3A_Multivariate_Brownian_motion
    The Brownian motion model we described above was for a single character. However, we often want to consider more than one character at once. This requires the use of multivariate models. The situation...The Brownian motion model we described above was for a single character. However, we often want to consider more than one character at once. This requires the use of multivariate models. The situation is more complex than the univariate case – but not much! In this section I will derive the expectation for a set of (potentially correlated) traits evolving together under a multivariate Brownian motion model.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/12%3A_Beyond_Birth-Death_models/12.03%3A_Variation_in_Diversification_Rates_through_Time
    In addition to considering rate variation across clades, we might also wonder whether birth and/or death rates have changed through time. For example, perhaps we think our clade is an adaptive radiati...In addition to considering rate variation across clades, we might also wonder whether birth and/or death rates have changed through time. For example, perhaps we think our clade is an adaptive radiation that experienced rapid diversification upon arrival to an island archipelago and slowed as this new adaptive zone got filled. This hypothesis is an example of density-dependent diversification, where diversification rate depends on the number of lineages that are present
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/11%3A_Fitting_Birth-Death_Models/11.0S%3A_11.S%3A_Fitting_Birth-Death_Models_(Summary)
    In this chapter, I described how to estimate parameters from birth-death models using data on species diversity and ages, and how to use patterns of tree balance to test hypotheses about changing birt...In this chapter, I described how to estimate parameters from birth-death models using data on species diversity and ages, and how to use patterns of tree balance to test hypotheses about changing birth and death rates. In the next chapter, we will explore elaborations on birth-death models, and discuss models that go beyond constant-rates birth-death models to analyze the diversity of life on Earth.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.03%3A_Simple_Quantitative_Genetics_Models_for_Brownian_Motion
    Consider the mean value of this trait, $\bar{z}$, in a population with an effective population size of N e (this is technically the variance effective population ) 2 . Since there is no selection, the...Consider the mean value of this trait, $\bar{z}$, in a population with an effective population size of N e (this is technically the variance effective population ) 2 . Since there is no selection, the phenotypic character will change due only to mutations and genetic drift. Note that all of these models require that the strength of selection is relatively weak, or else genetic variation of the character will be depleted by selection over time and the dynamics of trait evolution will change.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/09%3A_Beyond_the_Mk_Model/9.03%3A_Pagel%E2%80%99s_%CE%BB%2C_%CE%B4%2C_and_%CE%BA
    Interestingly, the overall lowest AIC score (and the most AIC weight, though only just more than 1/3 of the total) is on the ARD model with no additional Pagel parameters. I interpret this to mean tha...Interestingly, the overall lowest AIC score (and the most AIC weight, though only just more than 1/3 of the total) is on the ARD model with no additional Pagel parameters. I interpret this to mean that, for these data, the standard ARD model with no alterations is probably a reasonable fit to the data compared to the Pagel-style alternatives considered above, especially given the additional complexity of interpreting tree transformations in terms of evolutionary processes.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/14%3A_What_have_we_learned_from_the_trees/14.04%3A_A_hint_at_the_future_of_comparative_methods
    It is perilous to predict the future progress of science. Nonetheless, I will offer a few suggestions that I think might be productive avenues for work in comparative methods.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/12%3A_Beyond_Birth-Death_models/12.04%3A_Diversity-Dependent_Models
    Time-dependent models in the previous section are often used as a proxy to capture processes like key innovations or adaptive radiations. Many of these theories suggest that diversification rates shou...Time-dependent models in the previous section are often used as a proxy to capture processes like key innovations or adaptive radiations. Many of these theories suggest that diversification rates should depend on the number of species alive in a certain time or place, rather than time . Therefore, we might want to define speciation rate in a truly diversity dependent manner rather than using time as a proxy.
  • https://bio.libretexts.org/Bookshelves/Evolutionary_Developmental_Biology/Phylogenetic_Comparative_Methods_(Harmon)/03%3A_Introduction_to_Brownian_Motion/3.01%3A_Introduction_to_Brownian_Motion
    Imagine that you want to use statistical approaches to understand how traits change through time. This requires an exact mathematical specification of how evolution takes place. Obviously there are a ...Imagine that you want to use statistical approaches to understand how traits change through time. This requires an exact mathematical specification of how evolution takes place. Obviously there are a wide variety of models of trait evolution, from simple to complex. e.g., creating a model where a trait starts with a certain value and has some constant probability of changing in any unit of time or an alternative model that is more detailed and explicit and considers a large set of individuals.

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