Attempts to model form-function relationships for fossil plants rely on the facts that the physiological and structural requirements for plant growth, survival, and reproductive success are remarkably similar for the majority of extant and extinct species regardless of phyletic affiliation and that most of these requirements can be quantified by means of comparatively simple mathematical expressions drawn directly from the physical and engineering sciences. Owing in part to the advent and rapid expansion of computer technologies, the number of fossil plant form-function models has burgeoned in the last two decades and encompasses every level of biological organization ranging from molecular self-assembly to ecological and evolutionary dynamics. This recent and expansive interest in modeling fossil plant form-function relationships is discussed in the context of the general philosophy of modeling past biological systems and how the reliability of models can be examined (i.e., direct experimental manipulation or observation of the system being modeled). This philosophy is illustrated and methods of validating models are critiqued in terms of four models drawn from the author's work (the quantification of wind-induced stem bending stresses, wind pollination efficiency of early Paleozoic ovulate reproductive structures, population dynamics and species extinction in monotypic and “mixed” communities, and the adaptive radiation of early vascular land plants). The assumptions and logical (mathematical) consequences (predictions) of each model are broadly outlined, and, in each case, the model is shown to be overly simplistic despite its ability to predict the general or particular behavior or operation of the system modeled. Nonetheless, these four models, which illustrate some of pros and cons of modeling fossil form-function relationships, are argued to be pedagogically useful because, like all models, they expose the internal logical consistency of our basic assumptions about how organic form and function interrelate.

Functional analysis of fossils is and should remain a key component of paleobiological research. Despite recently expressed doubts, conceptual and methodological developments over the past 25 years indicate that robust and testable claims about function can be produced. Functional statements can be made in at least three different hierarchical contexts, corresponding to the degree of structural information available, the position in the phylogenetic hierarchy, and the degree of anatomical specificity. The paradigm approach, which dominated thinking about function in the 1960s and 1970s, has been supplanted with a methodology based on biomechanics. Paleobiomechanics does not assume optimality in organismal design, but determines whether structures were capable of carrying out a given function. The paradigm approach can best be viewed as a way of generating, rather than testing, functional hypotheses. Hypotheses about function can also be developed and supported by well-corroborated phylogenetic arguments. Additional functional evidence can be derived from studies of trace fossils and of taphonomy. New computer techniques, including “Artificial Life” studies, have the potential for producing far more detailed ideas about function and mode of life than have been previously possible. Functional analysis remains the basis for studies of the history of adaptation. It is also an essential component of many paleoecological and paleoenvironmental studies.

The origin of evolutionary novelty involves changes across the biological hierarchy: from genes and cells to whole organisms and ecosystems. Understanding the mechanisms behind the establishment of new designs involves integrating scientific disciplines that use different data and, often, different means of testing hypotheses. Discoveries from both paleontology and developmental genetics have shed new light on the origin of morphological novelties. The genes that play a major role in establishing the primary axes of the body and appendages, and that regulate the expression of the genes that are responsible for initiating the making of structures such as eyes, or hearts, are highly conserved between phyla. This implies that it is not new genes, per se, that underlie much of morphological innovation, but that it is changes in when and where these and other genes are expressed that constitute the underlying mechanistic basis of morphological innovation. Gene duplication is also a source of developmental innovation, but it is possible that it is not the increased number of genes (and their subsequent divergence) that is most important in the evolution of new morphologies; rather it may be the duplication of their regulatory regions that provides the raw material for morphological novelty. Bridging the gap between microevolution and macroevolution will involve understanding the mechanisms behind the production of morphological variation. It appears that relatively few genetic changes may be responsible for most of the observed phenotypic differences between species, at least in some instances. In addition, advances in our understanding of the mechanistic basis of animal development offer the opportunity to deepen our insight into the nature of the Cambrian explosion. With the advent of whole-genome sequencing, we should see accelerated progress in understanding the relationship between the genotype, phenotype, and environment: post-genomics paleontology promises to be most exciting.

Tree-based paleobiological studies use inferred phylogenies as models to test hypotheses about macroevolution and the quality of the fossil record. Such studies raise two concerns. The first is how model trees might bias results. The second is testing hypotheses about parameters that affect tree inference.

Bias introduced by model trees is explored for tree-based assessments of the quality of the fossil record. Several nuisance parameters affect tree-based metrics, including consistency of sampling probability, rates of speciation / extinction, patterns of speciation, applied taxonomic philosophy, and assumed taxonomy. The first two factors affect probabilistic assessments of sampling, but also can be tested and accommodated in sophisticated probability tests. However, the final three parameters (and the assumption of a correct phylogeny) do not affect probabilistic assessments.

Often paleobiologists wish to test hypotheses such as rates of character change or rates of preservation. Assumptions about such parameters are necessary in simple phylogenetic methods, even if the assumptions are that rates are homogeneous or that sampling is irrelevant. Likelihood tests that evaluate phylogenies in light of stratigraphic data and / or alternative hypotheses of character evolution can reduce assumptions about unknowns by testing numerous unknowns simultaneously. Such tests have received numerous criticisms, largely based in philosophy. However, such criticisms are based on incorrect depictions of the logical structures of parsimony and likelihood, misunderstandings about when arguments are probabilistic (as opposed to Boolean), overly restrictive concepts of when data can test a hypothesis, and simply incorrect definitions of some terms.

Likelihood methods can test multiparameter hypotheses about phylogeny and character evolution (i.e., rates, independence, etc.). The best hypothesis positing a single rate of independent character change (with no variation among character states) is determined for each topology. Hypotheses about rate variation among characters or across phylogeny, character independence, and different patterns of state evolution then are examined until one finds the simplest (i.e., fewest varying parameters) hypothesis that cannot be rejected given knowledge of a more complicated hypothesis. This is repeated for alternative topologies. An example is presented using hyaenids. Two trees are contrasted, one of which requires the minimum necessary steps and the other of which requires at least seven additional steps. Given either tree, likelihood rejects fewer than three general rates of character change and also rejects the hypothesis of independence among the characters. However, hypotheses of changes in rates across the tree do not add substantially to the tree likelihood. The likelihoods of the trees given stratigraphic data also are determined. Both morphologic and stratigraphic data suggest that the multiparameter hypothesis including the parsimony tree is significantly less likely than the multiparameter hypothesis including a different tree.