Applications of commonly used numerical techniques in diatom-based paleoecology are reviewed including: approaches used to model diatom taxa to important limnological variables; ordination and other commonly used multivariate approaches; and the myriad of approaches that are now being explored to infer environmental variables based on diatom assemblages.Modelling the response of individual diatom taxa to limnologically important variables is consistent with ecological theory and has been largely accomplished using approaches based on generalized linear models. These techniques have established that strong and significant relationships exist between the numerically dominant diatom taxa and important limnological variables (e.g., pH, nutrients, salinity). Null modelling approaches have also been used. However, inclusion of rare taxa in null models results in high rates of type-II errors, and consequently spurious claims that only a minority of diatoms have significant relationships to important limnological variables such as lakewater pH and nutrients.A variety of ordination techniques are widely used in diatom-based paleolimnological studies to aid in summarizing the main directions of variation in diatom assemblages, and to identify limnological variables that are strongly correlated to the diatom assemblages, both in time and space. More advanced ordination techniques, such as partial ordinations, are increasingly being used to assess the shared and unique variance attributable to groups of important limnological variables. Further, diatom-based approaches based on experimental designs with control lakes and appropriate multivariate statistics are now becoming increasingly common to assess, for example, the impact of forestry on water quality.A number of different diatom-based inference models based on the present-day relationships between diatom assemblages and limnological variables are now available for inferring important limnological variables. These approaches vary from simple approaches such as weighted-averaging to more complex approaches involving curve fitting and maximum likelihood, neural networks, and Bayesian statistics. All of these approaches have been shown to result in strong inference models, each using aspects of ecological information available from the diatom assemblages.

Serious environmental issues, including acid rain, eutrophication, and decreasing water availability, require knowledge of the: 1) baseline conditions (i.e., what were conditions like before human disturbance); 2) natural variability; and 3) time or level of disturbance when the system responded to the environmental change. This type of knowledge can only be obtained from a historical perspective, which is best achieved through actual measurements of environmental variables. Such records, however, rarely extend more than a few decades, which is usually insufficiently long to determine baseline conditions and natural variability. Diatoms, single celled algae characterized by a cell wall composed of opaline silica, preserved in lake sediments are one of the most widely used paleoindicators, and provide robust estimates of lakewater pH, nutrient concentration and lake level change. A variety of approaches have been developed to infer environmental variables using diatom data, and robust inferences of many environmental variables are now possible. Using paleolimnological techniques, fossil diatoms have been used to track pH, nutrients and lake levels. These records have significantly contributed to our understanding of the causes and impacts of lakewater acidification, eutrophication and hydrologic change, and provide a basis for developing effective management strategies.

Paleolimnological techniques have been used successfully to reconstruct environmental change in the Arctic and Antarctic. Diatoms are powerful indicators of environmental change because their community composition responds to changes in environmental conditions. As more regional diatom calibrations throughout the high latitude regions are achieved, the autecology of diatom taxa can be quantified and transfer functions for the driving environmental variables developed. In most instances, environmental variables related to physical, chemical, and climate-related characteristics are the main drivers affecting diatom distribution across polar aquatic bodies. A decline in ice cover and increase in growing season length results in an increase in diatom diversity as well as increased productivity, and increased thermal stratification in lakes (vs. shallow ponds). Because the siliceous cell wall preserves well in sediments, diatoms are among the most commonly used organisms used in paleolimnological analyses. Polar latitudes are experiencing amplification of the current global warming trend and as such, analyses of diatoms from high latitude lake and pond sediments are revealing the timing and extent of these trends. Diatom-based paleolimnological analyses are also being used to track the environmental impact of excess nutrient additions to lakes. Similar findings have also been reported from marine ecosystems.

Historical biogeography has recently experienced a significant advancement in three integrated areas. The first is the adoption of an ontology of complexity, replacing the traditional ontology of simplicity, or a priori parsimony; simple and elegant models of the biosphere are not sufficient for explaining the geographical context of the origin of species and their post-speciation movements, producing evolutionary radiations and complex multi-species biotas. The second is the development of a powerful method for producing area cladograms from complex data, especially cases of reticulated area relationships, without loss of information. That method, called Phylogenetic Analysis for Comparing trees (PACT), is described herein. The third element is the replacement of the model of maximum vicariance with the model called the Taxon Pulse hypothesis. PACT analysis of Hominoidea, Hyaenidae, and Proboscidea beginning in the Miocene, reveals that all three groups share a general episode of species formation in Africa in the early Miocene, followed by “out of Africa” expansion into Europe, Asia and North America, a second general episode of species formation in Asia in the mid-Miocene, followed by “out of Asia” expansion into Africa, Europe and North America. Finally, there were two additional “out of Africa” events during the late Miocene and into the Pliocene, the last one setting the stage for the emergence and spread ofHomo. In addition to these shared episodes of vicariance and dispersal, each group exhibits clade-specific within-area and peripheral isolates speciation events. The complex history of dispersal and speciation over largeareas exhibited by hominoids is part of a more general historyof biotic diversification by taxon pulses.