Micro and macroevolution: A continuum or two distinct types of change?

How microevolution and macroevolution are related is one of the major unanswered questions in evolutionary biology. The most-prevalent view is that microevolution and macroevolution are part of a continuum of one type of change and that macroevolution is the cumulative result of microevolution. Mathematics, however, distinguishes two fundamentally-different, singular types of change: change of a vector in its parameters versus its dimensions. This mathematical distinction may help to articulate the concept of evolution by distinction of two fundamentally different types of evolution: the change of the state vector of an organism in 1) its parameters (= ‘first-order evolution’) and 2) its dimensions (= ‘second-order evolution’). This distinction can be operationalized by identifying genes and regulatory elements in the nucleotide code of an organism as dimensions and the level of expression as parameters of its state vector. This operationalization allows to substitute the phenotype-based analysis of evolution with a genotype-based analysis and draws attention to the mechanisms that change the parameters or the dimensions of the state vector, respectively. We illustrate the distinction between first- and second-order evolution by a simulation of the adaptive dynamics of a population of digital amoebes, and reveal that micro- and macroevolution are two distinct types of change.

Methods
The methods applied in simulating first- and second-order evolution of a population of digital amoebes are: (1) interactive simulation, combining computerized and scripted manual actions; (2) prototyping, where  visualization of concepts and functionalities is leading, instead of computerization efficiency.

Excel is used in a 'free-style', as a tool for simulation and visualization of first- and second-order evolution. The scripted manual actions interacting with computerized actions as well as the clarification of the proceeding simulation process, are brought together in one Excel-file. The integrated file thus is not a standard, singular Excel-table or -spreadsheet, and therefore it does not meet the requirements for a standard, singular Excel-table or - spreadsheet.