Ernst Mayr and the modern concept of species

1. 

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   Fig. 1.

   Populations as lineages (modified from ref. 13). The population or population level lineage at a given instant in time is represented as a frequency distribution in two dimensions [x axis, trait variation; y axis, frequency (not shown)], whereas the time-extended population or population level lineage is represented by the 3D solid formed by extending the 2D frequency distribution through a third dimension (z axis, time). The three shaded distributions (a-c) represent cross sections of the time-extended population lineage at three different times. The population itself can be interpreted either as the 3D (time-extended) object, in which case it is equivalent to the lineage, or as one of the 2D (time-limited) objects, in which case it is equivalent to a cross section of the lineage.

   
   
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   Fig. 2.

   A highly simplified representation of the process of metapopulation lineage divergence (speciation) illustrating the conflicts caused by adopting different contingent properties of metapopulation lineages as necessary properties of species (modified from ref. 18). Progressive darkening and lightening of the daughter lineages represent their progressive divergence through time (bottom to top), and the numbered lines labeled SC (species criterion) 1-8 represent the times at which the daughter lineages acquire different properties relative to one another (e.g., when they become phenetically distinguishable, diagnosable by a fixed character difference, reciprocally monophyletic, reproductively incompatible, ecologically distinct, etc.). Before evolution of the first property (SC1), authors will agree there is a single species, and after evolution of the last property (SC8), they will agree there are two. Between these events, however, there will be disagreement among authors about whether one vs. two species are involved. Those disagreements result from authors adopting different contingent properties (species criteria) as the basis for their species definitions.