While evenness is understood to be maximal if all types (species, genotypes, alleles, etc.) are represented equally (via abundance, biomass, area, etc.), its opposite, maximal unevenness, either remains conceptually in the dark or is conceived as the type distribution that minimizes the applied evenness index. The latter approach, however, frequently leads to conceptual inconsistency due to the fact that the minimizing distribution is not specifiable or is monomorphic. The state of monomorphism, however, is indeterminate in terms of its evenness/unevenness characteristics. Indeed, the semantic indeterminacy also shows up in the observation that monomorphism represents a state of pronounced discontinuity for the established evenness indices. This serious conceptual inconsistency is latent in the widely held idea that evenness is an independent component of diversity. As a consequence, the established evenness indices largely appear as indicators of relative polymorphism rather than as indicators of evenness. In order to arrive at consistent measures of evenness/unevenness, it seems indispensable to determine which states are of maximal unevenness and then to assess the position of a given type distribution between states of maximal evenness and maximal unevenness. Since semantically, unevenness implies inequality among type representations, its maximum is reached if all type representations are equally different. For given number of types, this situation is realized if type representations, when ranked in descending order, show equal differences between adjacent types. We term such distributions “stepladders” as opposed to “plateaus” for uniform distributions. Two approaches to new evenness measures are proposed that reflect different perspectives on the positioning of type distributions between the closest stepladders and the closest plateaus. Their two extremes indicate states of complete evenness and complete unevenness, and the midpoint is postulated to represent the turning point between prevailing evenness and prevailing unevenness. The measures are graphically illustrated by evenness surfaces plotted above frequency simplices for three types, and by transects through evenness surfaces for more types. The approach can be generalized to include variable differences between types (as required in analyses of functional evenness) by simply replacing types with pairs of different types. Pairs, as the new types, can be represented by their abundances, for example, and these can be modified in various ways by the differences between the two types that form the pair. Pair representations thus consist of both the difference between the paired types and their frequency. Omission of pair frequencies leads to conceptual ambiguity. Given this specification of pair representations, their evenness/unevenness can be evaluated using the same indices developed for simple types. Pair evenness then turns out to quantify dispersion evenness.

Background: Declining resources due to climate change may endanger the persistence of populations by reducing fecundity and thus population fitness via effects on gamete production. The optimal mode of generative reproduction allocates the limited resources to ovule and pollen production in proportions that maximize the number of fertilized ovules in the population. In order to locate this optimum and derive reproduction modes that compensate for declined resources to maintain reproductive success, a model of gamete production, pollen dispersal, and ovule fertilization is developed. Specification of opportunities for compensation is given priority over specification of physiological or evolutionary mechanisms of adaptation. Thus model parameters summarize gametic production resources, resource investment per gamete, resource allocation as proportion of resources invested in ovules, and pollen density as size of the pollen dispersal range and proportion of pollen retained within the range. Retained pollen disperses randomly, and an ovule is fertilized if at least one pollen settles on its surface. The outcome is the expected number of fertilized ovules. Results: Maximization of fertilization success is found to require the investment of more gametic production resources in ovules than in pollen, irrespective of the parameter values. Resource decline can be compensated by adjusting the resource allocation if the maximum expected number of fertilized ovules after the decline is not less than the expected number the population experienced before the decline. Compensation is also possible under some conditions by increasing the pollen density, either by raising a low pollen retention or by shrinking the dispersal range. Conclusion: Fertilization success in populations affected by resource decline may be maintainable by adjustment of the sexual allocation of gametic production resources or by increasing pollen density. The results have implications for insect pollination, sexual allocation bias, management measures, and metapopulation fragmentation.

Most genetic studies of population differentiation are based on gene-pool frequencies. Population differences for gene associations that show up as deviations from Hardy-Weinberg proportions (homologous association) or gametic disequilibria (non-homologous association) are disregarded. Thus little is known about patterns of population differentiation at higher levels of genetic integration nor the causal forces.