A specification of mortality or survivorship provides respective explicit details about mortality's or survivorship's relationships with one or more other variables (e.g., age, sex, etc.). Previous studies have discovered and analyzed diverse specifications of mortality or survivorship; these discoveries and analyses suggest that additional specifications of mortality or survivorship have yet to be discovered and analyzed. In consistency with previous research, multivariable limited powered polynomials regression analyses of mortality and survivorship of selected humans (Swedes, 1760–2008) and selected insects (caged medflies) show age-specific, historical-time-specific, environmental-context-specific, and sex-specific mortality and survivorship. These analyses also present discoveries of hitherto unknown lifespan-specific, contemporary-aggregate-size-specific, and lifespan-aggregate-size-specific mortality and survivorship. The results of this investigation and results of previous research help identify variables for inclusion in regression models of mortality or survivorship. Moreover, these results and results of previous research strengthen the suggestion that additional specifications of mortality or survivorship have yet to be discovered and analyzed, and they also suggest that specifications of mortality and survivorship indicate corresponding specifications of frailty and vitality. Furthermore, the present analyses reveal the usefulness of a multivariable limited powered polynomials regression model-building approach. This article shows that much has yet to be learned about specifications of mortality or survivorship of diverse kinds of individuals in diverse times and places.

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Any cause that negatively affects mortality, positively affects mortality, negatively affects survivorship, and positively affects survivorship is tetraeffective (i.e., having four kinds of effects). However, until now, tetraeffective causes of mortality and survivorship have been undescribed, unidentified, unnamed, unrecognized, unclear, misconceived, unspecified, and unexplained. Here I describe, identify, name, recognize, elucidate, conceptualize, specify, and explain tetraeffective causes of mortality and survivorship. I show that every tetraeffective cause of mortality and survivorship combines corresponding at least one mortacause and at least one vitacause; "mortacause" refers here to a cause that positively affects mortality and negatively affects survivorship, and "vitacause" refers to a cause that positively affects survivorship and negatively affects mortality. I present strong rationales that suggest that every cause of mortality and survivorship is tetraeffective, and I present references to considerable previous evidence that I interpret to be suggestive evidence of tetraeffective causes of mortality and survivorship. Moreover, rigorous and thorough multivariable analyses of mortality and survivorship of humans and medflies provide here direct evidence of tetraeffective causes of mortality and survivorship, revealing best-fitting specifications dY/d(X p ) = a + bX p such that sign(a) = -sign(bX p ), where: Y indicates mortality or survivorship; X indicates age, lifespan, contemporary aggregate size, lifespan aggregate size, or historical time; dY/d(X p ) indicates composite effects of X p on Y; a indicates an Xspecific mortacause or vitacause; bX p indicates the corresponding opposite X-specific mortacause or vitacause; and coefficients a, b, and p denote respective X-specific and entityspecific constants. Thus description, identification, naming, recognition, elucidation, conception, specification, explanation, and demonstration of tetraeffective causes of mortality and survivorship usher a new paradigm of causes of mortality and survivorship and enable and promote further scientific research and practical applications. Figure 3. A causal structure of a tetraeffective cause of mortality and survivorship. X denotes a cause of mortality M and survivorship S, Xm denotes an X-specific mortacause, Xs denotes an X-specific vitacause, double dotted lines denote that Xm and Xv are X-specific, arrow → denotes positive effects, and arrow ----> denotes negative effects. Xm M Xv S X

A new theory and a new method, designated with the Hebrew letter Koof, reveal mathematical and graphic empirical identities of models, measurements, units, products, production, composites, composition, averages, factors, patterns, and