Online Resource 5 – Summary of all tests of Charnov and Downhower’s (1995) and Downhower and Charnov’s (1998) invariant rules

Recurrent violations of invariant rules for offspring size: evidence from turtles and the implications for small clutch size models

Oecologia

Njal Rollinson, Christopher B. Edge*, and Ron J. Brooks

*Corresponding Author,

Summary of all tests of Charnov and Downhower’s (1995) and Downhower and Charnov’s (1998) invariant rules. A “+” indicates that the assumption was not violated or the prediction was upheld, and a “−” indicates that the assumption was violated or the prediction was not upheld. CS~ES is the assumption that offspring size does not correlate with clutch size; Constant ES σ2 is the assumption that variation in offspring size is relatively similar within clutches, compared to among clutches; Resource conversion is the assumption that the increase in energy devoted to reproduction that is required to go from a clutch of size i to a clutch of size i+1 does not depend on clutch size. ES σ 2 decreases with CS is the prediction that the variance is offspring size decreases with clutch size; Symmetric convergence is the prediction that the variance in offspring size converges symmetrically on clutch size as clutch size increases; IR1 is the prediction that every observed value estimated from the left-hand side of Equation 1 (see main text) will not be significantly different than the corresponding predicted value on the right-hand side of the equation. When inferential statistics were not provided, we used figures and tables provided by the relevant study to judge whether the assumption or prediction was upheld. Ref is the relevant reference: (1) present study; (2) Guinnee et al. (2004) (3) Charnov et al. (1995); (4) Guinnee et al. (2005) (5) Kasparian et al. (2005) (6) Uller et al. (2009) (7) Uller and Olsson (2009)

Order / Species / CS~ES / Constant ES σ2 / Resource conversion / ES σ 2 decreases with CS / Symmetric convergence / IR1 / Ref
Testudines / Chrysemys picta / − / + / − / + / − / − / 1
Chelydra serpentina / − / + / − / + / − / − / 1
Glyptemys insculpta / + / + / + / + / + / + / 1
Cladocera / Daphina magna / − / + / + / + / − / − / 2
Cyprinodontiformes / Gambusia hubbsi / − / + / NA / + / − / NA / 3
Hymenoptera / Aphaereta pallipes / − / + / + / + / − / − / 4
Achrysocharoides zwoelferi / − / + / NA / + / − / + / 4
Laelius pedatus / − / + / + / − / − / − / 4
Metaphycus stanleyi / + / + / − / + / + / + / 4
Elachertus cacoeciae / − / + / NA / − / − / − / 4
Mastrus ridibundus / − / + / NA / − / − / − / 4
Rodentia / Cavea aperea / − / − / − / + / + / − / 5
Squamata / Eulamprus tympanum / − / NA / NA / − / − / − / 6
Eulamprus heatwolei / − / NA / NA / − / − / + / 6
Eulamprus quoyii / + / NA / NA / + / + / + / 6
Tiliqua rugosa / − / NA / NA / − / − / + / 6
Egernia whitii / − / NA / NA / + / − / + / 6
Niveoscincus microlepidotus / − / NA / NA / − / − / + / 6
Niveoscincus ocellatus / − / NA / NA / + / − / − / 6
Lampropholis mirabilis / − / NA / NA / − / − / − / 6
Bassiana duperreyi / + / NA / NA / − / − / + / 6
Amphibolurus muricatus / − / NA / NA / + / − / + / 6
Ctenophorus pictus / + / NA / NA / + / − / + / 6
Ctenophorus fordi / + / NA / NA / + / + / − / 6
Ctenophorus fordi / − / + / + / + / − / − / 7

Literature cited

Charnov EL, Downhower JF, Brown LP (1995) Optimal offspring size in small litters. Evolutionary Ecology 9:57–63

Guinnee MA, Bernal JS, Bezemer TM, Fidgen JG, Hardy ICW, Mayhew PJ, Mills NJ, West SA (2005) Testing predictions of small brood models using parasitoid wasps. Evolutionary Ecology Research 7:779–794

Guinnee MA, West SA, Little TJ (2004) Testing small clutch size models with Daphnia. American Naturalist 163:880–887

Kasparian K, Geibler E, Trillmich F (2005) Optimal offspring size in a small mammal: an exception to the tradeoff invariant life-history rule. Oikos 111:271–278

Uller T, Olsson M (2009) Offspring size-number trade-off in a lizard with small clutch sizes: tests of invariants and potential implications. Evolutionary Ecology 23:363–372

Uller T, While GM, Wapstra E, Warner DA, Goodman BA, Schwarzkopf L, Langkilde T, Doughty P, Radder RS, Rohr DH, Bull CM, Shine R, Olsson M (2009) Evaluation of offspring size-number invariants in 12 species of lizard. Journal of evolutionary biology 22:143–151