DOI: 10.5061/dryad.vx0k6djrp
title: A comparative analysis testing Werner's theory of complex life cycles

description: A popular theoretical model for explaining the evolution of complex life
 cycles was provided by Earl Werner. The theory predicts the size at which
 an individual should switch stages to maximise growth rate relative to
 mortality rate across the life history.  Werner’s theory assumes
 that body size does not change during the transition from one phase to
 another (e.g. from larva to adult)—a key assumption that has not been
 tested systematically but could alter the predictions of the
 model.  We quantified how growth rate and mass change across
 larval stages and metamorphosis for 105 species of fish, amphibians,
 insects, crustaceans and molluscs Across all taxonomic groups, we found
 support for Werner’s assumption that growth rates are maintained or
 increase around transitions. We found that changes in growth and mass were
 greatest during metamorphosis, and change in growth correlated with
 development time. Importantly, most species either gained or lost mass
 when switching to a new stage—a direct contradiction of Werner’s
 assumption. When we explored the consequences of energy loss and gain in a
 numerical model, we found that individuals should switch stages at a
 larger and smaller size, respectively, relative to what Werner’s standard
 theory predicts. Our results suggest that while there is support for
 Werner’s assumption regarding growth rates, mass changes profoundly alter
 the timing of transitions that are predicted to maximise fitness, and
 therefore the original model omits an important component that may
 contribute to the evolution of complex life cycles. Future studies should
 test for conditions that alter the costs of transitions, so that we can
 have a better understanding of how mass loss or gain affects fitness.
description: We conducted a comparative analysis of larval growth rates to
 test Werner's theory on complex life cycles. For each study, we
 extracted body mass and age data across immature stages during
 development. We noted whether transitions were between stages within the
 larval phase (e.g. from one larval stage to another), or whether
 transitions were from the larval phase to the adult phase (i.e.
 metamorphosis). Finally, we recorded the total number immature stages for
 each species.  To test Werner’s hypotheses across
 species, we first divided mass and age by the maximum size and age for
 that species, so that we were working with relative values (i.e. both mass
 and time bound between zero and one). We fit linear, quadratic and
 exponential models to the relative mass over time data for each larval
 stage and adult phase within species, and used Akaike Information
 Criterion (AIC) to select the most parsimonious model (Table S4; Akaike
 1978, Quinn and Keough 2002). In cases where the most parsimonious model
 yielded body mass predictions that were biologically irrelevant (e.g.
 negative values), we selected the next most parsimonious model. Using the
 body mass predictions from the fitted curves, we calculated derivatives as
 a measure of instantaneous growth rate (Anger 1991; see Figure S2 for
 example). For our response variable, we found the derivative at the last
 time point of the initial stage/phase and the derivative at the first time
 point in the next stage/phase (Figure 1). Then, we calculated the
 difference between the two derivatives. If the change in growth rate is a
 positive value, growth rate after transitioning is greater than growth
 rate before, while a negative value indicates growth rate before is
 greatest. As a second response variable, we calculated the change in
 mass—initial mass after transition to a new stage/phase minus the final
 mass in the initial stage/phase (Figure 1). If the change in mass is a
 positive value, the organism grew during the transition and if the change
 in mass is a negative value, the organism lost mass. Finally, for species
 with multiple larval stages (i.e. crustaceans and insects) we tested how
 change in growth rate and change in mass correlated with development
 time.