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Adaptive random search approaches have been shown to be effective for global optimization problems, where under certain conditions, the expected performance time increases only linearly with dimension. However, previous analyses assume that the objective function can be observed directly. We consider the case where the objective function must be estimated, often using a noisy function, as in simulation. We present a finite-time analysis of algorithm performance that combines estimation with a sampling distribution. We present a framework called Hesitant Adaptive Search with Estimation, and derive an upper bound on function evaluations that is cubic in dimension, under certain conditions. We extend the framework to Quantile Adaptive Search with Estimation, which focuses sampling points from a series of nested quantile level sets. The analyses suggest that computational effort is better expended on sampling improving points than refining estimates of objective function values during the progress of an adaptive search algorithm. 

Context-dependent trait exaggeration is a major contributor to phenotypic diversity. However, the genetic modifiers instructing development across multiple contexts remain largely unknown. We use the arthropod tibia, a hotspot for segmental differentiation, as a paradigm to assess the developmental mechanisms underlying the context-dependent structural exaggeration of size and shape through nutritional plasticity, sexual dimorphism and segmental differentiation. Using an RNAseq approach in the sexually dimorphic and male-polyphenic dung beetle Digitonthophagus gazella , we find that only a small portion (3.7%) of all transcripts covary positively in expression level with trait size across contexts. However, RNAi-mediated knockdown of the conserved sex-determination gene doublesex suggests that it functions as a context-dependent master mediator of trait exaggeration in D. gazella as well as the closely related dung beetle Onthophagus taurus . Taken together, our findings suggest (i) that the gene networks associated with trait exaggeration are highly dependent on the precise developmental context, (ii) that doublesex differentially shapes morphological exaggeration depending on developmental contexts and (iii) that this context-specificity of dsx -mediated trait exaggeration may diversify rapidly. This mechanism may contribute to the resolution of conflict arising from environment-dependent antagonistic selection among sexes and divergent developmental contexts in a wide range of animals. 

Understanding how novel complex traits originate is a foundational challenge in evolutionary biology. We investigated the origin of prothoracic horns in scarabaeine beetles, one of the most pronounced examples of secondary sexual traits in the animal kingdom. We show that prothoracic horns derive from bilateral source tissues; that diverse wing genes are functionally required for instructing this process; and that, in the absence of Hox input, prothoracic horn primordia transform to contribute to ectopic wings. Once induced, however, the transcriptional profile of prothoracic horns diverges markedly from that of wings and other wing serial homologs. Our results substantiate the serial homology between prothoracic horns and insects wings and suggest that other insect innovations may derive similarly from wing serial homologs and the concomitant establishment of structure-specific transcriptional landscapes. 

Simulation models commonly describe complex systems with no closed-form analytical representation. This paper proposes an algorithm for functions on continuous domains that fits into the nested partition framework and uses quantile estimation to rank regions and identify the most promising region. Additionally, we apply the optimal computational budget allocation (OCBA) method for allocating sample points using the normality property of quantile estimators. We prove that, for functions satisfying the Lipschitz condition, the algorithm converges in probability to a region that contains the true global optimum. The paper concludes with some numerical results.