Neuroanatomical shifts mirror patterns of ecological divergence in three diverse clades of mimetic butterflies

Microhabitat partitioning in heterogenous environments can support more diverse communities but may expose partitioned species to distinct perceptual challenges. Divergence across microhabitats could therefore lead to local adaptation to contrasting sensory conditions across small spatial scales, but this aspect of community structuring is rarely explored. Diverse communities of ithomiine butterflies provide an example where closely related species partition tropical forests, where shifts in mimetic coloration are tightly associated with shifts in habitat preference. We test the hypothesis that these mimetic and ecological shifts are associated with distinct patterns of sensory neural investment by comparing brain structure across 164 individuals of 16 species from three ithomiine clades. We find distinct brain morphologies between Oleriina and Hypothyris, which are mimetically homogenous and occupy a single microhabitat. Oleriina, which occurs in low‐light microhabitats, invests less in visual brain regions than Hypothyris, with one notable exception, Hyposcada anchiala, the only Oleriina sampled to have converged on mimicry rings found in Hypothyris. We also find that Napeogenes, which has diversified into a range of mimicry rings, shows intermediate patterns of sensory investment. We identify flight height as a critical factor shaping neuroanatomical diversity, with species that fly higher in the canopy investing more in visual structures. Our work suggests that the sensory ecology of species may be impacted by, and interact with, the ways in which communities of closely related organisms are adaptively assembled

A transference theorem for ergodic H1

The final version of this paper appears in: "Quarterly Journal of Mathematics" 48 (1997) 417-430. Print.In this paper, we extend the basic transference theorem for convolution operators on Lp spaces of Coifman and Weiss to H1 spaces

On a weak type (1, 1) inequality for a maximal conjugate function

The final version of this paper appears in: "Studia Mathematica" 125 (1997): 13-21. Print.In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of Hp spaces for 0 < p < ∞. In this paper, we show that their method extends to higher dimensions and yields a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus

Hardy martingales and Jensen's inequality

The final version of this paper appears in: "Bulletin of the Australian Mathematical Society" 55 (1997): 185-195. Print.Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus TN, where analyticity is defined using a lexicographic order on the dual group ZN. We show how, by using basic properties of orders on ZN, we can apply Garling's method in the study of analytic functions on an arbitrary compact abelian group with an arbitrary order on its dual group. We illustrate our approach by giving a new and simple proof of a famous generalized Jensen's Inequality due to Helson and Lowdenslager

Analytic measures and Bochner measurability

Many authors have made great strides in extending the celebrated F. and M. Riesz Theorem to various abstract settings. Most notably, we have, in chronological order, the work of Bochner, Helson and Lowdenslager, de Leeuw and Glicksberg, and Forelli. These formidable papers build on each other's ideas and provide broader extensions of the F. and M. Riesz Theorem. Our goal in this paper is to use the analytic Radon-Nikodym property and prove a representation theorem (Main Lemma 2.2 below) for a certain class of measure-valued mappings on the real line

An agent-based model clarifies the importance of functional and developmental integration in shaping brain evolution.

BACKGROUND: Vertebrate brain structure is characterised not only by relative consistency in scaling between components, but also by many examples of divergence from these general trends.. Alternative hypotheses explain these patterns by emphasising either 'external' processes, such as coordinated or divergent selection, or 'internal' processes, like developmental coupling among brain regions. Although these hypotheses are not mutually exclusive, there is little agreement over their relative importance across time or how that importance may vary across evolutionary contexts. RESULTS: We introduce an agent-based model to simulate brain evolution in a 'bare-bones' system and examine dependencies between variables shaping brain evolution. We show that 'concerted' patterns of brain evolution do not, in themselves, provide evidence for developmental coupling, despite these terms often being treated as synonymous in the literature. Instead, concerted evolution can reflect either functional or developmental integration. Our model further allows us to clarify conditions under which such developmental coupling, or uncoupling, is potentially adaptive, revealing support for the maintenance of both mechanisms in neural evolution. Critically, we illustrate how the probability of deviation from concerted evolution depends on the cost/benefit ratio of neural tissue, which increases when overall brain size is itself under constraint. CONCLUSIONS: We conclude that both developmentally coupled and uncoupled brain architectures can provide adaptive mechanisms, depending on the distribution of selection across brain structures, life history and costs of neural tissue. However, when constraints also act on overall brain size, heterogeneity in selection across brain structures will favour region specific, or mosaic, evolution. Regardless, the respective advantages of developmentally coupled and uncoupled brain architectures mean that both may persist in fluctuating environments. This implies that developmental coupling is unlikely to be a persistent constraint, but could evolve as an adaptive outcome to selection to maintain functional integration