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The environment could alter growth and resistance tradeoffs in plants by affecting the ratio of resource allocation to various competing traits. Yet, how and why functional tradeoffs change over time and space is poorly understood particularly in long-lived conifer species. By establishing four common-garden test sites for five lodgepole pine populations in western Canada, combined with genomic sequencing, we revealed the decoupling pattern and genetic underpinnings of tradeoffs between height growth, drought resistance based on δ13C and dendrochronology, and metrics of pest resistance based on pest suitability ratings. Height and δ13C correlation displayed a gradient change in magnitude and/or direction along warm-to-cold test sites. All cold test sites across populations showed a positive height and δ13C relationship. However, we did not observe such a clinal correlation pattern between height or δ13C and pest suitability. Further, we found that the study populations exhibiting functional tradeoffs or synergies to various degrees in test sites were driven by non-adaptive evolutionary processes rather than adaptive evolution or plasticity. Finally, we found positive genetic relationships between height and drought or pest resistance metrics and probed five loci showing potential genetic tradeoffs between northernmost and the other populations. Our findings have implications for deciphering the ecological, evolutionary, and genetic bases of the decoupling of functional tradeoffs due to environmental change.

We study shift spaces over a finite alphabet that can be approximated by mixing shifts of finite type in the sense of (pseudo)metrics connected to Ornstein’s $\\bar {d}$ metric ( $\\bar {d}$ -approachable shift spaces). The class of $\\bar {d}$ -approachable shifts can be considered as a topological analog of measure-theoretical Bernoulli systems. The notion of $\\bar {d}$ -approachability, together with a closely connected notion of $\\bar {d}$ -shadowing, was introduced by Konieczny, Kupsa, and Kwietniak [Ergod. Th. & Dynam. Sys. 43(3) (2023), 943–970]. These notions were developed with the aim of significantly generalizing specification properties. Indeed, many popular variants of the specification property, including the classic one and the almost/weak specification property, ensure $\\bar {d}$ -approachability and $\\bar {d}$ -shadowing. Here, we study further properties and connections between $\\bar {d}$ -shadowing and $\\bar {d}$ -approachability. We prove that $\\bar {d}$ -shadowing implies $\\bar {d}$ -stability (a notion recently introduced by Tim Austin). We show that for surjective shift spaces with the $\\bar {d}$ -shadowing property the Hausdorff pseudodistance ${\\bar d}^{\\mathrm {H}}$ between shift spaces induced by $\\bar {d}$ is the same as the Hausdorff distance between their simplices of invariant measures with respect to the Hausdorff distance induced by Ornstein’s metric $\\bar {d}$ between measures. We prove that without $\\bar {d}$ -shadowing this need not to be true (it is known that the former distance always bounds the latter). We provide examples illustrating these results, including minimal examples and proximal examples of shift spaces with the $\\bar {d}$ -shadowing property. The existence of such shift spaces was announced in the earlier paper mentioned above. It shows that $\\bar {d}$ -shadowing indeed generalizes the specification property.

We prove that every genuinely partially hyperbolic $\\mathbb {Z}^r$ -action by toral automorphisms can be perturbed in $C^1$ -topology, so that the resulting action is continuously conjugate, but not $C^1$ -conjugate, to the original one.

HSP90 is a ubiquitously expressed chaperone protein that regulates the maturation of numerous substrate proteins called ‘clients’. The glycoprotein fibronectin (FN) is an important protein of the extracellular matrix (ECM) and a client protein of HSP90. FN and HSP90 interact directly, and the FN ECM is regulated by exogenous HSP90 or HSP90 inhibitors. Here, we extend the analysis of the HSP90 – FN interaction. The importance of the N-terminal 70-kDa fragment of fibronectin (FN70) and FN type I repeat was demonstrated by competition for FN binding between HSP90 and the functional upstream domain (FUD) of the Streptococcus pyogenes F1 adhesin protein. Furthermore, His-HSP90α mutations F352A and Y528A (alone and in combination) reduced the association with full-length FN (FN-FL) and FN70 in vitro. Unlike wild type His-HSP90α, these HSP90 mutants did not enhance FN matrix assembly in the Hs578T cell line model when added exogenously. Interestingly, the HSP90 E353A mutation, which did not significantly reduce the HSP90 – FN interaction in vitro, dramatically blocked FN matrix assembly in Hs578T cell-derived matrices. Taken together, these data extend our understanding of the role of HSP90 in FN fibrillogenesis and suggest that promotion of FN ECM assembly by HSP90 is not solely regulated by the affinity of the direct interaction between HSP90 and FN.

Eaton (1992) considered a general parametric statistical model paired with an improper prior distribution for the parameter and proved that if a certain Markov chain, constructed using the model and the prior, is recurrent, then the improper prior is strongly admissible, which (roughly speaking) means that the generalized Bayes estimators derived from the corresponding posterior distribution are admissible. Hobert and Robert (1999) proved that Eaton’s Markov chain is recurrent if and only if its so-called conjugate Markov chain is recurrent. The focus of this paper is a family of Markov chains that contains all of the conjugate chains that arise in the context of a Poisson model paired with an arbitrary improper prior for the mean parameter. Sufficient conditions for recurrence and transience are developed and these are used to establish new results concerning the strong admissibility of non-conjugate improper priors for the Poisson mean.

In this paper, we consider random iterations of polynomial maps $z^{2} + c_{n}$ , where $c_{n}$ are complex-valued independent random variables following the uniform distribution on the closed disk with center c and radius r. The aim of this paper is twofold. First, we study the (dis)connectedness of random Julia sets. Here, we reveal the relationships between the bifurcation radius and connectedness of random Julia sets. Second, we investigate the bifurcation of our random iterations and give quantitative estimates of bifurcation parameters. In particular, we prove that for the central parameter $c = -1$ , almost every random Julia set is totally disconnected with much smaller radial parameters r than expected. We also introduce several open questions worth discussing.

For $\\mathscr {B} \\subseteq \\mathbb {N} $ , the $ \\mathscr {B} $ -free subshift $ X_{\\eta } $ is the orbit closure of the characteristic function of the set of $ \\mathscr {B} $ -free integers. We show that many results about invariant measures and entropy, previously only known for the hereditary closure of $ X_{\\eta } $ , have their analogues for $ X_{\\eta } $ as well. In particular, we settle in the affirmative a conjecture of Keller about a description of such measures [G. Keller. Generalized heredity in $\\mathcal B$ -free systems. Stoch. Dyn. 21(3) (2021), Paper No. 2140008]. A central assumption in our work is that $\\eta ^{*} $ (the Toeplitz sequence that generates the unique minimal component of $ X_{\\eta } $ ) is regular. From this, we obtain natural periodic approximations that we frequently use in our proofs to bound the elements in $ X_{\\eta } $ from above and below.

We consider orthogonally invariant probability measures on $\\operatorname {\\mathrm {GL}}_n(\\mathbb {R})$ and compare the mean of the logs of the moduli of eigenvalues of the matrices with the Lyapunov exponents of random matrix products independently drawn with respect to the measure. We give a lower bound for the former in terms of the latter. The results are motivated by Dedieu and Shub [On random and mean exponents for unitarily invariant probability measures on $\\operatorname {\\mathrm {GL}}_n(\\mathbb {C})$ . Astérisque 287 (2003), xvii, 1–18]. A novel feature of our treatment is the use of the theory of spherical polynomials in the proof of our main result.

For every $r\\in \\mathbb {N}_{\\geq 2}\\cup \\{\\infty \\}$ , we prove a $C^r$ -orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with one-dimensional orientation preserving center bundle. To be precise, for such a diffeomorphism f, if a point y is chain attainable from x through pseudo-orbits, then for any neighborhood U of x and any neighborhood V of y, there exist true orbits from U to V by arbitrarily $C^r$ -small perturbations. As a consequence, we prove that for $C^r$ -generic diffeomorphisms in this class, periodic points are dense in the chain recurrent set, and chain transitivity implies transitivity.

For integers a and $b\\geq 2$ , let $T_a$ and $T_b$ be multiplication by a and b on $\\mathbb {T}=\\mathbb {R}/\\mathbb {Z}$ . The action on $\\mathbb {T}$ by $T_a$ and $T_b$ is called $\\times a,\\times b$ action and it is known that, if a and b are multiplicatively independent, then the only $\\times a,\\times b$ invariant and ergodic measure with positive entropy of $T_a$ or $T_b$ is the Lebesgue measure. However, it is not known whether there exists a non-trivial $\\times a,\\times b$ invariant and ergodic measure. In this paper, we study the empirical measures of $x\\in \\mathbb {T}$ with respect to the $\\times a,\\times b$ action and show that the set of x such that the empirical measures of x do not converge to any measure has Hausdorff dimension one and the set of x such that the empirical measures can approach a non-trivial $\\times a,\\times b$ invariant measure has Hausdorff dimension zero. Furthermore, we obtain some equidistribution result about the $\\times a,\\times b$ orbit of x in the complement of a set of Hausdorff dimension zero.