Invasive plants’ ability to extend their range depends upon their local environment and both positive and negative interactions with native species. Interactions between invasive and native plants may be indirectly linked to the soil fungal community, which may enhance or suppress invasion through mutualism or parasitism. Many invasive plants preferentially select fungal communities or change soil chemistry to gain a competitive advantage, and such changes can remain even after the invader is removed, known as legacy effects. Linaria vulgaris is an invasive forb that is aggressive in the Western U.S. but is non-aggressive in the Midwestern U.S. We evaluated the relationship between soil abiotic properties, nitrogen (N) enrichment, arbuscular mycorrhizal fungal (AMF) community composition and L. vulgaris invasion in aggressive (CO) and non-aggressive (IL) populations. We collected soil from uninvaded and invaded sites in Gothic, CO, and near Chicago, IL, and sequenced AMF community composition in each site. Using the same soil, we grew L. vulgaris and native species for 120 days, with half of pots receiving N-fertilization, and harvested biomass. We also injected a 15N-labelled tracer in pots and analyzed plant tissue for 15N enrichment and N uptake rates (NUR). In CO soil, L. vulgaris rhizomes sprouted more in invaded soil, whereas in IL soil, L. vulgaris only sprouted in uninvaded soil. N-fertilization had no impact on biomass and NUR did not differ significantly between any treatment. AMF communities differed between the two sites but were not significantly influenced by invasion history. Our results suggest that L. vulgaris leaves legacy effects, but that these effects are different between aggressive and non-aggressive populations. Legacy effects may facilitate reinvasion in CO, but we did not find conclusive evidence of legacy effects in IL, and differences between the sites could be shaped by endemic AMF communities.

Let $\mathcal {A}$ be an abelian length category containing a d-cluster tilting subcategory $\mathcal {M}$. We prove that a subcategory of $\mathcal {M}$ is a d-torsion class if and only if it is closed under d-extensions and d-quotients. This generalises an important result for classical torsion classes. As an application, we prove that the d-torsion classes in $\mathcal {M}$ form a complete lattice. Moreover, we use the characterisation to classify the d-torsion classes associated to higher Auslander algebras of type $\mathbb {A}$, and give an algorithm to compute them explicitly. The classification is furthermore extended to the setup of higher Nakayama algebras.

Relatively, recent work by Jeganathan (2008, Cowles Foundation Discussion Paper 1649) and Wang (2014, Econometric Theory, 30(3), 509–535) on generalized martingale central limit theorems (MCLTs) implicitly introduces a new class of instrument arrays that yield (mixed) Gaussian limit theory irrespective of the persistence level in the data. Motivated by these developments, we propose a new semiparametric method for estimation and inference in nonlinear predictive regressions with persistent predictors. The proposed method that we term chronologically trimmed least squares (CTLS) is comparable to the IVX method of Phillips and Magdalinos (2009, Econometric inference in the vicinity of unity. Mimeo, Singapore Management University) and yields conventional inference in regressions where the nature and extent of persistence in the data are uncertain. In terms of model generality, our contribution to the existing literature is twofold. First, our covariate model space allows for both nearly integrated (NI) and fractional processes (stationary and nonstationary) as a special case, while the vast majority of articles in this area only consider NI arrays. Second, we allow for nonlinear regression functions. The CTLS estimator is obtained by applying certain chronological trimming to the OLS instruments using appropriate kernel functions of time trend variables. In particular, the instruments under consideration are a generalized (averaged) version of those widely used for time-varying parameter (TVP) models. For the purposes of our analysis, we develop a novel asymptotic theory for sample averages of various processes weighted by such kernel functionals which is of independent interest and highly relevant to the TVP literature. Leveraging our nonlinear framework, we also provide an investigation on the effects of misbalancing on the predictability hypothesis. A new methodology is proposed to mitigate misbalancing effects. These methods are used for exploring the predictability of SP500 returns.