Phenotype-environment correlations in a putative whitefish adaptive radiation

1. The adaptive radiation of fishes into benthic (littoral) and pelagic (lentic) morphs in post-glaciallakes has become an important model system for speciation. Although these systems are well stud-ied, there is little evidence of the existence of morphs that have diverged to utilize resources in theremaining principal lake habitat, the profundal zone.
2. Here, we tested phenotype-environment correlations of three whitefish (Coregonus lavaretus)morphs that have radiated into littoral, pelagic and profundal niches in northern Scandinavianlakes. We hypothesized that morphs in such trimorphic systems would have a morphology adaptedto one of the principal lake habitats (littoral, pelagic or profundal niches). Most whitefish popula-tions in the study area are formed by a single (monomorphic) whitefish morph, and we furtherhypothesized that these populations should display intermediate morphotypes and niche utiliza-tion. We used a combination of traditional (stomach content, habitat use, gill raker counts) andmore recently developed (stable isotopes, geometric morphometrics) techniques to evaluate pheno-type-environment correlations in two lakes with trimorphic and two lakes with monomorphicwhitefish.
3. Distinct phenotype-environment correlations were evident for each principal niche in whitefishmorphs inhabiting trimorphic lakes. Monomorphic whitefish exploited multiple habitats, hadintermediate morphology, displayed increased variance in gillraker-counts, and relied significantlyon zooplankton, most likely due to relaxed resource competition.
4. We suggest that the ecological processes acting in the trimorphic lakes are similar to each other,and are driving the adaptive evolution of whitefish morphs, possibly leading to the formation ofnew species.

Moving window kernel PCA for adaptive monitoring of nonlinear processes

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.