Structure and stability of genetic variance-covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three-spined stickleback.

The genetic variance-covariance matrix (G) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G-matrices is limited for two reasons. First, phenotypes are high-dimensional, whereas traditional statistical methods are tuned to estimate and analyse low-dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high-dimensional G-matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half-sib breeding design of three-spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low-temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability-as well as the similarity among G-matrices-may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G-matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G, they also illustrate that by enabling the estimation of large G-matrices, the BSFG method can improve predicted evolutionary responses to selection.

Evolution, plasticity and evolving plasticity of phenology in the tree species Alnus glutinosa.

Both traits and the plasticity of these traits are subject to evolutionary change and therefore affect the long-term persistence of populations and their role in local communities. We subjected clones from 12 different populations of Alnus glutinosa, located along a latitudinal gradient, to two different temperature treatments, to disentangle the distribution of genetic variation in timing of bud burst and bud burst plasticity within and among genotypes, populations, and regions. We calculated heritability and evolvability estimates for bud burst and bud burst plasticity and assessed the influence of divergent selection relative to neutral drift. We observed higher levels of heritability and evolvability for bud burst than for its plasticity, whereas the total phenological heritability and evolvability (i.e. combining timing of bud burst and bud burst plasticity) suggest substantial evolutionary potential with respect to phenology. Earlier bud burst was observed for the low-latitudinal populations than for the populations from higher latitudes, whereas the high-latitudinal populations did not show the expected delayed bud burst. This countergradient variation can be due to evolution towards increased phenological plasticity at higher latitudes. However, because we found little evidence for adaptive differences in phenological plasticity across the latitudinal gradient, we suggest differential frost tolerance as the most likely explanation for the observed phenological patterns in A. glutinosa.

Invasion rate of deer ked depends on spatiotemporal variation in host density.

Invasive parasites are of great global concern. Understanding the factors influencing the spread of invading pest species is a first step in developing effective countermeasures. Growing empirical evidence suggests that spread rates are essentially influenced by spatiotemporal dynamics of host-parasite interactions, yet approaches modelling spread rate have typically assumed static environmental conditions. We analysed invasion history of the deer ked (Lipoptena cervi) in Finland with a diffusion-reaction model, which assumed either the movement rate, the population growth rate, or both rates may depend on spatial and temporal distribution of moose (Alces alces), the main host of deer ked. We fitted the model to the data in a Bayesian framework, and used the Bayesian information criterion to show that accounting for the variation in local moose density improved the model's ability to describe the pattern of the invasion. The highest ranked model predicted higher movement rate and growth rate of deer ked with increasing moose density. Our results suggest that the historic increase in host density has facilitated the spread of the deer ked. Our approach illustrates how information about the ecology of an invasive species can be extracted from the spatial pattern of spread even with rather limited data.

Bringing habitat information into statistical tests of local adaptation in quantitative traits: a case study of nine-spined sticklebacks.

Detection of footprints of historical natural selection on quantitative traits in cross-sectional data sets is challenging, especially when the number of populations to be compared is small and the populations are subject to strong random genetic drift. We extend a recent Bayesian multivariate approach to differentiate between selective and neutral causes of population differentiation by the inclusion of habitat information. The extended framework allows one to test for signals of selection in two ways: by comparing the patterns of population differentiation in quantitative traits and in neutral loci, and by comparing the similarity of habitats and phenotypes. We illustrate the framework using data on variation of eight morphological and behavioral traits among four populations of nine-spined sticklebacks (Pungitius pungitius). In spite of the strong signal of genetic drift in the study system (average FST = 0.35 in neutral markers), strong footprints of adaptive population differentiation were uncovered both in morphological and behavioral traits. The results give quantitative support for earlier qualitative assessments, which have attributed the observed differentiation to adaptive divergence in response to differing ecological conditions in pond and marine habitats.

DRIFTSEL: an R package for detecting signals of natural selection in quantitative traits.

Approaches and tools to differentiate between natural selection and genetic drift as causes of population differentiation are of frequent demand in evolutionary biology. Based on the approach of Ovaskainen et al. (2011), we have developed an R package (DRIFTSEL) that can be used to differentiate between stabilizing selection, diversifying selection and random genetic drift as causes of population differentiation in quantitative traits when neutral marker and quantitative genetic data are available. Apart from illustrating the use of this method and the interpretation of results using simulated data, we apply the package on data from three-spined sticklebacks (Gasterosteus aculeatus) to highlight its virtues. DRIFTSEL can also be used to perform usual quantitative genetic analyses in common-garden study designs.

Roots and associated fungi drive long-term carbon sequestration in boreal forest.

Boreal forest soils function as a terrestrial net sink in the global carbon cycle. The prevailing dogma has focused on aboveground plant litter as a principal source of soil organic matter. Using (14)C bomb-carbon modeling, we show that 50 to 70% of stored carbon in a chronosequence of boreal forested islands derives from roots and root-associated microorganisms. Fungal biomarkers indicate impaired degradation and preservation of fungal residues in late successional forests. Furthermore, 454 pyrosequencing of molecular barcodes, in conjunction with stable isotope analyses, highlights root-associated fungi as important regulators of ecosystem carbon dynamics. Our results suggest an alternative mechanism for the accumulation of organic matter in boreal forests during succession in the long-term absence of disturbance.

Environmentally induced dispersal-related life-history syndrome in the tropical butterfly, Bicyclus anynana.

Dispersal is a key process for understanding the persistence of populations as well as the capacity of organisms to respond to environmental change. Therefore, understanding factors that may facilitate or constrain the evolution of dispersal is of crucial interest. Assessments of phenotypic variation in various behavioural, physiological and morphological traits related to insect dispersal and flight performance are common, yet very little is known about the genetic associations among these traits. We have used experiments on the butterfly Bicyclus anynana to estimate genetic variation and covariation in seven behavioural, physiological and morphological traits related to flight potential and hence dispersal. Our goal was to characterize the heritabilities and genetic correlations among these traits and thus to understand more about the evolution of dispersal-related life-history syndromes in butterflies. Using a version of the animal model, we showed that all of the traits varied between the sexes, and most were either positively or negatively (phenotypically and/or genetically) correlated with body size. Heritable variation was present in most traits, with the highest heritabilities estimated for body mass and thorax ratio. The variance in flight activity among multiple measurements for the same individual was high even after controlling for the prevailing environmental conditions, indicating the importance of behavioural switching and/or inherent randomness associated with this type of movement. A number of dispersal-related traits showed phenotypic correlations among one another, but only a few of these were associated with significant genetic correlations indicating that covariances between these traits in Bicyclus anynana are mainly environmentally induced.

Bayesian approaches in evolutionary quantitative genetics.

The study of evolutionary quantitative genetics has been advanced by the use of methods developed in animal and plant breeding. These methods have proved to be very useful, but they have some shortcomings when used in the study of wild populations and evolutionary questions. Problems arise from the small size of data sets typical of evolutionary studies, and the additional complexity of the questions asked by evolutionary biologists. Here, we advocate the use of Bayesian methods to overcome these and related problems. Bayesian methods naturally allow errors in parameter estimates to propagate through a model and can also be written as a graphical model, giving them an inherent flexibility. As packages for fitting Bayesian animal models are developed, we expect the application of Bayesian methods to evolutionary quantitative genetics to grow, particularly as genomic information becomes more and more associated with environmental data.

Spatially structured metapopulation models: global and local assessment of metapopulation capacity.

We model metapopulation dynamics in finite networks of discrete habitat patches with given areas and spatial locations. We define and analyze two simple and ecologically intuitive measures of the capacity of the habitat patch network to support a viable metapopulation. Metapopulation persistence capacity lambda(M) defines the threshold condition for long-term metapopulation persistence as lambda(M)>delta, where delta is defined by the extinction and colonization rate parameters of the focal species. Metapopulation invasion capacity lambda(I) sets the condition for successful invasion of an empty network from one small local population as lambda(I)>delta. The metapopulation capacities lambda(M) and lambda(I) are defined as the leading eigenvalue or a comparable quantity of an appropriate "landscape" matrix. Based on these definitions, we present a classification of a very general class of deterministic, continuous-time and discrete-time metapopulation models. Two specific models are analyzed in greater detail: a spatially realistic version of the continuous-time Levins model and the discrete-time incidence function model with propagule size-dependent colonization rate and a rescue effect. In both models we assume that the extinction rate increases with decreasing patch area and that the colonization rate increases with patch connectivity. In the spatially realistic Levins model, the two types of metapopulation capacities coincide, whereas the incidence function model possesses a strong Allee effect characterized by lambda(I)=0. For these two models, we show that the metapopulation capacities can be considered as simple sums of contributions from individual habitat patches, given by the elements of the leading eigenvector or comparable quantities. We may therefore assess the significance of particular habitat patches, including new patches that might be added to the network, for the metapopulation capacities of the network as a whole. We derive useful approximations for both the threshold conditions and the equilibrium states in the two models. The metapopulation capacities and the measures of the dynamic significance of particular patches can be calculated for real patch networks for applications in metapopulation ecology, landscape ecology, and conservation biology.

The metapopulation capacity of a fragmented landscape.

Ecologists and conservation biologists have used many measures of landscape structure to predict the population dynamic consequences of habitat loss and fragmentation, but these measures are not well justified by population dynamic theory. Here we introduce a new measure for highly fragmented landscapes, termed the metapopulation capacity, which is rigorously derived from metapopulation theory and can easily be applied to real networks of habitat fragments with known areas and connectivities. Technically, metapopulation capacity is the leading eigenvalue of an appropriate 'landscape' matrix. A species is predicted to persist in a landscape if the metapopulation capacity of that landscape is greater than a threshold value determined by the properties of the species. Therefore, metapopulation capacity can conveniently be used to rank different landscapes in terms of their capacity to support viable metapopulations. We present an empirical example on multiple networks occupied by an endangered species of butterfly. Using this theory, we may also calculate how the metapopulation capacity is changed by removing habitat fragments from or adding new ones into specific spatial locations, or by changing their areas. The metapopulation capacity should find many applications in metapopulation ecology, landscape ecology and conservation biology.