Rune Halvorsen Økland

On the variation explained by ordination and constrained ordination axes

Abstract. Total inertia (TI), the sum of eigenvalues for all ordination axes, is often used as a measure of total variation in a data set. By use of simulated data sets, I demonstrate that lack-of-fit of data to the response model implicit in any eigenvector ordination method results in polynomial distortion ordination axes, with eigenvalues that normally contribute 30–70% to TI (depending on data set properties). The amount of compositional variation extracted on ecologically interpretable ordination axes (structure axes) is thus underestimated by the eigenvalue-to-total-inertia ratio. I recommend that the current use of total inertia as a measure of compositional variation is discontinued. Eigenvalues of structure axes can, however, be used with some caution to indicate their relative importance. I also demonstrate that when the total inertia is partitioned on different sets of explanatory variables and unexplained variation by use of (partial) constrained ordination, (35) 50–85% of the variation ‘unexplained’ by the supplied explanatory variables represents lack-of-fit of data to model. Thus, the common interpretation of ‘unexplained variation’ as random variation (‘noise’) or coenoclinal variation caused by unmeasured explanatory variables, is generally inappropriate. I recommend a change of focus from the variation-explained-to-total inertia ratio and ‘unexplained’ variation to relative amounts of variation explained by different sets of explanatory variables.

Canonical Correspondence Analysis with variation partitioning: some comments and an application

. This study presents an alternative treatment of data from a comprehensive vegetation study in which the main gradient structure of boreal coniferous forest vegetation in southern Norway was investigated by ordination techniques. The data sets include vegetation samples of different plot sizes, supplied with measurements of 33 environmental explanatory variables (classified in four groups) and nine spatial explanatory variables derived from geographical coordinates. Partitioning the variation of the species-sample plot matrices on different sets of explanatory variables is performed by use of (partial) Canonical Correspondence Analysis. Several aspects of vegetation-environment relationships in the investigation area are discussed on the basis of results obtained by the new method. Generally, ca. 35% of the variation in species abundances are explained by environmental and spatial variables. The results indicate support for the hypothesis of macro-scale topographic control over the differentiation of the vegetation, more strongly so in pine than in spruce forest where soil nutrients play a major role. Towards finer scales, the primary topographical and topographically dependent factors lose importance, and vegetational differentiation is more strongly affected by the accumulated effects of the vegetation (including the tree stand) on soils, shading, litter fall, etc. The fraction of variation in species abundance explained by significant environmental variables was found to be ca. twice as large as the fraction explained by spatial variables. The fraction of variation explained by the supplied variables differed between data sets; it was lower for cryptogams than for vascular plants, and lower for smaller than for larger sample plots. Possible reasons for these patterns are discussed. Some methodological aspects of CCA with variation partitioning are discussed: improvements, necessary precautions, and the advantages over alternative methods.

Disturbance severity and community resilience in a boreal forest

We studied the resilience of southeastern Norwegian old-growth Picea abies forest floor vegetation to experimental disturbance. Five treatments, differing in depth of removal of vegetation and soil layers and making up a gradient in disturbance severity, and three controls, were replicated 10 times. The experiment was analyzed with respect to the full species composition before and for seven years after treatment. The soil-buried propagule bank and local environmental conditions were recorded before treatment. Total cover of vascular plants and bryophytes and lichens increased slowly after treatment and was still below pre-disturbance levels after seven years. The rate of succession, measured as change in floristic dissimilarity between recordings made in successive years, declined with time for all treatments. The magnitude of vegetation change was strongly influenced by disturbance severity. DCA ordination revealed a main gradient in species composition from undisturbed forest floor to severely disturbed vegetation three years after disturbance, while in the fourth year, the direction of vegetation change turned in the direction of pre- disturbance positions. The turning point represented the maximum abundance of pioneer species (e.g., Luzula pilosa and Pohlia nutans) relative to dominant species before the disturbance (e.g., Dicranum majus and Hylocomium splendens). The return to pre-distur- bance positions from the fourth year was, however, slow and will probably take 5-25 more years to be completed if current trends continue. DCA ordination revealed two additional, interpretable, gradients in vegetation; one related to pulses of regeneration from the soil- buried propagule bank; the other represented a gradient in pre-disturbance environmental conditions. We demonstrate that one vegetation gradient related to time after disturbance is insufficient to account for the full complexity of revegetation processes following dis- turbance.

Data manipulation and gradient length estimation in DCA ordination

The effects of different kinds of data manipu- lation on gradient length estimation by non-linear rescal- ing (as in DCA ordination) are evaluated by considering the first axis in DCA ordinations of 11 field data sets from four investigations. Gradient length estimates are de- pendent on the range of the abundance scale; the more the scale favours the quantitative aspect (abundance) of the data over the qualitative aspect (presence), the longer the DCA axes. The gradient length estimate decreases when infre- quent species are deleted. A new formula is proposed to replace the option for downweighting of rare species in DCA, as the option presently available has some undesir- able properties. Some implications for interpretation of gradient length estimates by non-linear rescaling in gen- eral (and in DCA in particular) and for comparison of gradient length estimates between studies, are discussed. The potential of non-linear rescaling of gradients for estimation of P3 diversity is emphasized.

Dynamics of understory vegetation in an old-growth boreal coniferous forest, 1988 -1993

. Understorey vegetation changes in a South Norwegian old-growth coniferous forest were studied between 1988 and 1993 in 200 1-m2 vegetation plots. Our aims were to quantify the amount of between-year compositional change, and to elaborate the environmental basis for long-term vegetation change, including the previously identified gradient structure with a major gradient related to topography (and soil nutrient status and soil depth) and a minor gradient reflecting paludification and canopy coverage. Species richness (yearly mean and cumulative species number) and change in species richness differed between vascular plants and cryptogams, and between forest types. The number of vascular plant species decreased in pine forest in dry years; bryophyte species number increased in spruce forest. Statistically significant vegetation change, as tested by constrained ordination (CCA) with time as the constraining variable, is demonstrated for most one-year periods and for the five-year period in most forest types. Vegetation change along identified gradients, measured as plot displacement along DCA ordination axes, also occurred. The magnitude of year-to-year vegetation change was related neither to forest type nor to one-year period; different responses to climatic and environmental change were observed in each forest type. The largest average displacement observed, from medium-rich spruce forest towards poor spruce forest, was interpreted as a long-term trend. Humus-layer pH decreased by ca. 0.25 units from 1988 to 1993, most strongly in medium-rich spruce forest where exchangeable Ca decreased and Al and Mn increased strongly. Our study supports the hypothesis that vascular plants show a long-term and broad-scale response to soil acidification. Change in bryophyte composition is linked to some very long growing-seasons. Detailed analysis of short-term vegetation dynamics enhances the interpretation of long-term changes and stresses the complementarity of univariate and multivariate methods in the analysis of vegetation change.

Population Biology of the Clonal Moss Hylocomium Splendens in Norwegian Boreal Spruce Forests. I. Demography

1 Hylocomium splendens is a perennial clonal moss with annual periodicity in the emergence of new modules. New growing points usually emerge in spring and develop into mature segments their second summer. Population increase is brought about by ramification (branching) of the youngest segment or by regeneration from older parts of the shoot system. 2 A technique for nondestructive re-identification of segments in permanent plots is devised. Precise demographic information on 9206 growing points and 7602 mature segments was obtained by following 119 local populations in seven Norwegian reference areas for monitoring during 3 years. The dry weight of each mature segment was estimated from morphological field measurements. 3 The potential of each mature segment for production of new growing points was strongly size-dependent; c. 40% of the variation in a segments size was explained by the size of its mother segment. Integration within segment chains was largely restricted to neighbouring segments. The number offspring growing points (by ramification as well as regeneration) was positively size-dependent, while termination risk was negatively size-dependent. Mature segments produced by regeneration were smaller, while segments produced by ramification were larger than the average segment. Strong apical dominance was demonstrated. 4 Mortality and branching rates, averaged over populations, areas and years, are reported. Annual recruitment was 32.3%; 23.3% by regeneration, 7.5% by ramification, and 1.5% by accidentally introduced shoots. Annual mortality was 19.7%. 6.8% by loss, 1.9% by grazing, and 1 1.0% by termination for other reasons. 5 Demographic data for growing points and mature segments were analysed separately by stage-structured transition matrix models. The total population increased every year (average A = 1.10-1.11). Vital rates were strongly size-dependent. The contributions of ramification and regeneration to increase in i were equal as ramification occurred in large segments with high probability for survival. 6 Ramification is considered important for maintenance of size and risk-spreading among ramets under favourable conditions, while high regenerative ability facilitates resilience to, and recovery after, disturbance. The ecological significance of size is discussed. 7 Hylocomium splendens is closely similar to clonal forest vascular plants in major demographic traits, e.g. size-dependence of fitness and branching patterns.

Revegetation following experimental disturbance in a boreal old-growth Picea abies forest

. We studied revegetation patterns after experimental fine-scale disturbance (e.g. uprooting) in an old-growth Picea abies forest in southeastern Norway. An experimental severity gradient was established by manipulation of the depth of soil disturbance; two types of disturbed areas were used. Species recovery was recorded in the disturbed patches in three successive years after disturbance. The cover of vascular plants and, even more so the cover of bryophytes and lichens, recovered slowly after disturbance. The least severe treatments (removal of vegetation and removal of vegetation and the litter layer) was followed by the fastest recovery. The mean number of vascular plant species was usually higher three years after disturbance than before disturbance, while the opposite was true for bryophytes. Several vascular plant species that were abundant in intact forest floor vegetation (Vaccinium myrtillus, V. vitis-idaea and Deschampsia flexuosa) recovered during a three-year period primarily by resprouting from intact rhizomes and clonal in-growth. Other important recovery mechanisms included germination from a soil-buried propagule bank (e.g. Luzula pilosa, Plagiothecium laetum agg., Pohlia nutans and Polytrichum spp.) and dispersal of propagules into the disturbed patches (e.g. Betula pubescens and Picea abies). Microsite limitation seemed to occur in several species that were abundant in the soil propagule bank (e.g. the ferns Athyrium filix-femina, Gymnocarpium dryopteris and Phegopteris connectilis) but which did not appear in disturbed patches. Disturbance severity influenced revegetation patterns, recorded both as trajectories of vegetation composition in a DCA ordination space and as change in floristic dissimilarity. The length of the successional path (compositional change measured in β-diversity units) increased with increasing disturbance severity, and was also influenced by the area of the disturbed patch and the distance to intact vegetation. The rate of succession depended on the method by which it was measured; decreasing year by year in floristic space, while first decreasing and then increasing in ordination space. The reason for this difference is explained.

Patterns of bryophyte associations at different scales in a Norwegian boreal spruce forest

. Patterns of associations between 36 bryophytes and their relationships with trends in α- and β-diversity were studied at five spatial scales (from 1 m2 to 1/256 m2) in a Norwegian boreal spruce forest. The range and dispersion of α-diversity values in the data were significantly higher than in comparable model data sets, indicating varation from favourable to unfavourable conditions for bryophytes at all scales, particularly with increasing cover of the upper layers. The number of positive associations was significantly higher than predicted from a random distribution, for all sample plot sizes except the smallest. For the most frequent species, this number decreased with decreasing sample plot size. The excess of positive associations was due to the presence of (1) α-diversity trends, as demonstrated by a stochastic simulation, and (2) β-diversity (variation along environmental gradients). A microscale coenocline from dominance of large forest floor mosses to small liverworts, is added to two broad-scale coenoclines demonstrated earlier. Facilitation - positive density-dependence caused by more favourable moisture conditions within dense stands - is discussed as a possible third cause of excess positive associations. The number of significant negative associations was generally low, and deviated neither from theoretical values assuming random distribution of species, nor from predicted values accounting for α-diversity trends. The low proportion of negative associations, even in the presence of β-diversity trends, suggests that interspecific competition is not important in this vegetation. Several alternatives to competition are discussed; (1) static mechanisms for avoidance of competition, (2) mobility, and (3) the importance of density-independent mortality, in particular due to fine-scale disturbance. Simulation studies for assessing the effects of α-diversity trends on species associations are emphasized.

Species response curves along environmental gradients. A case study from SE Norwegian swamp forests

Abstract Vegetation science has relied on untested paradigms relating to the shape of species response curves along environmental gradients. To advance in this field, we used the HOF approach to model response curves for 112 plant species along six environmental gradients and three ecoclines (as represented by DCA ordination axes) in SE Norwegian swamp forests. Response curve properties were summarized in three binary response variables: (1) model unimodal or monotonous (determinate) vs. indeterminate; (2) for determinate models, unimodal vs. monotonous and (3) for unimodal models, skewed vs. symmetric. We used logistic regression to test the influence, singly and jointly, of seven predictor variables on each of three response variables. Predictor variables included gradient type (environmental or ecocline) and length (compositional turnover); species category (vascular plant, moss, Sphagnum or hepatic), species frequency and richness, tolerance (the fraction of the gradient along which the species occurs) and position of species along each gradient. The probability for fitting a determinate model increased as the main occurrence of species approached gradient extremes and with increasing species tolerance and frequency and gradient length. Appearance of unimodal models was favoured by low species tolerance and disfavoured by closeness of species to gradient extremes. Appearance of skewed models was weakly related to predictors but was slightly favoured by species optima near gradient extremes. Contrary to the results of previous studies, species category, gradient type and variation in species richness along gradients did not contribute independently to model prediction. The overall best predictors of response curve shape were position along the gradient (relative to extremes) and tolerance; the latter also expressing gradient length in units of compositional turnover. This helps predicting species responses to gradients from gradient specific species properties. The low proportion of skewed response curves and the large variation of species response curves along all gradients indicate that skewed response curves is a smaller problem for the performance of ordination methods than often claimed. We find no evidence that DCA ordination increases the unimodality, or symmetry, of species response curves more than expected from the higher compositional turnover along ordination axes. Thus ordination axes may be appropriate proxies for ecoclines, applicable for use in species response modelling. Abbreviations: GAM = Generalized Additive Model; GLM = Generalized linear model; HOF = Huisman-Olff-Fresco; LNMDS = Local Non-metric Multidimensional Scaling. Nomenclature: Lid & Lid (1994); Frisvoll et al. (1995); Krog et al. (1994), except for Polytrichastrum G.L.Sm., which is not recognized as distinct from Polytrichum Hedw. Several groups of related taxa were treated collectively.

Population Biology of the Clonal Moss Hylocomium Splendens in Norwegian Boreal Spruce Forests. II. Effects of Density

1 Hylocomium splendens is a perennial clonal moss in which new modules may emerge annually by ramification of the current mature segment or by regeneration, the time-delayed development from dormant buds. Demographic information on 14 776 growing points was obtained by following 119 Norwegian boreal spruce forest populations for 5 years. The dry weight of each mature segment was estimated from morphological field measurements. 2 The mean size of mature segments was positively correlated with the density (cover) of the bryophyte layer; a density increase from 0 to 100% was associated with a doubling in mean size. This relationship is attributed to the improved moisture conditions, and hence to prolonged periods with positive net photosynthesis, in dense stands. Mean size was not significantly related to the density of Hylocomium splendens growing points, suggesting that interactions in bryophyte stands are mainly with neighbours regardless of species. 3 The frequency of regeneration declined with increasing density, notably when the effects of segment size were corrected for. Negative density-dependence of regeneration is considered to be due to reduction of light-induced bud initiation in dense stands. 4 The size-corrected mortality (termination and loss) rate was not related to density. Danger of burial in the moss carpet, causing about one tenth of all terminations and losses, increased strongly with density and affected c. 5% of all growing points at high densities. 5 At high densities, Hylocomium splendens populations are not regulated by a negative relationship between size and density, but by a combination of reduced branching (ramification and regeneration) and increased danger of burial in the bryophyte carpet. However, such high densities are infrequent in the forest floor (affecting less than 10% of the area investigated). It is suggested that differences in history due to finescale disturbance and microenvironmental variation are reflected in size differences of individual Hylocomium splendens segments, and that this is the major factor that keeps boreal forest bryophyte populations at low densities.