Application Fields of the Empirical Regression - A Case Study

Empirical regression is defined as conditional expected value based on an estimation of a twodimensional density. It is a modelfree mathematical means for a first evaluation of measured data of an unknown stochastical relation between two quantities. The numerical procedures may be applied for calculation of the mean course of an unknown relation hidden in the measured data. Disregarding the statistical background an other aspect of application is the analyzing of time series, especially smoothing of time series and modelfree recording of the trend component in non-stationary time series. The calculated regression curve provides an objective basis for comparing of different measured courses as well as for a further evaluation, e. g. in respect of a suitable choice of an analytical expression. The possibility of interpolation and the smoothing properties of empirical regression give essential advantages for internal regression as one step in the process of model construction.     

Climate‐induced changes in the distribution of freshwater fish: observed and predicted trends

1. Climate change could be one of the main threats faced by aquatic ecosystems and freshwater biodiversity. Improved understanding, monitoring and forecasting of its effects are thus crucial for researchers, policy makers and biodiversity managers. 2. Here, we provide a review and some meta‐analyses of the literature reporting both observed and predicted climate‐induced effects on the distribution of freshwater fish. After reviewing three decades of research, we summarise how methods in assessing the effects of climate change have evolved, and whether current knowledge is geographically or taxonomically biased. We conducted multispecies qualitative and quantitative analyses to find out whether the observed responses of freshwater fish to recent changes in climate are consistent with those predicted under future climate scenarios. 3. We highlight the fact that, in recent years, freshwater fish distributions have already been affected by contemporary climate change in ways consistent with anticipated responses under future climate change scenarios: the range of most cold‐water species could be reduced or shift to higher altitude or latitude, whereas that of cool‐ and warm‐water species could expand or contract. 4. Most evidence about the effects of climate change is underpinned by the large number of studies devoted to cold‐water fish species (mainly salmonids). Our knowledge is still incomplete, however, particularly due to taxonomic and geographic biases. 5. Observed and expected responses are well correlated among families, suggesting that model predictions are supported by empirical evidence. The observed effects are of greater magnitude and show higher variability than the predicted effects, however, indicating that other drivers of changes may be interacting with climate and seriously affecting freshwater fish. 6. Finally, we suggest avenues of research required to address current gaps in what we know about the climate‐induced effects on freshwater fish distribution, including (i) the need for more long‐term data analyses, (ii) the assessment of climate‐induced effects at higher levels of organisation (e.g. assemblages), (iii) methodological improvements (e.g. accounting for uncertainty among projections and species’ dispersal abilities, combining both distributional and empirical approaches and including multiple non‐climatic stressors) and (iv) systematic confrontation of observed versus predicted effects across multi‐species assemblages and at several levels of biological organisation (i.e. populations and assemblages).     

Invasion facilitates hybridization with introgression in the Rattus rattus species complex

Biological invasions result in novel species interactions, which can have significant evolutionary impacts on both native and invading taxa. One evolutionary concern with invasions is hybridization among lineages that were previously isolated, but make secondary contact in their invaded range(s). Black rats, consisting of several morphologically very similar but genetically distinct taxa that collectively have invaded six continents, are arguably the most successful mammalian invaders on the planet. We used mitochondrial cytochrome b sequences, two nuclear gene sequences (Atp5a1 and DHFR) and nine microsatellite loci to examine the distribution of three invasive black rat lineages (Rattus tanezumi, Rattus rattus I and R. rattus IV) in the United States and Asia and to determine the extent of hybridization among these taxa. Our analyses revealed two mitochondrial lineages that have spread to multiple continents, including a previously undiscovered population of R. tanezumi in the south‐eastern United States, whereas the third lineage (R. rattus IV) appears to be confined to Southeast Asia. Analyses of nuclear DNA (both sequences and microsatellites) suggested significant hybridization is occurring among R. tanezumi and R. rattus I in the United States and also suggest hybridization between R. tanezumi and R. rattus IV in Asia, although further sampling of the latter species pair in Asia is required. Furthermore, microsatellite analyses suggest unidirectional introgression from both R. rattus I and R. rattus IV into R. tanezumi. Within the United States, introgression appears to be occurring to such a pronounced extent that we were unable to detect any nuclear genetic signal for R. tanezumi, and a similar pattern was detected in Asia.     

Quantitative study and modelling of the litter decomposition in a European alluvial forest. Is there an influence of overstorey tree species on the decomposition of ivy litter (Hedera helix L.)?

The influence on the decomposition rate of ivy litter (Hedera helix L.) of three ligneous overstorey species (oak, Quercus robur L., white poplar, Populus alba and ash, Fraxinus excelsior L.) that support ivy was studied in an alluvial hardwood forest. The ivy provides an abundant litter at the end of spring. The decomposition of ivy litter and the nutrient release rate were analyzed over four months during the growing season of the canopy trees, the hypothesis being that throughfall could slow down the mass loss rate of ivy depending on the support species. Mathematical models for mass loss and nutrient (P, N, K and Mg) release rates were developed. Mass loss rate and the release rate of magnesium, nitrogen and phosphorus show significant differences depending on species whereas no influence of species was observed on the release rate of potassium. The results illustrate the significant effect of oak compared to ash and poplar in slowing down mass loss rate and nitrogen, phosphorus and magnesium release rates. The mass loss rate over time under the three species followed the proposed exponential model, whereas the release rates of phosphorus and magnesium did not follow this model. This model is fitted to the data in two cases out of three for potassium. Magnesium and potassium are released more rapidly when nitrogen accumulates and the phosphorus content does not change significantly. No species × date interaction was observed, except in the case of magnesium. The species effect is interpreted as an effect of composition of throughfalls and presence or absence of inhibitory substances such as phenolic compounds.     

Species Invasiveness in Biological Invasions: A Modelling Approach

The study of invasiveness, the traits that enable a species to invade a habitat, and invasibility, the habitat characteristics that determine its susceptibility to the establishment and spread of an invasive species, provide a useful conceptual framework to formulate the biological invasion problem in a modelling context. Another important aspect is the complex interaction emerging among the invader species, the noninvader species already present in the habitat, and the habitat itself. Following a modelling approach to the biological invasion problem, we present a spatially explicit cellular automaton model (Interacting Multiple Cellular Automata (IMCA)). We use field parameters from the invader Gleditsia triacanthos and the native Lithraea ternifolia in montane forests of central Argentina as a case study to compare outputs and performance of different models. We use field parameters from another invader, Ligustrum lucidum, and the native Fagara coco from the same system to run the cellular automaton model. We compare model predictions with invasion values from aerial photographs. We discuss in detail the importance of factors affecting species invasiveness, and give some insights into habitat invasibility and the role of interactions between them. Finally, we discuss the relevance of mathematical modelling for studying and predicting biological invasions. The IMCA model provided a suitable context for integrating invasiveness, invasibility, and the interactions. In the invasion system studied, the presence of an invader's juvenile bank not only accelerated the rate of invasion but was essential to ensure invasion. Using the IMCA model, we were able to determine that not only adult survival but particularly longevity of the native species influenced the spread velocity of the invader, at least when a juvenile bank is present. Other factors determining velocity of invasion detected by the IMCA model were seed dispersal distance and age of reproductive maturity. We derived relationships between species' adult survival, fecundity and longevity of both theoretical and applied relevance for biological invasions. Invasion velocities calculated from the aerial photographs agreed well with predictions of the IMCA model.     

Predictable changes in trophic community structure along a spatial disturbance gradient in streams

1. We assessed insect and resource standing stocks along a spatial gradient of flood disturbance in 19 sub-alpine Swedish streams to test the prediction that change in trophic structure arises from the joint action of disturbance, which affect basal resources, and resource-control, which ties the response of the consumers to the response of the resources.
2. Trophic structure, quantified as scores of non-metric multidimensional scaling based on the biomass of insect trophic groups, changed predictably along the disturbance gradient. In early summer, predators and algae feeders decreased relative to suspension feeders with increasing disturbance; in autumn, algae feeders decreased relative to leaf feeders with increasing disturbance.
3. Across the disturbance gradient, the biomass of algae-, deposit- and leaf-feeders was principally controlled by the availability of the respective resource (algae, fine detritus and coarse detritus), while disturbance only had subsidiary effects on algae feeders in early summer.
4. Overall, patterns in trophic-group biomass along the disturbance gradient were more likely to reflect indirect effects of disturbance via impact on the resources, which reverberated to the consumers because of resource-control, rather than direct effects. In contrast with the view that stream communities are the result of stochastic colonization following disturbance events, in the study streams the trophic structure of insect assemblages is predictable and partly organized by resource-control across a broad range of disturbance conditions.     

An optimized differential heat conduction solution microcalorimeter for thermal kinetic measurements

Heat conduction calorimeters are widely used in biological sciences, but baseline instability, low resolution, electrical noise and motion artifacts have limited their utility. Two main sources of noise, baseline fluctuation or drift and a motion artifact, were traced to amplifier drift, a small (0.015°C) gradient within the constant temperature cylinder, and the method of installing the thermopiles. The addition of heaters to the top and bottom of the cylinder reduced the gradient to approximately 0.003°C and greatly reduced the slow component of the motion artifact. The drift error was reduced by proper mounting of the amplifier and its external components and the enclosure of the calorimeter in a temperature-controlled box.An R-C model of the heat flow in the calorimeter was developed which was employed to discover several means of increasing sensitivity without increasing the rise-time of the calorimeter. Analysis, also based on the model, showed that variations in the air gap between the cell holder can be a major source of error when the calorimeter is used to investigate the kinetics of a chemical reaction. This analysis also showed that the time for the heat to flow through the solution through the solution in the cell can be the dominant factor in determining the rise-time of the instrument.The heat conduction calorimeter described here has improved characterics: a baseline stability of 200 nJ · s^?1 (peak-to-peak) over a 48 h period; a resolution of 200 nJ · s^?1; a sensitivity of 6.504 ± 0.045 J · V^?1 · s^?1 referred to the sensor output; and a rise-time of 122 s for the 10–90% response.