Items 1-20 of 411

• Journal Article

#### Knowledge of Student Teachers on Sustainable Land Use Issues–Knowledge Types Relevant for Teacher Education ﻿

Sustainability 2020; 12(20) p.1-20: Art. 8332
For restructuring educational processes and institutions toward Sustainable Development, teachers’ knowledge and competences are crucial. Due to the high relevance of teachers’ content knowledge, this study aimed to (i) assess Sustainable Development-relevant knowledge by differentiating between situational, conceptual and procedural knowledge, (ii) find out via item response theory modelling how these theoretically distinguished knowledge types can be empirically supported, and (iii) link the knowledge dimension(s) to related constructs. We developed a paper-and-pencil test to assess these three knowledge types (N = 314). A two-dimensional structure that combines situational and conceptual knowledge and that distinguishes situational/conceptual knowledge from procedural knowledge, fits the data best (EAP/PV situational/conceptual: 0.63; EAP/PV procedural: 0.67). Student teachers at master level outperformed bachelor level students in situational/conceptual knowledge but master level students did not differ from students at bachelor level regarding procedural knowledge. We observed only slight correlations between the two knowledge dimensions and the content-related motivational orientations of professional action competence. Student teachers’ deficits in procedural knowledge can be attributed to the small number of Education for Sustainable Development-relevant courses attended. Systematically fostering procedural knowledge in teacher education could promote achieving cognitive learning objectives associated with Sustainable Development Goals in the long term.
• Journal Article

#### Selection markers for transformation of the sequenced reference monokaryon Okayama 7/#130 and homokaryon AmutBmut of Coprinopsis cinerea ﻿

Fungal Biology and Biotechnology. 2020 Oct 12;7(1):15
• Journal Article

#### Validating the Efficiency of the FeS$_2$ Method for Elucidating the Mechanisms of Contaminant Removal Using Fe$_0$/H$_2$O Systems ﻿

Processes 2020; 8(9) p.1-16: Art. 1162
There is growing interest in using pyrite minerals (FeS$_2$) to enhance the efficiency of metallic iron (Fe$^0$) for water treatment (Fe$^0$/H$_2$O systems). This approach contradicts the thermodynamic predicting suppression of FeS$_2$ oxidation by Fe$^0$ addition. Available results are rooted in time series correlations between aqueous and solid phases based on data collected under various operational conditions. Herein, the methylene blue method (MB method) is used to clarify the controversy. The MB method exploits the differential adsorptive affinity of MB onto sand and sand coated with iron corrosion products to assess the extent of Fe$^0$ corrosion in Fe$^0$/H$_2$O systems. The effects of the addition of various amounts of FeS$_2$ to a Fe$^0$/sand mixture (FeS$_2$ method) on MB discoloration were characterized in parallel quiescent batch experiments for up to 71 d (pH$_0$ = 6.8). Pristine and aged FeS$_2$ specimens were used. Parallel experiments with methyl orange (MO) and reactive red 120 (RR120) enabled a better discussion of the achieved results. The results clearly showed that FeS$_2$ induces a pH shift and delays Fe precipitation and sand coating. Pristine FeS$_2$ induced a pH shift to values lower than 4.5, but no quantitative MB discoloration occurred after 45 d. Aged FeS$_2$ could not significantly shift the pH value (final pH ≥ 6.4) but improved the MB discoloration. The used systematic sequence of experiments demonstrated that adsorption and coprecipitation are the fundamental mechanisms of contaminant removal in Fe$^0$/H$_2$O systems. This research has clarified the reason why a FeS$_2$ addition enhances the efficiency of Fe$^0$ environmental remediation.
• Journal Article

#### A new dataset on plant occurrences on smallislands, including species abundances andfunctional traits across different spatial scales ﻿

Biodiversity Data Journal 2020; 8 p.1-16: Art. e55275
Background We introduce a new dataset of woody plants on 60 small tropical islands located in the Raja Ampat archipelago in Indonesia. The dataset includes incidence, abundance and functional trait data for 57 species. All islands were sampled using a standardised transect and plot design providing detailed information on plant occurrences at different spatial scales ranging from the local (plot and transect scale) to the island scale. In addition, the dataset includes information on key plant functional traits linked to species dispersal, resource acquisition and competitive strategies. The dataset can be used to address ecological questions connected to the species-area relationship and community assembly processes on small islands and in isolated habitats. New information The dataset yields detailed information on plant community structure and links incidence, abundance and functional trait data at different spatial scales. Furthermore, this is the first plant-island dataset for the Raja Ampat archipelago, a remote and poorly studied region, and provides important new information on species occurrences.
• Journal Article

#### Quantitative Modelling and Perspective Taking: Two Competencies of Decision Making for Sustainable Development ﻿

Sustainability 2020; 12(17) p.1-32: Art. 6980
Land use change, natural resource use and climate change are challenging Sustainable Development issues (SDGs 13–15). Fostering the competencies to deal with such issues is one core task for current educational endeavors. Among these competencies, decision-making competencies are central. In detail, we investigate how learners evaluate alternative decision-making options to improve existing competence models. We exemplify our competence modelling approach using the designation of a Marine Protected Area. The cross-sectional sample consists of secondary school students and student teachers (N = 760). Partial Credit modelling shows that quantitative modelling of decision-making options is a different competence dimension than perspective taking if contextualized for Sustainable Development. In quantitative modelling, mathematical modelling is used to evaluate and reflect on decision-making options. Perspective taking covers the ability to consider different normative perspectives on Sustainable Development issues. Both dimensions show plausible (latent) correlations with related constructs within the nomological net, i.e., with qualitative arguing, economic literacy, mathematical competencies, reading competencies and analytical problem solving. Furthermore, person-abilities increase with level of education for both dimensions. The identified competence dimensions quantitative modelling and perspective taking were successfully modelled and shown to be distinct; the resulting measuring instrument is reliable and valid.
• Journal Article

#### Trophic level and basal resource use of soil animals are hardly affected by local plant associations in abandoned arable land ﻿

Ecology and Evolution 2020; 10(15) p.8279-8288
Plants provide resources and shape the habitat of soil organisms thereby affecting the composition and functioning of soil communities. Effects of plants on soil communities are largely taxon‐dependent, but how different functional groups of herbaceous plants affect trophic niches of individual animal species in soil needs further investigation. Here, we studied the use of basal resources and trophic levels of dominating soil meso‐ and macrofauna using stable isotope ratios of carbon and nitrogen in arable fallow systems 3 and 14–16 years after abandonment. Animals were sampled from the rhizosphere of three plant species of different functional groups: a legume (Medicaco sativa), a nonlegume herb (Taraxacum officinale), and a grass (Bromus sterilis). We found virtually no consistent effects of plant identity on stable isotope composition of soil animals and on thirteen isotopic metrics that reflect general food‐web structure. However, in old fallows, the carbon isotope composition of some predatory macrofauna taxa had shifted closer to that of co‐occurring plants, which was particularly evident for Lasius, an aphid‐associated ant genus. Trophic levels and trophic‐chain lengths in food webs were similar across plant species and fallow ages. Overall, the results suggest that variations in local plant diversity of grassland communities may little affect the basal resources and the trophic level of prey consumed by individual species of meso‐ and macrofauna belowground. By contrast, successional changes in grassland communities are associated with shifts in the trophic niches of certain species, reflecting establishment of trophic interactions with time, which shapes the functioning and stability of soil food webs.
• Journal Article

#### Land-Use and Health Issues in Malagasy Primary Education—A Delphi Study ﻿

Sustainability 2020; 12(15) p.1-31: Art. 6212
Education for Sustainable Development (ESD) plays a key role in Sustainable Development. In low-income countries like Madagascar, this key role is particularly relevant to primary education. However, the curricula lack a comprehensive ESD approach that incorporates regional issues. In Madagascar, sustainable land-use practices (Sustainable Development Goals 12, 15) and health prevention (SDGs 2, 3, 6) are educational challenges. Procedural knowledge allows problem-solving regarding unsustainable developments. We adapted and further developed a measure of ESD-relevant procedural knowledge. Considering curricula, sustainability standards, research, and a two-round Delphi study (n = 34 experts), we identified regionally relevant land-use practices and health-protective behavior. After the experts rated the effectiveness and possibility of implementation of courses of actions, we calculated an index of what to teach under given Malagasy (regional) conditions. Combined with qualitative expert comments, the study offers insights into expert views on land-use and health topics: For example, when teaching ESD in Northeast Madagascar, sustainable management of cultivation and soil is suitable, particularly when linked to vanilla production. Health-protective behavior is ultimately more difficult to implement in rural than in urban areas. These results are important for further curricula development, for ESD during primary education, and because they give insights into the topics teacher education should address.
• Journal Article

#### Mycoparasite Hypomyces odoratus infests Agaricus xanthodermus fruiting bodies in nature ﻿

AMB Express. 2020 Aug 13;10(1):141
Abstract Mycopathogens are serious threats to the crops in commercial mushroom cultivations. In contrast, little is yet known on their occurrence and behaviour in nature. Cobweb infections by a conidiogenous Cladobotryum-type fungus identified by morphology and ITS sequences as Hypomyces odoratus were observed in the year 2015 on primordia and young and mature fruiting bodies of Agaricus xanthodermus in the wild. Progress in development and morphologies of fruiting bodies were affected by the infections. Infested structures aged and decayed prematurely. The mycoparasites tended by mycelial growth from the surroundings to infect healthy fungal structures. They entered from the base of the stipes to grow upwards and eventually also onto lamellae and caps. Isolated H. odoratus strains from a diseased standing mushroom, from a decaying overturned mushroom stipe and from rotting plant material infected mushrooms of different species of the genus Agaricus while Pleurotus ostreatus fruiting bodies were largely resistant. Growing and grown A. xanthodermus and P. ostreatus mycelium showed degrees of resistance against the mycopathogen, in contrast to mycelium of Coprinopsis cinerea. Mycelial morphological characteristics (colonies, conidiophores and conidia, chlamydospores, microsclerotia, pulvinate stroma) and variations of five different H. odoratus isolates are presented. In pH-dependent manner, H. odoratus strains stained growth media by pigment production yellow (acidic pH range) or pinkish-red (neutral to slightly alkaline pH range).
• Journal Article

#### The integrated stress response induces R-loops and hinders replication fork progression ﻿

Cell Death & Disease 2020; 11(7) p.1-16: Art. 538
The integrated stress response (ISR) allows cells to rapidly shutdown most of their protein synthesis in response to protein misfolding, amino acid deficiency, or virus infection. These stresses trigger the phosphorylation of the translation initiation factor eIF2alpha, which prevents the initiation of translation. Here we show that triggering the ISR drastically reduces the progression of DNA replication forks within 1 h, thus flanking the shutdown of protein synthesis with immediate inhibition of DNA synthesis. DNA replication is restored by compounds that inhibit eIF2alpha kinases or re-activate eIF2alpha. Mechanistically, the translational shutdown blocks histone synthesis, promoting the formation of DNA:RNA hybrids (R-loops), which interfere with DNA replication. R-loops accumulate upon histone depletion. Conversely, histone overexpression or R-loop removal by RNaseH1 each restores DNA replication in the context of ISR and histone depletion. In conclusion, the ISR rapidly stalls DNA synthesis through histone deficiency and R-loop formation. We propose that this shutdown mechanism prevents potentially detrimental DNA replication in the face of cellular stresses.
• Journal Article

#### Target‐oriented habitat and wildlife management: estimating forage quantity and quality of semi‐natural grasslands with Sentinel‐1 and Sentinel‐2 data ﻿

Remote Sensing in Ecology and Conservation p.1-18
Semi‐natural grasslands represent ecosystems with high biodiversity. Their conservation depends on the removal of biomass, for example, through grazing by livestock or wildlife. For this, spatially explicit information about grassland forage quantity and quality is a prerequisite for efficient management. The recent advancements of the Sentinel satellite mission offer new possibilities to support the conservation of semi‐natural grasslands. In this study, the combined use of radar (Sentinel‐1) and multispectral (Sentinel‐2) data to predict forage quantity and quality indicators of semi‐natural grassland in Germany was investigated. Field data for organic acid detergent fibre concentration (oADF ), crude protein concentration (CP ), compressed sward height (CSH ) and standing biomass dry weight (DM ) collected between 2015 and 2017 were related to remote sensing data using the random forest regression algorithm. In total, 102 optical‐ and radar‐based predictor variables were used to derive an optimized dataset, maximizing the predictive power of the respective model. High $R^2$ values were obtained for the grassland quality indicators oADF ($R^2$ = 0.79, RMSE = 2.29%) and CP ($R^2$ = 0.72, RMSE = 1.70%) using 15 and 8 predictor variables respectively. Lower R 2 values were achieved for the quantity indicators CSH ($R^2$ = 0.60, RMSE = 2.77 cm) and DM ($R^2$ = 0.45, RMSE = 90.84 g/m²). A permutation‐based variable importance measure indicated a strong contribution of simple ratio‐based optical indices to the model performance. In particular, the ratios between the narrow near‐infrared and red‐edge region were among the most important variables. The model performance for oADF , CP and CSH was only marginally increased by adding Sentinel‐1 data. For DM , no positive effect on the model performance was observed by combining Sentinel‐1 and Sentinel‐2 data. Thus, optical Sentinel‐2 data might be sufficient to accurately predict forage quality, and to some extent also quantity indicators of semi‐natural grassland.
• Journal Article

#### Association between milk consumption and child growth for children aged 6–59 months ﻿

Scientific Reports 2020; 10(1) p.1-9: Art. 6730
Apart from high levels of energy, proteins, micro- and macronutrients, milk contains calcium and the insulin-like growth factor-1 that are of major relevance for children’s development and growth. Using Demographic and Health Survey data between 1990 and 2017 with information on milk consumption and anthropometric measurements from all low- and middle-income countries available, we investigate whether milk consumption in childhood is associated with stunting, wasting, and underweight. We specify logistic regression models and adjust for a range of covariates and fixed effects on the primary sampling unit level. We analyze heterogeneity in the association by wealth quintiles and age groups and present country-specific estimates. The final samples for wasting, underweight and stunting include 668.463, 693.376, and 673.177 observations of children aged 6 to 59 months, respectively. Our results suggest that milk consumption is associated with a reduced probability of being underweight of 1.4 percentage points (95% confidence interval −0.02, −0.01) and a reduced probability of being stunted of 1.9 percentage points (95% confidence interval −0.02, −0.01). The association for wasting is not robust. The association is stronger for children from wealthier households, which might indicate that milk consumption is a proxy for better overall nutrition or socio-economic status.
• Journal Article

#### Effect of Grazing System on Grassland Plant Species Richness and Vegetation Characteristics: Comparing Horse and Cattle Grazing ﻿

Sustainability 2020; 12(8) p.1-17: Art. 3300
Horses are of increasing relevance in agriculturally managed grasslands across Europe. There is concern to what extent grazing with horses is a sustainable grassland management practice. The effect of longer-term horse grazing on the vegetation characteristics of grasslands has received little attention, especially in comparison to grazing cattle. Our study analyses the relative importance of grazing system (grazer species and regime) and grassland management for vegetation characteristics in grasslands as indicator for sustainable management. We monitored grassland vegetation in western central Germany and compared paddocks grazed by horses under two different regimes, continuous (HC) vs. rotational (HR), to paddocks grazed by cattle (C) under similar trophic site conditions. We observed more plant species and more High Nature Value indicator species on HC compared to C. The vegetation of C was more grazing tolerant and had higher forage value than HC. Regardless of the grazing regime, the competitive component was lower, the stress-tolerant component higher and the floristic contrast between patch-types stronger on HC and HR paddocks compared to C. Species richness was strongly influenced by the extent of the floristic contrast. Our results emphasize the potential of horse grazing for biodiversity in agriculturally managed grasslands.
• Journal Article

#### Performance of Modern Varieties of Festuca arundinacea and Phleum pratense as an Alternative to Lolium perenne in Intensively Managed Sown Grasslands ﻿

Agronomy 2020; 10(4) p.1-13: Art. 540
In future, grass swards need to be adapted to climate change and interactions of management and site are becoming more important. The persistence of Lolium perenne on peatland or during dry periods is limited and alternative forage species are required. We tested the performance of a modern variety of Festuca arundinacea and Phleum pratense as an alternative to Lolium perenne on clay, peat, and sandy soils. Each of these grasses was sown as main species in mixture with Poa pratensis and Trifolium repens and the mixtures were subjected to different frequencies of defoliation. Differences in yield proportions in the third year were significantly influenced by main species, site and their interaction. Remaining mass proportions of main species after three years were smallest on peat; on all sites Festuca arundinacea showed the highest persistence and largest yield, followed by Lolium perenne. Mass proportions of Phleum pratense were small on peat soils and Phleum had been replaced there by Holcus lanatus, and by Lolium perenne and Poa pratensis on the clay and sandy soils. We conclude that the choice of grass species in mixtures is a management tool to control stability and productivity of grass swards under specific site conditions.
• Journal Article

#### Modeling the Shape of Synaptic Spines by Their Actin Dynamics ﻿

Frontiers in Synaptic Neuroscience 2020; 12 p.1-19: Art. 9
Dendritic spines are the morphological basis of excitatory synapses in the cortex and their size and shape correlates with functional synaptic properties. Recent experiments show that spines exhibit large shape fluctuations that are not related to activity-dependent plasticity but nonetheless might influence memory storage at their synapses. To investigate the determinants of such spontaneous fluctuations, we propose a mathematical model for the dynamics of the spine shape and analyze it in 2D—related to experimental microscopic imagery—and in 3D. We show that the spine shape is governed by a local imbalance between membrane tension and the expansive force from actin bundles that originates from discrete actin polymerization foci. Experiments have shown that only few such polymerization foci co-exist at any time in a spine, each having limited life time. The model shows that the momentarily existing set of such foci pushes the membrane along certain directions until foci are replaced and other directions may now be affected. We explore these relations in depth and use our model to predict shape and temporal characteristics of spines from the different biophysical parameters involved in actin polymerization. Approximating the model by a single recursive equation we finally demonstrate that the temporal evolution of the number of active foci is sufficient to predict the size of the model-spines. Thus, our model provides the first platform to study the relation between molecular and morphological properties of the spine with a high degree of biophysical detail.
• Journal Article

#### Airborne Tree Crown Detection for Predicting Spatial Heterogeneity of Canopy Transpiration in a Tropical Rainforest ﻿

Remote Sensing 2020; 12(4) p.1-16: Art. 651
Tropical rainforests comprise complex 3D structures and encompass heterogeneous site conditions; their transpiration contributes to climate regulation. The objectives of our study were to test the relationship between tree water use and crown metrics and to predict spatial variability of canopy transpiration across sites. In a lowland rainforest of Sumatra, we measured tree water use with sap flux techniques and simultaneously assessed crown metrics with drone-based photogrammetry. We observed a close linear relationship between individual tree water use and crown surface area (R$^2$ = 0.76, n = 42 trees). Uncertainties in predicting stand-level canopy transpiration were much lower using tree crown metrics than the more conventionally used stem diameter. 3D canopy segmentation analyses in combination with the tree crown–water use relationship predict substantial spatial heterogeneity in canopy transpiration. Among our eight study plots, there was a more than two-fold difference, with lower transpiration at riparian than at upland sites. In conclusion, we regard drone-based canopy segmentation and crown metrics to be very useful tools for the scaling of transpiration from tree- to stand-level. Our results indicate substantial spatial variation in crown packing and thus canopy transpiration of tropical rainforests.
• Journal Article

#### Using a Citizen Science Approach with German Horse Owners to Study the Locomotion Behaviour of Horses on Pasture ﻿

Sustainability 2020; 12(5) p.1-12: Art. 1835
Engaging farmers as citizen scientists may be a cost-effcient way to answering applied research questions aimed at more sustainable land use. We used a citizen science approach with German horse farmers with a dual goal. Firstly, we tested the practicability of this approach for answering ‘real-life’ questions in variable agricultural land-use systems. Secondly, we were interested in the knowledge it can provide about locomotion of horses on pasture and the management factors influencing this behaviour. Out of 165 volunteers, we selected 40 participants to record locomotion of two horses on pasture and provide information on their horse husbandry and pasture management. We obtained complete records for three recording days per horse from 28 participants, resulting in a dataset on more individual horses than any other Global Positioning System study published in the last 30 years. Time spent walking was greatest for horses kept in box-stall stables, and walking distance decreased with increasing grazing time. This suggests that restrictions in pasture access may increase stress on grass swards through running and trampling, severely challenging sustainable pasture management. Our study, involving simple technology, clear instructions and rigorous quality assessment, demonstrates the potential of citizen science actively involving land managers in agricultural research.
• Journal Article

#### The Economy of Canopy Space Occupation and Shade Production in Early- to Late-Successional Temperate Tree Species and Their Relation to Productivity ﻿

Forests 2020; 11(3) p.1-18: Art. 317
Light capture is linked to occupation of canopy space by tree crowns, which requires investment of carbon and nutrients. We hypothesize that (i) late-successional trees invest more in casting shade than in occupying space than early-successional trees, and (ii) shade production and crown volume expansion are generally greater in more productive species. For six Central European early-successional (Betula pendula, Pinus sylvestris), mid/late-successional (Quercus petraea, Carpinus betulus), and late-successional tree species (Tilia cordata, Fagus sylvatica), we measured through full-tree harvests (1) crown volume, (2) the costs of canopy space exploration (carbon (C) and nutrients invested to fill crown volume), of space occupation (annual foliage production per volume), and of shade production (foliage needed to reduce light transmittance), and (3) related the costs to aboveground productivity (ANPP). The C and nutrient costs of canopy volume exploration and occupation were independent of the species’ seral stage, but increased with ANPP. In contrast, the cost of shade production decreased from early-to late-successional species, suggesting that the economy of shade production is more decisive for the competitive superiority of late-successional species than the economy of canopy space exploration and occupation.
• Journal Article

#### Probing the Environment of Emerin by Enhanced Ascorbate Peroxidase 2 (APEX2)-Mediated Proximity Labeling ﻿

Cells 2020; 9(3) p.1-18: Art. 605
Emerin is one of the best characterized proteins of the inner nuclear membrane, but can also occur at the level of the endoplasmic reticulum. We now use enhanced ascorbate peroxidase 2 (APEX2) to probe the environment of emerin. APEX2 can be used as a genetic tag that produces short-lived yet highly reactive biotin species, allowing the modification of proteins that interact with or are in very close proximity to the tagged protein. Biotinylated proteins can be isolated using immobilized streptavidin and analyzed by mass spectrometry. As an alternative to the standard approach with a genetic fusion of APEX2 to emerin, we also used RAPIDS (rapamycin- and APEX-dependent identification of proteins by SILAC), a method with improved specificity, where the peroxidase interacts with the protein of interest (i.e., emerin) only upon addition of rapamycin to the cells. We compare these di erent approaches, which, together, identify well-known interaction partners of emerin like lamin A and the lamina associated polypeptide 1 (LAP1), as well as novel proximity partners.
• Journal Article

#### Dbp5/DDX19 between Translational Readthrough and Nonsense Mediated Decay ﻿

International Journal of Molecular Sciences 2020; 21(3) p.1-13: Art. 1085
The DEAD-box protein Dbp5 (human DDX19) remodels RNA-protein complexes. Dbp5 functions in ribonucleoprotein export and translation termination. Termination occurs, when the ribosome has reached a stop codon through the Dbp5 mediated delivery of the eukaryotic termination factor eRF1. eRF1 contacts eRF3 upon dissociation of Dbp5, resulting in polypeptide chain release and subsequent ribosomal subunit splitting. Mutations in DBP5 lead to stop codon readthrough, because the eRF1 and eRF3 interaction is not controlled and occurs prematurely. This identifies Dbp5/DDX19 as a possible potent drug target for nonsense suppression therapy. Neurodegenerative diseases and cancer are caused in many cases by the loss of a gene product, because its mRNA contained a premature termination codon (PTC) and is thus eliminated through the nonsense mediated decay (NMD) pathway, which is described in the second half of this review. We discuss translation termination andNMDin the light of Dbp5/DDX19 and subsequently speculate on reducing Dbp5/DDX19 activity to allow readthrough of the PTC and production of a full-length protein to detract the RNA from NMD as a possible treatment for diseases.
• Journal Article

#### The number of k-mer matches between two DNA sequences as a function of k and applications to estimate phylogenetic distances ﻿

PLOS ONE 2020; 15(2) p.1-18: Art. e0228070
We study the number $N_k$ of length-k word matches between pairs of evolutionarily related DNA sequences, as a function of k. We show that the Jukes-Cantor distance between two genome sequences—i.e. the number of substitutions per site that occurred since they evolved from their last common ancestor—can be estimated from the slope of a function $F$ that depends on $N_k$ and that is affine-linear within a certain range of $k$. Integers kmin and $k_{max}$ can be calculated depending on the length of the input sequences, such that the slope of $F$ in the relevant range can be estimated from the values $F(k_{min})$ and $F(k_{max})$. This approach can be generalized to so-called Spaced-word Matches (SpaM), where mismatches are allowed at positions specified by a user-defined binary pattern. Based on these theoretical results, we implemented a prototype software program for alignment-free sequence comparison called Slope-SpaM. Test runs on real and simulated sequence data show that Slope-SpaM can accurately estimate phylogenetic distances for distances up to around 0.5 substitutions per position. The statistical stability of our results is improved if spaced words are used instead of contiguous words. Unlike previous alignment-free methods that are based on the number of (spaced) word matches, Slope-SpaM produces accurate results, even if sequences share only local homologies.