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LED-absorption-QEPAS sensor for biogas plants

LED-absorption-QEPAS sensor for biogas plants

E-Mail: michael.koehring@hhi.fraunhofer.de; Tel.: +49-5321-6855-153. Academic Editor: Vittorio M.N. Passaro Received: 20 March 2015 / Accepted: 13 May 2015 / Published: 22 May 2015 Abstract: A new sensor for methane and carbon dioxide concentration measurements in biogas plants is presented. LEDs in the mid infrared spectral region are implemented as low cost light source. The combination of quartz-enhanced photoacoustic spectroscopy with an absorption path leads to a sensor setup suitable for the harsh application environment. The sensor system contains an electronics unit and the two gas sensors; it was designed to work as standalone device and was tested in a biogas plant for several weeks. Gas concentration dependent measurements show a precision better than 1% in a range between 40% and 60% target gas concentration for both sensors. Concentration dependent measurements with different background gases show a considerable decrease in cross sensitivity against the major components of biogas in direct comparison to common absorption based sensors. Keywords: optical sensing; spectroscopy; photoacoustic; absorption; biogas
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Assessing the potential contribution of excess heat from biogas plants towards decarbonising German residential heating

Assessing the potential contribution of excess heat from biogas plants towards decarbonising German residential heating

A further uncertainty arises from the age of biogas plants. It is impossible to estimate how the plants will continue to operate when the Renewable Energy Sources Act ends after twenty years. The age profile of the existing plants means that some of these plants will cease to benefit from the feed-in tariffs upon which they rely to be economical. After this time, their continued operation is uncertain. The plants should already have broken even after twenty years, as studies have shown payback periods in the region of 7-12 years depending on the substrate and the output (Balussou et al. 2011). Hence the plant may continue to operate, but the negative impact on the economics of losing the FITs could force the operators to seek other business models such as biomethane uprading and feed in (cf. section 2). In the absence of new business models, the plants might be forced to close, which would mean the excess heat considered here is no longer available. However, this study aimed to assess the current technical potential for excess heat use from biogas plants, and there are always future uncertainties associated with such analyses. Potential future business models for biogas plant operators in a post-EEG context will be the subject of a future contribution.
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Improved detection of extended spectrum beta-lactamase (ESBL)-producing Escherichia coli in input and output samples of German biogas plants by a selective pre-enrichment procedure

Improved detection of extended spectrum beta-lactamase (ESBL)-producing Escherichia coli in input and output samples of German biogas plants by a selective pre-enrichment procedure

ent but highly similar BOX-genotypes but were in general assigned to the same phylogenetic E. coli groups and contained partially different sets of ESBL genes (bla CTX-M , bla TEM , bla CTX-M and bla TEM or bla SHV ) and among the bla CTX-M genes, genes of different CTX-M-groups, group 1, 2, or 9 ( Table 1 ). Comparative analysis of MLST data, phylo-grouping and ESBL gene identification showed for example that isolates identified as ST1210 that originate from input samples of different biogas plants (BGA 001 and 006) carried ESBL genes of different CTX-M types. A potential transfer of isolates of the same ST-type/E. coli phylogroup with an ESBL gene of the same CTX-M group was indicated twice, for three isolates of ST410/A  (A, but with yiaA detection) and three isolates of ST58/B1 all carrying CTX-M-1 group genes. ST410 iso- lates were isolated from two input and a subsequent output sample of BGA 001, and the iso- lates of ST58 of two input and a subsequent output samples of BGA 015. Isolates with an identical assignment however were also detected from other BGAs indicating a more common abundance of those in manure or biogas plant output samples. An example of a stable presence of a specific ST type in a specific livestock husbandry or even a biogas plant reactor over a lon- ger time period was indicated by the two isolates identified as ST398/A carrying an ESBL gene of the CTX-M-1 group, because the isolates were isolated in 2012 from an input samples of BGA 001 and in 2013 from an output sample of the same biogas plant.
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View of Socio-Economic Factors of Small Hydropower and Biogas Plants and their Implications for Rural Energy Poverty Alleviation in Kirinyaga, Kenya

View of Socio-Economic Factors of Small Hydropower and Biogas Plants and their Implications for Rural Energy Poverty Alleviation in Kirinyaga, Kenya

12 176 US$ (54 m 3 ) and 26,090 US$ (124 m 3 ); which is not affordable to many households that live on less than US$ 2/day [16]. The cost of fuel wood in Kirinyaga ranges from 3.8-12 US$ per month while the cost of kerosene is about 3 US$ [17]. These fuels are thus more affordable to low income earners. The SHP and biogas plants have been studied in Kenya, specifically regarding adoption, technology, and challenges. Kathamba (1.2 kW) and Thima (2.2 kW) have been documented as the first pilot SHP plants in Kirinyaga [18]-[20]. Later, the United Nations Industrial Development Organization [21] started Kibae SHP and this led to a mushrooming of other projects. The Kenya Tea Development Authority is constructing Nyamindi SHP (1.8MW) [22] and the National Irrigation Board has constructed two plants with a capacity of 20 kW along irrigation canals [23]. Biogas is recommended to solve environmental and energy problems in Africa [24], though it has been found that socio-economic factors affect adoption of biogas technology in Nakuru [25]. Furthermore, inadequate documentation of biogas production in Kenya makes the sustainability assessment of the biogas plants challenging [26]. SHP development has contributed to electrification in Kenya but is still under-utilized [27]. However, little is known regarding the contribution of SHP and biogas to rural energy poverty alleviation; which this paper addresses.
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Agricultural biogas plants a systematic analysis of strengths, weaknesses, opportunities and threats / Thomas Brudermann, Corinna Mitterhuber & Alfred Posch

Agricultural biogas plants a systematic analysis of strengths, weaknesses, opportunities and threats / Thomas Brudermann, Corinna Mitterhuber & Alfred Posch

We have to note that the relatively low acceptance of biogas plants by residents has repeatedly been seen as a problem. In a couple of cases, residents complained about expected high levels of smell, noise and traffic, and indeed a couple of planned projects have had to be shut down, or scaled down, as a result of public protests. This is not entirely reflected in the rather low relative ranking found for this issue (p=0.108). However, despite the low relative threat level reported here, it is important to take the concerns of residents seriously. The use of participatory approaches in planning and implementation is likely to be one means of preempting any buildup of resistance: More scope needs to be made available for residents to become involved in projects, e.g. in the planning process or as co-owners or customers.
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Life cycle assessment and modeling approaches as a combined evaluation tool for sustainable control strategies at biogas plants

Life cycle assessment and modeling approaches as a combined evaluation tool for sustainable control strategies at biogas plants

Nowadays, feed control of full-scale biogas plants is often performed by rules of thumb or simple calculation, al- though some attempts were made for optimal control of the feed rate at stable operation conditions, e.g., based on the ADM1 [40]. A first step towards a closed loop control is the availability of suitable models. In this study, the AM2 was evaluated for the application at dynamic process operation, caused by a fluctuating feedstock load. The calibration of the AM2 at a pilot-scale biogas plant was only feasible with a verification of the uncertainty in the model parameters, due to the nonlinearity of the biogas process. Very slow reactions occur when anaerobic microorganisms are fed in a dynamic real-time process, so the optimization using a complex and nonlinear process model seems to be a suitable approach. This is of special interest, when the loading rate is changed, e.g., for a better integration of biogas production and energy generation from it into smart systems. Then, a certain variation of the biogas synthesis rate is achieved by changing the feeding intervals, thus, creating a dynamic provision of biogas and energy. First attempts in this way have shown that this concept is suitable to gain a 9-fold variation in the biogas production if the process was fed every two days with dried distillers’ grains in lab-scale bio- reactors [41]. If more demanding conditions are used, e.g., a combination of rapidly and slowly digestible feedstock, any model-based approach might be useful to predict the feed- stock load for various biogas production scenarios and for control purposes.
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Multi-fidelity Modeling and Optimization of Biogas Plants

Multi-fidelity Modeling and Optimization of Biogas Plants

Islam et al. [19] analyze the impact of di fferent fac- tors on production of biogas in di fferent biogas plants of Bangladesh. The data was collected from 18 poultry farms. Their analysis is based on collected data from survey, Internet, and other sources. To obtain further in- sight in the behavior of biogas plants, simulation models such as the ADM1 can be used. ADM1 is very popular and the nowadays most complex mathematical model used to simulate the anaerobic digestion process (for a review see [3]). In several publications it is utilized to dynamically model full-scale agricultural and industrial biogas plants [5, 23, 29]. ADM1 is a structured model incorporating disintegration and hydrolysis, acidogen- esis, acetogenesis, and methanogenenesis steps. The ADM1 is implemented as a sti ff differential equation system in a MATLAB R toolbox for biogas plant model-
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Operating performance of full-scale agricultural biogas plants in Germany and China : results of a year-round monitoring program

Operating performance of full-scale agricultural biogas plants in Germany and China : results of a year-round monitoring program

Note that all three CN BGPs faced difficulties of stable substrate supply due to stricter environmental protection requirements in the livestock sector in China, especially around Beijing, where many livestock farms closed down; (3) CHP incorporation for electricity and heat production, instead of direct supply to households for CN BGPs as the rural energy supply is transformed gradually to electricity. In this way, generated heat can be supplied internally to circumvent the high cost of heating the digesters (20–40% of the total operation cost); (4) from the policy makers aspect, a Chinese government subsidy should be granted on a performance basis to encourage the proper operation of the BGPs. In Germany, starting in 2021, many of the BGPs will no longer receive fixed FiT, meaning some of them may shut down if they are not able to find new business models. Biogas operators are encouraged to find more income sources to tackle the financial difficulties, such as the heat supply to local communities or feeding electricity into the grid during high-demand periods to receive the flexibility premium; and finally, (5) establishment of regular BGP performance monitoring with professional advice and support to the BGP operators.
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Biogas im Ökolandbau: Wirtschaftlichkeit im Spannungsfeld zwischen Produktionssystem und Politik

Biogas im Ökolandbau: Wirtschaftlichkeit im Spannungsfeld zwischen Produktionssystem und Politik

While the generation of power from anaerobic digestion during its pioneer-stage in Germany was predominantly developed on organic farms, biogas production in organ- ic farming never expanded to the same extent as in conventional agriculture. Besides various other aspects, this appears to be mainly due to economic reasons related to specific production requirements. This paper therefore analyses the framework condi- tions of organic biogas generation and assesses its monetary implications on produc- tion economics. A comparison of organic and conventional generation of power from biogas displays the advantages of conventional biogas plants, especially concerning lower capital and input costs. However, frequently changing political preconditions further aggravate the economic situation for biogas production in both farming sys- tems. Finally, a new calculation approach, considering monetary benefits from agro- nomic effects of an integrated biogas generation in organic agriculture is proposed.
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Improving biogas production by sugar beet silage co-fermentation: an approach for on-demand biogas energy

Improving biogas production by sugar beet silage co-fermentation: an approach for on-demand biogas energy

Biogas has become a well-established energy resource, especially through the use of renewable biomass i.e. energy crops. The advantages of using energy crops in biogas production are high biogas yield (Weiland, 2010), reducing greenhouse gas emission (Meyer-Aurich et al., 2016), increasing soil nutrients by crop rotations (Björnsson et al., 2013), mitigating disposal problems of agricultural residues (Zhang and Zhang, 1999). Unsolicited problems, however, were realized during mono-digestion of energy crops such as low buffering capacity (Braun et al., 2010), foam formation as well as various physical damages (Bachmann, 2015). Animal manure as co-feedstock is beneficial as it balances the missing nutrients, and therefore gas production rate increases (Comparetti et al., 2013). Nevertheless, the availability of manure can be locally limited due to increasing demand. Demirel and Scherer (2009) reported that about 15% of German biogas plants were operated without manure addition because of logistic problems. Manure limitation emphasizes to focus on another feedstocks and sugar beet silage is considered as an option, since sugar beet contains high alkalinity within the range of 2.5-6 g CaCO 3 -equivalents L -1 (Scherer et al.,
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Parameters for sustainable and demand-oriented biogas production

Parameters for sustainable and demand-oriented biogas production

The enormous biogas expansion in the last decades led to an innovative technical engineering process and a great variability in the utilized substrates. While in the 1990s most agricultural biogas plants were based on manure and food remains, the substrate diversity has shifted over the last decades. In 2004 the total feedstock mixture composed mainly of livestock residues and residue materials from industry and agriculture (87 % fresh weight (FW)). Only six years later, the share of energy crops on the total feedstock was 46 % (FW) (DBFZ 2011). A large study on biogas production in Germany considered 413 biogas plants of which 61 were analysed in detail (Gemmeke et al. 2009). It showed that an average biogas plant uses a higher share of renewable energy plants than livestock residues. The livestock residues account in average for 37 % FW of the total substrate input. The highest share of livestock residues is cattle manure with a share of 24 % of the total substrate input. Fewer than 60 % of the analysed biogas plants utilized cattle manure in their feedstock. Renewable energy plants take the other share of 63 % (FW) of the total substrate input. More detailed, the utilized energy plants are mainly maize silage, accounting for 48 % FW of the total substrate input, and grass (including grass silage) with 10 % FW. The survey showed that more than 94 % of the analysed biogas plants have maize silage in their feedstock.
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Maizification of the landscape for biogas production? Identifying the likelihood of silage maize for biogas in Brandenburg from 2008-2018

Maizification of the landscape for biogas production? Identifying the likelihood of silage maize for biogas in Brandenburg from 2008-2018

important variables found in the existing literature but our approach could be augmented several ways, e.g., by including variables such as social networks production and social institutions (Bock und Polach et al., 2015; Venghaus and Acosta, 2018). Besides, for the WEC variable used in this study, we relied on intra-state values and did not account for neighbouring areas that could provide biogas silage maize for plants, or that have biogas plants which could influence the area of investigation. Thirdly, the process to determine the weights of the variables in the AHP process may be further qualified by including additional input from focus groups on top of the literature used and the expert knowledge. However, the purpose of selecting this methodology was to show the potential for identifying spatiotemporal dynamics affecting the likelihood of biogas silage maize cultivation in Brandenburg. The results can, of course, only approximate the reality. However, it exploits and explores the potential of the IACS data in combination with the data on biogas plants, linking energy production with the respective land use. IACS is the most complete and reliable dataset within agricultural data, combining a remarkable level of detail on space, time, and content in one dataset, and therefore being a crucial pillar for future policy modelling and a novel solution for the geographical science (Tóth and Kučas, 2016).
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Quantifying the externalities of renewable energy plants using wellbeing data: The case of biogas

Quantifying the externalities of renewable energy plants using wellbeing data: The case of biogas

We cannot be sure whether a household that is allocated to the treatment group is indeed subject to externalities caused by a biogas plant in its surroundings. This has several reasons: first, we proxy externalities caused by biogas plants through treat- ment radii, which implicitly assumes that externalities decrease in distance to the near- est plant, and are present for any individual at any point in time. This, however, is unlikely to be the case: for example, local weather conditions may greatly reduce externalities. Second, households may adopt mitigating behaviour, for example, by installing air filters, better sealings, or simply opening windows less often. Finally, we only have information on private households: individuals living in places like nursing homes are excluded, and so are temporary visitors such as tourists. We cannot make counterfactual claims about individuals who might have moved and did not do so be- cause of installations. In terms of time use, people spend considerable amounts of time outside their private homes, for example at work, and may thus be less permanently affected. Our identified effects – ˆ δ treat , ˆ δ intens2 , and ˆ δ τ – should thus be interpreted as lower-bound, intention-to-treat effects for stayers.
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Biogas residues

Biogas residues

digestates from biogas production should be based on analyses of the digested material because the feedstock material is not only altered due to the volatilisation of CH 4 and CO 2 but also due to gaseous losses of N and S and precipitation of minerals. The analyses should also be repeated in adequate intervals since the elemental composition of digestates can vary over time, especially in co-fermentation biogas plants. This probably also applies to the degree of stability of digestates which may strongly influence the mineralisation and potential for priming in soils. In life cycle assessments, the potential of digestates to promote priming and thus additional GHG emissions to the atmosphere should urgently be accounted for. The maximisation of biogas yield is essential for the economic feasibility of biogas plants but the original intention to reduce GHG emissions during the production of energy needs to be considered as well. When energy is produced in a less polluting way, but the resulting digestate causes additional GHG emissions after application to arable land, this original intention may be failed. Therefore, these two concerns – economic feasibility and positive life cycle assessment of biogas plants – need to be conciliated. Actually, this seems to be a great challenge in practice since the economic feasibility of biogas plants strongly depends on the sponsorship by the EEG, which has been revised in 2014 and reduces many of the benefits for plant operators now. The costs for the promotion of bioenergy and the expansion of maize monocultures, for example, have led to this revision and resulted in a recent slow-down of newly built biogas plants. While 1,270 biogas plants have been built in 2011 in Germany, only 340 and 335 have been established in 2012 and 2013, respectively (Fachverband Biogas 2014). This gives reason for early in-depth research in those areas so that misdirected investment and belated political corrections can be avoided.
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Biogas production from the perspective of sustainable development

Biogas production from the perspective of sustainable development

1054 impact of factors related to the biogas production process on society is greater (over 1.7 times) than the impact on the natural environment. Despite the environmental and socio-economic benefits, there are certain obstacles to the production of biogas. The biogas production process is affected by a variety of stimuli and barriers (Lantz et al., 2007). The technologies of renewable energy production face a number of obstacles including, among others: technical, market, economic and financial barriers, institutional, political and regulatory barriers, as well as social and environmental obstacles (Painuly, 2001). These barriers were found to vary completely, depending on the geographical location. For example, in Romania, the production and use of biogas is uncommon due to the market barriers, lack of knowledge and experience (farmers, installation operators, etc.) and insufficient access to sources of finance (Mateescu et al., 2008). In Rwanda, however, the main obstacles to biogas installations include financial, technical, socio-cultural and institutional barriers. The most important challenges are potential biogas users who cannot afford high installation costs, and loans from banks are difficult to obtain (Rupf et al., 2015). In Poland, there are many barriers to the investment process and access to the sources of funding. The obstacle is also associated with legal regulations, social barriers (little acceptance of biogas plants by local residents), mainly resulting from the deficiencies in the education regarding biogas production in a biogas plant. (Igliński et al., 2012; McCormick, Kåberger, 2007).
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Quantifying the Externalities of Renewable Energy Plants Using Wellbeing Data: The Case of Biogas

Quantifying the Externalities of Renewable Energy Plants Using Wellbeing Data: The Case of Biogas

biogas plants. In this approach, the relationship between respondents’ self-reports and installations in their surroundings remains covert. We use the universe of biogas plants constructed in Germany during the 2000 to 2012 period (more than 13, 000 installations) and a spatial difference-in-differences de- sign that exploits exact geographical coordinates of households and installations. We find limited evidence on negative externalities of biogas plants, partly confirming results from previous studies using stated and revealed preferences. In particular, we find that the construction of a biogas plant inside a 2, 000 metres radius around households has a significant, negative effect on the self-reported life satisfaction of household members, holding everything else (including real estate prices) constant. However, when compar- ing overall treatment effects of biogas plants to those of wind turbines obtained using the same methodology, impacts turn out to be smaller (about 8% of a standard deviation versus 11%) and much more spatially confined (detectable up to 2, 000 metres versus 4, 000 metres) (Krekel and Zerrahn, 2017). As with wind turbines, impacts are likely to be lower bounds: our research design focuses on respondents interviewed in private households while deliberately excluding individuals who move (either between treat- ment and control group, or within either group) during the observation period. If such moving is in any way related to the construction of biogas plants in their surroundings, these individuals are arguably the most adversely affected.
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Wildpflanzen-Samen in der Biogas-Anlage: Screening des Überlebensrisikos verschiedener Arten

Wildpflanzen-Samen in der Biogas-Anlage: Screening des Überlebensrisikos verschiedener Arten

Stichwörter: Biogas-Reaktor, Temperatur, Thermoresistenz, Überlebens-Risiko, Wildpflanzen-Arten Abstract If plant seeds enter a biogas reactor there is the risk of surviving anaerobic digestion and spreading with the digestate application. Recently, a large number of wildflower species can enter the biogas chain due to the use of wildflower seed mixtures for the production of biogas. The contamination risk associated with these species cannot be reliably estimated as there is a lack of systematic research on the survival of seeds from different plant species. As seed survival in biogas plants mainly depends on temperature and exposure time, the investigation of the species´ thermoresistance is a first step to close this gap of knowledge.
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Effiziente Verstromung von Biogas in einem SOFC-System : Entwicklung, Charaktersieirung und Betriebsverhalten

Effiziente Verstromung von Biogas in einem SOFC-System : Entwicklung, Charaktersieirung und Betriebsverhalten

Um die Frage zu beantworten, welche Auswirkungen variierende Biogaszusammensetzun- gen auf den Betrieb des Biogas-SOFC-Systems haben, fanden Untersuchungen mit 55, 67 und 80 Vol.-% statt. Die Systemleistung und der Wirkungsgrad des Biogas-SOFC-Systems steigen bei gleicher chemischer Eingangsleistung mit zunehmender Methankonzentration an, ab 80 Vol.-% Methan kann keine Leistungs- und Wirkungsgradsteigerung mehr erreicht werden. Des Weiteren wurden variierende Eingangsvolumenströme und der Einfluss der dosierten Wassermenge analysiert. Mit steigender chemischer Eingangsleistung und glei- cher Methankonzentration steigt auch die elektrische Leistung, dies führt zu einem nahezu konstanten Systemwirkungsgrad. Höhere Methankonzentrationen liefern, bei annähernd gleicher chemischer Eingangsleistung, deutlich höhere Leistungen und Systemwirkungsgra- de. Diese Untersuchungen wurden an der Biogasanlage der Nordzucker AG, Werk Uelzen wiederholt und bestätigt. Im Systembetrieb zeigte sich immer wieder, dass bei hohen Me- thangehalten die Nachbrennkammer schnell überhitzt und bei niedrigen Methangehalten durch die fehlende thermische Integration der Kathodenabluft nicht ausreichend Wärme für den Reformer bereitgestellt werden konnte. Hier müssten weitere Untersuchungen mit einer neu dimensionierten Nachbrennkammer, welcher die Kathodenabluft direkt zugeführt wird, erfolgen, um die thermische Stabilität des Biogas-SOFC-Systems bei Methangehalten unter 50 Vol.-% und über 80 Vol.-% langfristig beurteilen zu können.
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Membrane-based removal of volatile methylsiloxanes from biogas

Membrane-based removal of volatile methylsiloxanes from biogas

76 | 6. PDMS: VMS separation performance Table 6-1 clearly shows that both permeability and selectivity towards carbon dioxide and methane increase with the molecular size of the siloxane. Accordingly, the most difficult siloxane to remove from biogas should be L2, the easiest L4 and D5. Permeability was calculated assuming a membrane area of 7.05 cm² as the permeating flow was from the lumen side of the fibres outwards. Interestingly, for the calculation of permeance, it was experimentally shown that it does not matter whether the gas permeates into the fibre or the other way around. At equal partial pressure differences, permeate flow is quasi-identical in both cases, leading to the assumption that the effective permeation area corresponds to the smallest area, given by the inner diameter of the fibres. However, this value may vary. According to the manufacturer’s information, the wall thickness of the fibres is between 35 and 45 µm. Own measurements using PDMS film (Table 5-2) with known permeation area and thickness revealed a carbon dioxide permeability of 2680 Barrer at 20°C. The manufacturer plasma- treats the membrane to enhance mechanical stability and potting properties; this leads to a decrease in permeability of estimated 15% (olson@medarray.com, 2010). The calculated permeability of 2200 Barrer in Table 6-1 is therefore very plausible. This implies that the mean fibre wall thickness is rather 45 than 35 µm. Assuming 45 µm as fibre wall thickness, the VMS permeabilities in Table 6-1 are also similar to the values determined using the cup method as shown in the previous chapter (Figure 5-5). No matter which method is used to calculate permeability, the respective permeability of L3, L4 and D4 is practically identical. The cup method yields slightly higher D5 permeability but massively overestimates L2 permeability, probably, as previously suggested, due to swelling and associated plasticisation.
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Modelling dispersal in plants

Modelling dispersal in plants

The outcome of unambiguous paternity analyses targeting dispersal kernel fitting comprises the locations of all potential pollen donors within the study area, the locations of selected mother plants, and the paternal origin of seed samples harvested from the mothers. Such data sets can be interpreted as complex marked point patterns (Stoyan & Stoyan 1994), and related spatial analysis methods allow estimation of empirical pollen dispersal kernels and should be able to reveal whether estimated dispersal probabilities at increasing distances are statistically informative, especially with regard to potentially non-random patterns of individual plants. Broadly, randomizing individual identities over all potential donors, while keeping the spatial attributes of the remaining paternity data, provides a null random mating model against which the empirical pollen dispersal kernel can be confronted. Then, simulation envelopes for the null model, constructed via Monte Carlo procedures, allow for formal testing whether the empirical pollen dispersal kernel significantly differs from that expected under random mating, and therefore how informative paternity data is at different distances for kernel fit purposes.
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