Light history-dependent respiration explains the hysteresis in the daily ecosystem metabolism of seagrass

Oxygen flux between aquatic ecosystems and the water column is a measure of ecosystem metabolism. However, the oxygen flux varies during the day in a “hysteretic” pattern: there is higher net oxygen production at a given irradiance in the morning than in the afternoon. In this study, we investigated the mechanism responsible for the hysteresis in oxygen flux by measuring the daily pattern of oxygen flux, light, and temperature in a seagrass ecosystem (Zostera muelleri in Swansea Shoals, Australia) at three depths. We hypothesised that the oxygen flux pattern could be due to diel variations in either gross primary production or respiration in response to light history or temperature. Hysteresis in oxygen flux was clearly observed at all three depths. We compared this data to mathematical models, and found that the modification of ecosystem respiration by light history is the best explanation for the hysteresis in oxygen flux. Light history-dependent respiration might be due to diel variations in seagrass respiration or the dependence of bacterial production on dissolved organic carbon exudates. Our results indicate that the daily variation in respiration rate may be as important as the daily changes of photosynthetic characteristics in determining the metabolic status of aquatic ecosystems.

Society by Numbers : Studies on Model-Based Explanations in the Social Sciences

The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

A new data source for fisheries resource assessment: genetic estimates of the effective number of spawners. Final Report to the Fisheries Research and Development Corporation.

The development of innovative methods of stock assessment is a priority for State and Commonwealth fisheries agencies. It is driven by the need to facilitate sustainable exploitation of naturally occurring fisheries resources for the current and future economic, social and environmental well being of Australia. This project was initiated in this context and took advantage of considerable recent achievements in genomics that are shaping our comprehension of the DNA of humans and animals. The basic idea behind this project was that genetic estimates of effective population size, which can be made from empirical measurements of genetic drift, were equivalent to estimates of the successful number of spawners that is an important parameter in process of fisheries stock assessment. The broad objectives of this study were to 1. Critically evaluate a variety of mathematical methods of calculating effective spawner numbers (Ne) by a. conducting comprehensive computer simulations, and by b. analysis of empirical data collected from the Moreton Bay population of tiger prawns (P. esculentus). 2. Lay the groundwork for the application of the technology in the northern prawn fishery (NPF). 3. Produce software for the calculation of Ne, and to make it widely available. The project pulled together a range of mathematical models for estimating current effective population size from diverse sources. Some of them had been recently implemented with the latest statistical methods (eg. Bayesian framework Berthier, Beaumont et al. 2002), while others had lower profiles (eg. Pudovkin, Zaykin et al. 1996; Rousset and Raymond 1995). Computer code and later software with a user-friendly interface (NeEstimator) was produced to implement the methods. This was used as a basis for simulation experiments to evaluate the performance of the methods with an individual-based model of a prawn population. Following the guidelines suggested by computer simulations, the tiger prawn population in Moreton Bay (south-east Queensland) was sampled for genetic analysis with eight microsatellite loci in three successive spring spawning seasons in 2001, 2002 and 2003. As predicted by the simulations, the estimates had non-infinite upper confidence limits, which is a major achievement for the application of the method to a naturally-occurring, short generation, highly fecund invertebrate species. The genetic estimate of the number of successful spawners was around 1000 individuals in two consecutive years. This contrasts with about 500,000 prawns participating in spawning. It is not possible to distinguish successful from non-successful spawners so we suggest a high level of protection for the entire spawning population. We interpret the difference in numbers between successful and non-successful spawners as a large variation in the number of offspring per family that survive – a large number of families have no surviving offspring, while a few have a large number. We explored various ways in which Ne can be useful in fisheries management. It can be a surrogate for spawning population size, assuming the ratio between Ne and spawning population size has been previously calculated for that species. Alternatively, it can be a surrogate for recruitment, again assuming that the ratio between Ne and recruitment has been previously determined. The number of species that can be analysed in this way, however, is likely to be small because of species-specific life history requirements that need to be satisfied for accuracy. The most universal approach would be to integrate Ne with spawning stock-recruitment models, so that these models are more accurate when applied to fisheries populations. A pathway to achieve this was established in this project, which we predict will significantly improve fisheries sustainability in the future. Regardless of the success of integrating Ne into spawning stock-recruitment models, Ne could be used as a fisheries monitoring tool. Declines in spawning stock size or increases in natural or harvest mortality would be reflected by a decline in Ne. This would be good for data-poor fisheries and provides fishery independent information, however, we suggest a species-by-species approach. Some species may be too numerous or experiencing too much migration for the method to work. During the project two important theoretical studies of the simultaneous estimation of effective population size and migration were published (Vitalis and Couvet 2001b; Wang and Whitlock 2003). These methods, combined with collection of preliminary genetic data from the tiger prawn population in southern Gulf of Carpentaria population and a computer simulation study that evaluated the effect of differing reproductive strategies on genetic estimates, suggest that this technology could make an important contribution to the stock assessment process in the northern prawn fishery (NPF). Advances in the genomics world are rapid and already a cheaper, more reliable substitute for microsatellite loci in this technology is available. Digital data from single nucleotide polymorphisms (SNPs) are likely to super cede ‘analogue’ microsatellite data, making it cheaper and easier to apply the method to species with large population sizes.

Evolution of sex ratios in social hymenoptera: consequences of finite brood size

Evolutionarily stable sex ratios are determined for social hymenoptera under local mate competition (LMC) and when the brood size is finite. LMC is modelled by the parameter d. Of the reproductive progeny from a single foundress nest, a fraction d disperses (outbreeding), while (1-d) mate amongst themselves (sibmating). When the brood size is finite, d is taken to be the probability of an offspring dispersing, and similarly, r, the proportion of male offspring, the probability of a haploid egg being laid. Under the joint influence of these two stochastic processes, there is a nonzero probability that some females remain unmated in the nest. As a result, the optimal proportion of males (corresponding to the evolutionarily stable strategy, ESS) is higher than that obtained when the brood size is infinite. When the queen controls the sex ration, the ESS becomes more female biased under increased inbreeding (lower d), However, the ESS under worker control shows an unexpected pattern, including an increase in the proportion of males with increased inbreeding. This effect is traced to the complex interaction between inbreeding and local mate competition.

ANZIAM 2015

The 51st ANZIAM Conference was held on 1–5 February 2015 in the Outrigger Hotel, Surfers Paradise, Australia. A total of 229 people registered for the conference, with nine plenary presentations, 78 student presentations and 107 non-student presentations. Highlights of the conference included the plenary talks, presentations by the 2014 Michell and ANZIAM Medalists, the Women in Mathematics Lunch and the Conference Dinner and Awards Ceremony. The main conference was followed by a one-day workshop entitled ‘Discrete mathematical models in the life sciences’, held at Queensland University of Technology, Brisbane, on February 6, 2015.

Harvest strategy evaluations and co-management for the Moreton Bay Trawl Fishery

Non-Technical Summary Seafood CRC Project 2009/774. Harvest strategy evaluations and co-management for the Moreton Bay Trawl Fishery Principal Investigator: Dr Tony Courtney, Principal Fisheries Biologist Fisheries and Aquaculture, Agri-Science Queensland Department of Agriculture, Fisheries and Forestry Level B1, Ecosciences Precinct, Joe Baker St, Dutton Park, Queensland 4102 Email: tony.courtney@daff.qld.gov.au Project objectives: 1. Review the literature and data (i.e., economic, biological and logbook) relevant to the Moreton Bay trawl fishery. 2. Identify and prioritise management objectives for the Moreton Bay trawl fishery, as identified by the trawl fishers. 3. Undertake an economic analysis of Moreton Bay trawl fishery. 4. Quantify long-term changes to fishing power for the Moreton Bay trawl fishery. 5. Assess priority harvest strategies identified in 2 (above). Present results to, and discuss results with, Moreton Bay Seafood Industry Association (MBSIA), fishers and Fisheries Queensland. Note: Additional, specific objectives for 2 (above) were developed by fishers and the MBSIA after commencement of the project. These are presented in detail in section 5 (below). The project was an initiative of the MBSIA, primarily in response to falling profitability in the Moreton Bay prawn trawl fishery. The analyses were undertaken by a consortium of DAFF, CSIRO and University of Queensland researchers. This report adopted the Australian Standard Fish Names (http://www.fishnames.com.au/). Trends in catch and effort The Moreton Bay otter trawl fishery is a multispecies fishery, with the majority of the catch composed of Greasyback Prawns (Metapenaeus bennettae), Brown Tiger Prawns (Penaeus esculentus), Eastern King Prawns (Melicertus plebejus), squid (Uroteuthis spp., Sepioteuthis spp.), Banana Prawns (Fenneropenaeus merguiensis), Endeavour Prawns (Metapenaeus ensis, Metapenaeus endeavouri) and Moreton Bay bugs (Thenus parindicus). Other commercially important byproduct includes blue swimmer crabs (Portunus armatus), three-spot crabs (Portunus sanguinolentus), cuttlefish (Sepia spp.) and mantis shrimp (Oratosquilla spp.). Logbook catch and effort data show that total annual reported catch of prawns from the Moreton Bay otter trawl fishery has declined to 315 t in 2008 from a maximum of 901 t in 1990. The number of active licensed vessels participating in the fishery has also declined from 207 in 1991 to 57 in 2010. Similarly, fishing effort has fallen from a peak of 13,312 boat-days in 1999 to 3817 boat-days in 2008 – a 71% reduction. The declines in catch and effort are largely attributed to reduced profitability in the fishery due to increased operational costs and depressed prawn prices. The low prawn prices appear to be attributed to Australian aquacultured prawns and imported aquacultured vannamei prawns, displacing the markets for trawl-caught prawns, especially small species such as Greasyback Prawns which traditionally dominated landings in Moreton Bay. In recent years, the relatively high Australian dollar has resulted in reduced exports of Australian wild-caught prawns. This has increased supply on the domestic market which has also suppressed price increases. Since 2002, Brown Tiger Prawns have dominated annual reported landings in the Moreton Bay fishery. While total catch and effort in the bay have declined to historically low levels, the annual catch and catch rates of Brown Tiger Prawns have been at record highs in recent years. This appears to be at least partially attributed to the tiger prawn stock having recovered from excessive effort in previous decades. The total annual value of the Moreton Bay trawl fishery catch, including byproduct, is about $5 million, of which Brown Tiger Prawns account for about $2 million. Eastern King Prawns make up about 10% of the catch and are mainly caught in the bay from October to December as they migrate to offshore waters outside the bay where they contribute to a large mono-specific trawl fishery. Some of the Eastern King Prawns harvested in Moreton Bay may be growth overfished (i.e., caught below the size required to maximise yield or value), although the optimum size-at-capture was not determined in this study. Banana Prawns typically make up about 5% of the catch, but can exceed 20%, particularly following heavy rainfall. Economic analysis of the fishery From the economic survey, cash profits were, on average, positive for both fleet segments in both years of the survey. However, after the opportunity cost of capital and depreciation were taken into account, the residual owner-operator income was relatively low, and substantially lower than the average share of revenue paid to employed skippers. Consequently, owner-operators were earning less than their opportunity cost of their labour, suggesting that the fleets were economically unviable in the longer term. The M2 licensed fleet were, on average, earning similar boat cash profits as the T1/M1 fleet, although after the higher capital costs were accounted for the T1/M1 boats were earning substantially lower returns to owner-operator labour. The mean technical efficiency for the fleet as a whole was estimated to be 0.67. That is, on average, the boats were only catching 67 per cent of what was possible given their level of inputs (hours fished and hull units). Almost one-quarter of observations had efficiency scores above 0.8, suggesting a substantial proportion of the fleet are relatively efficient, but some are also relatively inefficient. Both fleets had similar efficiency distributions, with median technical efficiency score of 0.71 and 0.67 for the M2 and T1/M1 boats respectively. These scores are reasonably consistent with other studies of prawn trawl fleets in Australia, although higher average efficiency scores were found in the NSW prawn trawl fleet. From the inefficiency model, several factors were found to significantly influence vessel efficiency. These included the number of years of experience as skipper, the number of generations that the skipper’s family had been fishing and the number of years schooling. Skippers with more schooling were significantly more efficient than skippers with lower levels of schooling, consistent with other studies. Skippers who had been fishing longer were, in fact, less efficient than newer skippers. However, this was mitigated in the case of skippers whose family had been involved in fishing for several generations, consistent with other studies and suggesting that skill was passed through by families over successive generations. Both the linear and log-linear regression models of total fishing effort against the marginal profit per hour performed reasonably well, explaining between 70 and 84 per cent of the variation in fishing effort. As the models had different dependent variables (one logged and the other not logged) this is not a good basis for model choice. A better comparator is the square root of the mean square error (SMSE) expressed as a percentage of the mean total effort. On this criterion, both models performed very similarly. The linear model suggests that each additional dollar of average profits per hour in the fishery increases total effort by around 26 hours each month. From the log linear model, each percentage increase in profits per hour increases total fishing effort by 0.13 per cent. Both models indicate that economic performance is a key driver of fishing effort in the fishery. The effect of removing the boat-replacement policy is to increase individual vessel profitability, catch and effort, but the overall increase in catch is less than that removed by the boats that must exit the fishery. That is, the smaller fleet (in terms of boat numbers) is more profitable but the overall catch is not expected to be greater than before. This assumes, however, that active boats are removed, and that these were also taking an average level of catch. If inactive boats are removed, then catch of the remaining group as a whole could increase by between 14 and 17 per cent depending on the degree to which costs are reduced with the new boats. This is still substantially lower than historical levels of catch by the fleet. Fishing power analyses An analysis of logbook data from 1988 to 2010, and survey information on fishing gear, was performed to estimate the long-term variation in the fleet’s ability to catch prawns (known as fishing power) and to derive abundance estimates of the three most commercially important prawn species (i.e., Brown Tiger, Eastern King and Greasyback Prawns). Generalised linear models were used to explain the variation in catch as a function of effort (i.e., hours fished per day), vessel and gear characteristics, onboard technologies, population abundance and environmental factors. This analysis estimated that fishing power associated with Brown Tiger and Eastern King Prawns increased over the past 20 years by 10–30% and declined by approximately 10% for greasybacks. The density of tiger prawns was estimated to have almost tripled from around 0.5 kg per hectare in 1988 to 1.5 kg/ha in 2010. The density of Eastern King Prawns was estimated to have fluctuated between 1 and 2 kg per hectare over this time period, without any noticeable overall trend, while Greasyback Prawn densities were estimated to have fluctuated between 2 and 6 kg per hectare, also without any distinctive trend. A model of tiger prawn catches was developed to evaluate the impact of fishing on prawn survival rates in Moreton Bay. The model was fitted to logbook data using the maximum-likelihood method to provide estimates of the natural mortality rate (0.038 and 0.062 per week) and catchability (which can be defined as the proportion of the fished population that is removed by one unit of effort, in this case, estimated to be 2.5 ± 0.4 E-04 per boat-day). This approach provided a method for industry and scientists to develop together a realistic model of the dynamics of the fishery. Several aspects need to be developed further to make this model acceptable to industry. Firstly, there is considerable evidence to suggest that temperature influences prawn catchability. This ecological effect should be incorporated before developing meaningful harvest strategies. Secondly, total effort has to be allocated between each species. Such allocation of effort could be included in the model by estimating several catchability coefficients. Nevertheless, the work presented in this report is a stepping stone towards estimating essential fishery parameters and developing representative mathematical models required to evaluate harvest strategies. Developing a method that allowed an effective discussion between industry, management and scientists took longer than anticipated. As a result, harvest strategy evaluations were preliminary and only included the most valuable species in the fishery, Brown Tiger Prawns. Additional analyses and data collection, including information on catch composition from field sampling, migration rates and recruitment, would improve the modelling. Harvest strategy evaluations As the harvest strategy evaluations are preliminary, the following results should not be adopted for management purposes until more thorough evaluations are performed. The effects, of closing the fishery for one calendar month, on the annual catch and value of Brown Tiger Prawns were investigated. Each of the 12 months (i.e., January to December) was evaluated. The results were compared against historical records to determine the magnitude of gain or loss associated with the closure. Uncertainty regarding the trawl selectivity was addressed using two selectivity curves, one with a weight at 50% selection (S50%) of 7 g, based on research data, and a second with S50% of 14 g, put forward by industry. In both cases, it was concluded that any monthly closure after February would not be beneficial to the industry. The magnitude of the benefit of closing the fishery in either January or February was sensitive to which mesh selectivity curve that was assumed, with greater benefit achieved when the smaller selectivity curve (i.e., S50% = 7 g) was assumed. Using the smaller selectivity (S50% = 7 g), the expected increase in catch value was 10–20% which equates to $200,000 to $400,000 annually, while the larger selectivity curve (S50% = 14 g) suggested catch value would be improved by 5–10%, or $100,000 to $200,000. The harvest strategy evaluations showed that greater benefits, in the order of 30–60% increases in the tiger annual catch value, could have been obtained by closing the fishery early in the year when annual effort levels were high (i.e., > 10,000 boat-days). In recent years, as effort levels have declined (i.e., ~4000 boat-days annually), expected benefits from such closures are more modest. In essence, temporal closures offer greater benefit when fishing mortality rates are high. A spatial analysis of Brown Tiger Prawn catch and effort was also undertaken to obtain a better understanding of the prawn population dynamics. This indicated that, to improve profitability of the fishery, fishers could consider closing the fishery in the period from June to October, which is already a period of low profitability. This would protect the Brown Tiger Prawn spawning stock, increase catch rates of all species in the lucrative pre-Christmas period (November–December), and provide fishers with time to do vessel maintenance, arrange markets for the next season’s harvest, and, if they wish, work at other jobs. The analysis found that the instantaneous rate of total mortality (Z) for the March–June period did not vary significantly over the last two decades. As the Brown Tiger Prawn population in Moreton Bay has clearly increased over this time period, an interesting conclusion is that the instantaneous rate of natural mortality (M) must have increased, suggesting that tiger prawn natural mortality may be density-dependent at this time of year. Mortality rates of tiger prawns for June–October were found to have decreased over the last two decades, which has probably had a positive effect on spawning stocks in the October–November spawning period. Abiotic effects on the prawns The influence of air temperature, rainfall, freshwater flow, the southern oscillation index (SOI) and lunar phase on the catch rates of the four main prawn species were investigated. The analyses were based on over 200,000 daily logbook catch records over 23 years (i.e., 1988–2010). Freshwater flow was more influential than rainfall and SOI, and of the various sources of flow, the Brisbane River has the greatest volume and influence on Moreton Bay prawn catches. A number of time-lags were also considered. Flow in the preceding month prior to catch (i.e., 30 days prior, Logflow1_30) and two months prior (31–60 days prior, Logflow31_60) had strong positive effects on Banana Prawn catch rates. Average air temperature in the preceding 4-6 months (Temp121_180) also had a large positive effect on Banana Prawn catch rates. Flow in the month immediately preceding catch (Logflow1_30) had a strong positive influence on Greasyback Prawn catch rates. Air temperature in the preceding two months prior to catch (Temp1_60) had a large positive effect on Brown Tiger Prawn catch rates. No obvious or marked effects were detected for Eastern King Prawns, although interestingly, catch rates declined with increasing air temperature 4–6 months prior to catch. As most Eastern King Prawn catches in Moreton Bay occur in October to December, the results suggest catch rates decline with increasing winter temperatures. In most cases, the prawn catch rates declined with the waxing lunar phase (high luminance/full moon), and increased with the waning moon (low luminance/new moon). The SOI explains little additional variation in prawn catch rates (~ <2%), although its influence was higher for Banana Prawns. Extrapolating findings of the analyses to long-term climate change effects should be interpreted with caution. That said, the results are consistent with likely increases in abundance in the region for the two tropical species, Banana Prawns and Brown Tiger Prawns, as coastal temperatures rise. Conversely, declines in abundance could be expected for the two temperate species, Greasyback and Eastern King Prawns. Corporate management structures An examination of alternative governance systems was requested by the industry at one of the early meetings, particularly systems that may give them greater autonomy in decision making as well as help improve the marketing of their product. Consequently, a review of alternative management systems was undertaken, with a particular focus on the potential for self-management of small fisheries (small in terms of number of participants) and corporate management. The review looks at systems that have been implemented or proposed for other small fisheries internationally, with a particular focus on self-management as well as the potential benefits and challenges for corporate management. This review also highlighted particular opportunities for the Moreton Bay prawn fishery. Corporate management differs from other co-management and even self-management arrangements in that ‘ownership’ of the fishery is devolved to a company in which fishers and government are shareholders. The company manages the fishery as well as coordinates marketing to ensure that the best prices are received and that the catch taken meets the demands of the market. Coordinated harvesting will also result in increased profits, which are returned to fishers in the form of dividends. Corporate management offers many of the potential benefits of an individual quota system without formally implementing such a system. A corporate management model offers an advantage over a self-management model in that it can coordinate both marketing and management to take advantage of this unique geographical advantage. For such a system to be successful, the fishery needs to be relatively small and self- contained. Small in this sense is in terms of number of operators. The Moreton Bay prawn fishery satisfies these key conditions for a successful self-management and potentially corporate management system. The fishery is small both in terms of number of participants and geography. Unlike other fisheries that have progressed down the self-management route, the key market for the product from the Moreton Bay fishery is right at its doorstep. Corporate management also presents a number of challenges. First, it will require changes in the way fishers operate. In particular, the decision on when to fish and what to catch will be taken away from the individual and decided by the collective. Problems will develop if individuals do not join the corporation but continue to fish and market their own product separately. While this may seem an attractive option to fishers who believe they can do better independently, this is likely to be just a short- term advantage with an overall long-run cost to themselves as well as the rest of the industry. There are also a number of other areas that need further consideration, particularly in relation to the allocation of shares, including who should be allocated shares (e.g. just boat owners or also some employed skippers). Similarly, how harvesting activity is to be allocated by the corporation to the fishers. These are largely issues that cannot be answered without substantial consultation with those likely to be affected, and these groups cannot give these issues serious consideration until the point at which they are likely to become a reality. Given the current structure and complexity of the fishery, it is unlikely that such a management structure will be feasible in the short term. However, the fishery is a prime candidate for such a model, and development of such a management structure in the future should be considered as an option for the longer term.

Evaluating and validating abundance monitoring methods in the absence of populations of known size: review and application to a passive tracking index

Rarely is it possible to obtain absolute numbers in free-ranging populations and although various direct and indirect methods are used to estimate abundance, few are validated against populations of known size. In this paper, we apply grounding, calibration and verification methods, used to validate mathematical models, to methods of estimating relative abundance. To illustrate how this might be done, we consider and evaluate the widely applied passive tracking index (PTI) methodology. Using published data, we examine the rationality of PTI methodology, how conceptually animal activity and abundance are related and how alternative methods are subject to similar biases or produce similar abundance estimates and trends. We then attune the method against populations representing a range of densities likely to be encountered in the field. Finally, we compare PTI trends against a prediction that adjacent populations of the same species will have similar abundance values and trends in activity. We show that while PTI abundance estimates are subject to environmental and behavioural stochasticity peculiar to each species, the PTI method and associated variance estimate showed high probability of detection, high precision of abundance values and, generally, low variability between surveys, and suggest that the PTI method applied using this procedure and for these species provides a sensitive and credible index of abundance. This same or similar validation approach can and should be applied to alternative relative abundance methods in order to demonstrate their credibility and justify their use.

Influences of Allee effects in the spreading of malignant tumours

A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371–379, 2014] evidences that the Allee effect—in its strong form, the requirement of a minimum density for cell growth—is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Performance evaluation of elitist-mutated multi-objective particle swarm optimization for integrated water resources management

Optimal allocation of water resources for various stakeholders often involves considerable complexity with several conflicting goals, which often leads to multi-objective optimization. In aid of effective decision-making to the water managers, apart from developing effective multi-objective mathematical models, there is a greater necessity of providing efficient Pareto optimal solutions to the real world problems. This study proposes a swarm-intelligence-based multi-objective technique, namely the elitist-mutated multi-objective particle swarm optimization technique (EM-MOPSO), for arriving at efficient Pareto optimal solutions to the multi-objective water resource management problems. The EM-MOPSO technique is applied to a case study of the multi-objective reservoir operation problem. The model performance is evaluated by comparing with results of a non-dominated sorting genetic algorithm (NSGA-II) model, and it is found that the EM-MOPSO method results in better performance. The developed method can be used as an effective aid for multi-objective decision-making in integrated water resource management.

A particle filtering approach for structural system identification in vehicle–structure interaction problems

The problem of identification of parameters of a beam-moving oscillator system based on measurement of time histories of beam strains and displacements is considered. The governing equations of motion here have time varying coefficients. The parameters to be identified are however time invariant and consist of mass, stiffness and damping characteristics of the beam and oscillator subsystems. A strategy based on dynamic state estimation method, that employs particle filtering algorithms, is proposed to tackle the identification problem. The method can take into account measurement noise, guideway unevenness, spatially incomplete measurements, finite element models for supporting structure and moving vehicle, and imperfections in the formulation of the mathematical models. Numerical illustrations based on synthetic data on beam-oscillator system are presented to demonstrate the satisfactory performance of the proposed procedure.

Association between molecular variation in the phosphoglucose isomerase (Pgi) locus and migration propensity in the Glanville fritillary butterfly

Habitat fragmentation produces patches of suitable habitat surrounded by unfavourable matrix habitat. A species may persist in such a fragmented landscape in an equilibrium between the extinctions and recolonizations of local populations, thus forming a metapopulation. Migration between local populations is necessary for the long-term persistence of a metapopulation. The Glanville fritillary butterfly (Melitaea cinxia) forms a metapopulation in the Åland islands in Finland. There is migration between the populations, the extent of which is affected by several environmental factors and variation in the phenotype of individual butterflies. Different allelic forms of the glycolytic enzyme phosphoglucose isomerase (Pgi) has been identified as a possible genetic factor influencing flight performance and migration rate in this species. The frequency of a certain Pgi allele, Pgi-f, follows the same pattern in relation to population age and connectivity as migration propensity. Furthermore, variation in flight metabolic performance, which is likely to affect migration propensity, has been linked to genetic variation in Pgi or a closely linked locus. The aim of this study was to investigate the association between Pgi genotype and the migration propensity in the Glanville fritillary both at the individual and population levels using a statistical modelling approach. A mark-release-recapture (MRR) study was conducted in a habitat patch network of M. cinxia in Åland to collect data on the movements of individual butterflies. Larval samples from the study area were also collected for population level examinations. Each butterfly and larva was genotyped at the Pgi locus. The MRR data was parameterised with two mathematical models of migration: the Virtual Migration Model (VM) and the spatially explicit diffusion model. VM model predicted and observed numbers of emigrants from populations with high and low frequencies of Pgi-f were compared. Posterior predictive data sets were simulated based on the parameters of the diffusion model. Lack-of-fit of observed values to the model predicted values of several descriptors of movements were detected, and the effect of Pgi genotype on the deviations was assessed by randomizations including the genotype information. This study revealed a possible difference in the effect of Pgi genotype on migration propensity between the two sexes in the Glanville fritillary. The females with and males without the Pgi-f allele moved more between habitat patches, which is probably related to differences in the function of flight in the two sexes. Females may use their high flight capacity to migrate between habitat patches to find suitable oviposition sites, whereas males may use it to acquire mates by keeping a territory and fighting off other intruding males, possibly causing them to emigrate. The results were consistent across different movement descriptors and at the individual and population levels. The effect of Pgi is likely to be dependent on the structure of the landscape and the prevailing environmental conditions.

Tetrahydrofuran Clathrate Hydrate Formation

We report on the formation of tetrahydrofuran clathrate hydrate studied by x-ray Raman scattering measurements at the oxygen K edge. A comparison of x-ray Raman spectra measured from water-tetrahydrofuran mixtures and tetrahydrofuran hydrate at different temperatures supports stochastic hydrate formation models rather than models assuming hydrate precursors. This is confirmed by molecular dynamics simulations and density functional theory calculations of x-ray Raman spectra. In addition, changes in the spectra of tetrahydrofuran hydrate with temperatures close to the hydrate's dissociation temperature were observed and may be connected to changes in hydrate's local structure due to the formation of hydrogen bonds between guest and water molecules.

J. B. S. Haldane, Ernst Mayr and the Beanbag Genetics Dispute

Starting from the early decades of the twentieth century, evolutionary biology began to acquire mathematical overtones. This took place via the development of a set of models in which the Darwinian picture of evolution was shown to be consistent with the laws of heredity discovered by Mendel. The models, which came to be elaborated over the years, define a field of study known as population genetics. Population genetics is generally looked upon as an essential component of modern evolutionary theory. This article deals with a famous dispute between J. B. S. Haldane, one of the founders of population genetics, and Ernst Mayr, a major contributor to the way we understand evolution. The philosophical undercurrents of the dispute remain relevant today. Mayr and Haldane agreed that genetics provided a broad explanatory framework for explaining how evolution took place but differed over the relevance of the mathematical models that sought to underpin that framework. The dispute began with a fundamental issue raised by Mayr in 1959: in terms of understanding evolution, did population genetics contribute anything beyond the obvious? Haldane's response came just before his death in 1964. It contained a spirited defense, not just of population genetics, but also of the motivations that lie behind mathematical modelling in biology. While the difference of opinion persisted and was not glossed over, the two continued to maintain cordial personal relations.

Integrated Reservoir Operation Modeling for Irrigation Systems - A Multi-Objective Approach

An integrated reservoir operation model is presented for developing effective operational policies for irrigation water management. In arid and semi-arid climates, owing to dynamic changes in the hydroclimatic conditions within a season, the fixed cropping pattern with conventional operating policies, may have considerable impact on the performance of the irrigation system and may affect the economics of the farming community. For optimal allocation of irrigation water in a season, development of effective mathematical models may guide the water managers in proper decision making and consequently help in reducing the adverse effects of water shortage and crop failure problems. This paper presents a multi-objective integrated reservoir operation model for multi-crop irrigation system. To solve the multi-objective model, a recent swarm intelligence technique, namely elitist-mutated multi-objective particle swarm optimisation (EM-MOPSO) has been used and applied to a case study in India. The method evolves effective strategies for irrigation crop planning and operation policies for a reservoir system, and thereby helps farming community in improving crop benefits and water resource usage in the reservoir command area.