Competitive interactions in social foragers

Empirical and theoretical investigations of aspects of the ideal free distribution (IFD) are presented, with particular emphasis on interactions between individuals within foraging groups. An overview of the theory is presented, and the implications of the work included in this thesis to ideal free distribution theory are discussed. The effect of group size on the relative competitive ability of individual fish within a foraging group is shown to be dependent upon the difference in body size between two focus individuals in a group, but this difference itself has no direct effect on relative competitive ability. A subsequent empirical test of a novel mathematical tool reveals that there is no simple general rule for describing how relative competitive ability will change with group size, and that very specific knowledge of the system under study is needed in order to produce robust predictions. The relative abilities of individual chiclids to obtain food under scramble competition are shown to be highly repeatable between trials. However, when given a choice between two patches differing only in their temporal variability in input about an identical mean, an individual's rank based on intake in one patch was uncorrelated with either its uptake in the other patch or its intake in either of two different trial types. The basis for, and consequence of, this dependence of relative competitive ability on the context of the foraging situation are discussed. The general case (previously unexposed in the literature) where the effect of interference can vary between patches is examined. Simulations from an individual-based model reveal a decrease in the number of stable equilibrium distributions as the competitive advantage of the dominant phenotype declines in one patch, leading eventually to a single stable equilibrium, in which both phenotypes are found on both patches

Improving the tensile strength of carbon nanotube spun yarns using a modified spinning process

A modified process for the dry spinning of carbon nanotube (CNT) yarn is reported. The approach gives an improved structure of CNT bundles in the web drawn from the CNT forest and in the yarn produced from the twisted web leading to improved mechanical properties of the yarn. The process enables many different mechanical and physical treatments to be applied to the individual stages of the pure CNT spinning system, and may allow potential for the development of complex spinning processes such as polymer–CNT-based composite yarns. The tensile strength and yarn/web structure of yarn spun using this approach have been investigated and evaluated using standard tensile testing methods along with scanning electron microscopy. The experimental results show that the tensile properties were significantly improved. The effect of heat treatments and other yarn constructions on the tensile properties are also reported

The Essential Stability of Local Error Control for Dynamical Systems

Although most adaptive software for initial value problems is designed with an accuracy requirement—control of the local error—it is frequently observed that stability is imparted by the adaptation. This relationship between local error control and numerical stability is given a firm theoretical underpinning. The dynamics of numerical methods with local error control are studied for three classes of ordinary differential equations: dissipative, contractive, and gradient systems. Dissipative dynamical systems are characterised by having a bounded absorbing set B which all trajectories eventually enter and remain inside. The exponentially contractive problems studied have a unique, globally exponentially attracting equilibrium point and thus they are also dissipative since the absorbing set B may be chosen to be a ball of arbitrarily small radius around the equilibrium point. The gradient systems studied are those for which the set of equilibria comprises isolated points and all trajectories are bounded so that each trajectory converges to an equilibrium point as t → ∞. If the set of equilibria is bounded then the gradient systems are also dissipative. Conditions under which numerical methods with local error control replicate these large-time dynamical features are described. The results are proved without recourse to asymptotic expansions for the truncation error. Standard embedded Runge–Kutta pairs are analysed together with several nonstandard error control strategies. Both error per step and error per unit step strategies are considered. Certain embedded pairs are identified for which the sequence generated can be viewed as coming from a small perturbation of an algebraically stable scheme, with the size of the perturbation proportional to the tolerance τ. Such embedded pairs are defined to be essentially algebraically stable and explicit essentially stable pairs are identified. Conditions on the tolerance τ are identified under which appropriate discrete analogues of the properties of the underlying differential equation may be proved for certain essentially stable embedded pairs. In particular, it is shown that for dissipative problems the discrete dynamical system has an absorbing set B_τ and is hence dissipative. For exponentially contractive problems the radius of B_τ is proved to be proportional to τ. For gradient systems the numerical solution enters and remains in a small ball about one of the equilibria and the radius of the ball is proportional to τ. Thus the local error control mechanisms confer desirable global properties on the numerical solution. It is shown that for error per unit step strategies the conditions on the tolerance τ are independent of initial data while for error per step strategies the conditions are initial-data dependent. Thus error per unit step strategies are considerably more robust

Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems

The numerical approximation of dissipative initial value problems by fixed time-stepping Runge–Kutta methods is considered and the asymptotic features of the numerical and exact solutions are compared. A general class of ordinary differential equations, for which dissipativity is induced through an inner product, is studied throughout. This class arises naturally in many finite dimensional applications (such as the Lorenz equations) and also from the spatial discretization of a variety of partial differential equations arising in applied mathematics. It is shown that the numerical solution defined by an algebraically stable method has an absorbing set and is hence dissipative for any fixed step-size h > 0. The numerical solution is shown to define a dynamical system on the absorbing set if h is sufficiently small and hence a global attractor A_h exists; upper-semicontinuity of A_h at h = 0 is established, which shows that, for h small, every point on the numerical attractor is close to a point on the true global attractor A. Under the additional assumption that the problem is globally Lipschitz, it is shown that if h is sufficiently small any method with positive weights defines a dissipative dynamical system on the whole space and upper semicontinuity of A_h at h = 0 is again established. For gradient systems with globally Lipschitz vector fields it is shown that any Runge–Kutta method preserves the gradient structure for h sufficiently small. For general dissipative gradient systems it is shown that algebraically stable methods preserve the gradient structure within the absorbing set for h sufficiently small. Convergence of the numerical attractor is studied and, for a dissipative gradient system with hyperbolic equilibria, lower semicontinuity at h = 0 is established. Thus, for such a system, A_h converges to A in the Hausdorff metric as h → 0

Model Problems in Numerical Stability Theory for Initial Value Problems

In the past numerical stability theory for initial value problems in ordinary differential equations has been dominated by the study of problems with simple dynamics; this has been motivated by the need to study error propagation mechanisms in stiff problems, a question modeled effectively by contractive linear or nonlinear problems. While this has resulted in a coherent and self-contained body of knowledge, it has never been entirely clear to what extent this theory is relevant for problems exhibiting more complicated dynamics. Recently there have been a number of studies of numerical stability for wider classes of problems admitting more complicated dynamics. This on-going work is unified and, in particular, striking similarities between this new developing stability theory and the classical linear and nonlinear stability theories are emphasized. The classical theories of A, B and algebraic stability for Runge–Kutta methods are briefly reviewed; the dynamics of solutions within the classes of equations to which these theories apply—linear decay and contractive problems—are studied. Four other categories of equations—gradient, dissipative, conservative and Hamiltonian systems—are considered. Relationships and differences between the possible dynamics in each category, which range from multiple competing equilibria to chaotic solutions, are highlighted. Runge-Kutta schemes that preserve the dynamical structure of the underlying problem are sought, and indications of a strong relationship between the developing stability theory for these new categories and the classical existing stability theory for the older problems are given. Algebraic stability, in particular, is seen to play a central role. It should be emphasized that in all cases the class of methods for which a coherent and complete numerical stability theory exists, given a structural assumption on the initial value problem, is often considerably smaller than the class of methods found to be effective in practice. Nonetheless it is arguable that it is valuable to develop such stability theories to provide a firm theoretical framework in which to interpret existing methods and to formulate goals in the construction of new methods. Furthermore, there are indications that the theory of algebraic stability may sometimes be useful in the analysis of error control codes which are not stable in a fixed step implementation; this work is described

Cool Sex? Hibernation and Reproduction Overlap in the Echidna

During hibernation there is a slowing of all metabolic processes, and thus it is normally considered to be incompatible with reproduction. In Tasmania the egg-laying mammal, the echidna (Tachyglossus aculeatus) hibernates for several months before mating in mid-winter, and in previous studies we observed males with females that were still hibernating. We monitored the reproductive activity of radio-tracked echidnas by swabbing the reproductive tract for sperm while external temperature loggers provided information on the timing of hibernation. Additional information was provided by camera traps and ultrasound imaging. More than a third of the females found in mating groups were torpid, and the majority of these had mated. Some females re-entered deep torpor for extended periods after mating. Ultrasound examination showed a developing egg in the uterus of a female that had repeatedly re-entered torpor. The presence of fresh sperm in cloacal swabs taken from this female on three occasions after her presumed date of fertilization indicated she mated several times after being fertilized. The mating of males with torpid females is the result of extreme competition between promiscuous males, while re-entry into hibernation by pregnant females could improve the possibility of mating with a better quality male

Density-and trait-mediated effects of a parasite and a predator in a tri-trophic food web

1. Despite growing interest in ecological consequences of parasitism in food webs, relatively little is known about effects of parasites on long-term population dynamics of non-host species or about whether such effects are density- or trait- mediated. 2. We studied a tri-trophic food chain comprised of: (i) a bacterial basal resource (Serratia fonticola), (ii) an intermediate consumer (Paramecium caudatum), (iii) a top predator (Didinium nasutum), and (iv) a parasite of the intermediate consumer (Holospora undulata). A fully-factorial experimental manipulation of predator and parasite presence/absence was combined with analyses of population dynamics, modelling, and analyses of host (Paramecium) morphology and behavior. 3. Predation and parasitism each reduced the abundance of the intermediate consumer (Paramecium), and parasitism indirectly reduced the abundance of the basal resource (Serratia). However, in combination, predation and parasitism had non-additive effects on the abundance of the intermediate consumer, as well as on that of the basal resource. In both cases, the negative effect of parasitism seemed to be effaced by predation. 4. Infection of the intermediate consumer reduced predator abundance. Modelling and additional experimentation revealed that this was most likely due to parasite reduction of intermediate host abundance (a density-mediated effect), as opposed to changes in predator functional or numerical response. 5. Parasitism altered morphological and behavioural traits, by reducing host cell length and increasing the swimming speed of cells with moderate parasite loads. Additional tests showed no significant difference in Didinium feeding rate on infected and uninfected hosts, suggesting that the combination of these modifications does not affect host vulnerability to predation. However, estimated rates of encounter with Serratia based on these modifications were higher for infected Paramecium than for uninfected Paramecium. 6. A mixture of density-mediated and trait-mediated indirect effects of parasitism on non- host species creates rich and complex possibilities for effects of parasites in food webs that should be included in assessments of possible impacts of parasite eradication or introduction

Phenotypic Variance Predicts Symbiont Population Densities in Corals: A Modeling Approach

We test whether the phenotypic variance of symbionts (Symbiodinium) in corals is closely related with the capacity of corals to acclimatize to increasing seawater temperatures. Moreover, we assess whether more specialist symbionts will increase within coral hosts under ocean warming. The present study is only applicable to those corals that naturally have the capacity to support more than one type of Symbiodinium within the lifetime of a colony; for example, Montastraea annularis and Montastraea faveolata.The population dynamics of competing Symbiodinium symbiont populations were projected through time in coral hosts using a novel, discrete time optimal-resource model. Models were run for two Atlantic Ocean localities. Four symbiont populations, with different environmental optima and phenotypic variances, were modeled to grow, divide, and compete in the corals under seasonal fluctuations in solar insolation and seawater temperature. Elevated seawater temperatures were input into the model 1.5 degrees C above the seasonal summer average, and the symbiont population response was observed for each location. The models showed dynamic fluctuations in Symbiodinium populations densities within corals. Population density predictions for Lee Stocking Island, the Bahamas, where temperatures were relatively homogenous throughout the year, showed a dominance of both type 2, with high phenotypic variance, and type 1, a high-temperature and high-insolation specialist. Whereas the densities of Symbiodinium types 3 and 4, a high-temperature, low-insolation specialist, and a high-temperature, low-insolation generalist, remained consistently low. Predictions for Key Largo, Florida, where environmental conditions were more seasonally variable, showed the coexistence of generalists (types 2 and 4) and low densities of specialists (types 1 and 3). When elevated temperatures were input into the model, population densities in corals at Lee Stocking Island showed an emergence of high-temperature specialists. However, even under high temperatures, corals in the Florida Keys were dominated by generalists.Predictions at higher seawater temperatures showed endogenous shuffling and an emergence of the high-temperature Symbiodinium specialists, even though their phenotypic variance was low. The model shows that sustaining these "hidden" specialists becomes advantageous under thermal stress conditions, and shuffling symbionts may increase the corals' capacity to acclimatize but not adapt to climatechange-induced ocean warming

Crawling to Collapse: Ecologically Unsound Ornamental Invertebrate Fisheries

Background: Fishery management has historically been an inexact and reactionary discipline, often taking action only after a critical stock suffers overfishing or collapse. The invertebrate ornamental fishery in the State of Florida, with increasing catches over a more diverse array of species, is poised for collapse. Current management is static and the lack of an adaptive strategy will not allow for adequate responses associated with managing this multi-species fishery. The last decade has seen aquarium hobbyists shift their display preference from fish-only tanks to miniature reef ecosystems that include many invertebrate species, creating increased demand without proper oversight. The once small ornamental fishery has become an invertebrate-dominated major industry supplying five continents. Methodology/Principal Findings: Here, we analyzed the Florida Marine Life Fishery (FLML) landing data from 1994 to 2007 for all invertebrate species. The data were organized to reflect both ecosystem purpose (in the wild) and ecosystem services (commodities) for each reported species to address the following question: Are ornamental invertebrates being exploited for their fundamental ecosystem services and economic value at the expense of reef resilience? We found that 9 million individuals were collected in 2007, 6 million of which were grazers. Conclusions/Significance: The number of grazers now exceeds, by two-fold, the number of specimens collected for curio and ornamental purposes altogether, representing a major categorical shift. In general, landings have increased 10-fold since 1994, though the number of licenses has been dramatically reduced. Thus, despite current management strategies, the FLML Fishery appears to be crawling to collapse

Rapid decreases in relative testes mass among monogamous birds but not in other vertebrates

Larger testes produce more sperm and therefore improve reproductive success in the face of sperm competition. Adaptation to social mating systems with relatively high and low sperm competition are therefore likely to have driven changes in relative testes size in opposing directions. Here, we combine the largest vertebrate testes mass dataset ever collected with phylogenetic approaches for measuring rates of morphological evolution to provide the first quantitative evidence for how relative testes mass has changed over time. We detect explosive radiations of testes mass diversity distributed throughout the vertebrate tree of life: bursts of rapid change have been frequent during vertebrate evolutionary history. In socially monogamous birds, there have been repeated rapid reductions in relative testes mass. We see no such pattern in other monogamous vertebrates; the prevalence of monogamy in birds may have increased opportunities for investment in alternative behaviours and physiologies allowing reduced investment in expensive testes