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AimUnderstanding the processes driving population declines in migratory species can be challenging. Not only are monitoring data spatially and temporally sparse, but conditions in one location can carry over to indirectly (and disproportionately) affect the population in another location. Here, we explore whether remote factors can sequentially, and potentially cumulatively, influence local population fluctuations in declining populations of shorebirds.LocationMoreton Bay (Australia) and the East Asian–Australasian Flyway.MethodsWe use N‐mixture models to account for variable observer effort and estimate yearly population growth rate. We then use least squares regressions to correlate population growth rates with remotely sensed climate anomalies at different migratory stages. From this, we estimate species‐specific climate sensitivity indices and explore whether species which are declining more rapidly, or which rely more heavily on areas undergoing rapid habitat loss, have higher climate sensitivity indices.ResultsWe find that species which rely more on the Yellow Sea during migratory stopover (a region which has undergone severe habitat loss) are more sensitive to rainfall anomalies in their Arctic breeding grounds, suggesting that habitat loss reduces the resilience of shorebirds to climate extremes. Furthermore, species with higher sensitivities to climatic conditions during stopover are also those which are declining quickest, suggesting that declining populations may also be less resilient to climate fluctuations at bottleneck sites. We also observed species‐specific correlations between climate anomalies at all migratory stages and population growth rates, primarily for eastern curlew and lesser sand plover.Main conclusionBy applying methods in combination, it is possible to use citizen science data from a single location in a flyway of over 160 sites up to 11,680 km apart, to investigate how different stressors correlate with local population dynamics. published

Monitoring to detect population declines is widespread, but also costly. There is, consequently, a need to optimize monitoring to maximize cost-effectiveness. Here we develop a quantitative decision analysis framework for how to optimally allocate resources for monitoring among species. By keeping the framework simple, we analytically establish two new principles about which species are optimal to monitor for detecting declines: (1) those that lie on the boundary between species being allocated resources for conservation action and species that are not and (2) those with the greatest uncertainty in whether they are declining. These two principles are in addition to other factors that are also important in monitoring decisions, such as complementarity. We demonstrate the efficacy of these principles when other factors are not present, and show how the two principles can be combined. This analysis demonstrates that the most cost-effective species to monitor are ones where the information gained from monitoring is most likely to change the allocation of funds for action, not necessarily the most vulnerable or endangered. We suggest these results are general and apply to all ecological monitoring, not just of biological species: monitoring and information are only valuable when they are likely to change how people act.

At the heart of our efforts to protect threatened species, there is a controversial debate about whether to give priority to cost-effective actions or whether focusing solely on the most endangered species will ultimately lead to preservation of the greatest number of species. By framing this debate within a decision-analytic framework, we show that allocating resources solely to the most endangered species will typically not minimise the number of extinctions in the long-term, as this does not account for the risk of less endangered species going extinct in the future. It is only favoured when our planning timeframe is short or we have a long-term view and we are optimistic about future conditions. Conservation funding tends to be short-term in nature, which biases allocations to more endangered species. Our work highlights the need to consider resource allocation for biodiversity over the long-term; 'preventive conservation', rather than just short-term fire-fighting.

Classifying species according to their risk of extinction is a common practice and underpins much conservation activity. The reliability of such classifications rests on the accuracy of threat categorizations, but very little is known about the magnitude and types of errors that might be expected. The process of risk classification involves combining information from many sources, and understanding the quality of each source is critical to evaluating the overall status of the species. One common criterion used to classify extinction risk is a decline in abundance. Because abundance is a direct measure of conservation status, counts of individuals are generally the preferred method of evaluating whether populations are declining. Using the thresholds from criterion A of the International Union for Conservation of Nature (IUCN) Red List (critically endangered, decline in abundance of >80% over 10 years or 3 generations; endangered, decline in abundance of 50-80%; vulnerable, decline in abundance of 30-50%; least concern or near threatened, decline in abundance of 0-30%), we assessed 3 methods used to detect declines solely from estimates of abundance: use of just 2 estimates of abundance; use of linear regression on a time series of abundance; and use of state-space models on a time series of abundance. We generated simulation data from empirical estimates of the typical variability in abundance and assessed the 3 methods for classification errors. The estimates of the proportion of falsely detected declines for linear regression and the state-space models were low (maximum 3-14%), but 33-75% of small declines (30-50% over 15 years) were not detected. Ignoring uncertainty in estimates of abundance (with just 2 estimates of abundance) allowed more power to detect small declines (95%), but there was a high percentage (50%) of false detections. For all 3 methods, the proportion of declines estimated to be >80% was higher than the true proportion. Use of abundance data to detect species at risk of extinction may either fail to detect initial declines in abundance or have a high error rate.

Resonant modes of an elliptic membrane are computed for a wide range of frequencies using a Galerkin formulation. Results are confirmed using Mathieu functions and finite-element methods. Algorithms and their implementations are described to handle Dirichlet or Neumann boundary conditions and draw animations or contour plots of the modal surfaces. The methods agree to four or more digit accuracy for the first one hundred modes. The effects of high function order and high frequency parameter upon the convergence of the modified Mathieu function series are discussed and quantified. The Galerkin method is conceptually simple and requires only an eigenvalue solver without the need of special functions.

Laplace's equation is solved via separation of variables in toroidal coordinates for the electrostatic potential external to a conducting torus placed in a uniform electric field and excited by an arbitrarily located point charge. The accuracy of the static thin-wire kernel approximation in an integral equation applied to the circular loop is verified using the exact results in the limit as the toroid shrinks to a ring. An equivalent lineal charge density from the exact solution agrees remarkably well with the integral equation solution for the conducting ring. Since the singularity in the Helmholtz Green's function for the electrodynamic problem is the static singularity considered herein, the results confirm the applicability of the thin-wire kernel to the scattering and radiation problems of the circular loop.

Summary 1 Dispersal limitation is widely invoked to explain species coexistence and cooperation in the face of competition and cheating. However, empirical evidence from natural ecosystems for the stabilizing effect of space is sparse. 2 We use a Neotropical ant–plant and its ant symbionts to show how mutual dispersal limitation brings about the stable persistence of coexistence and mutualism. 3 We demonstrate that two ant genera exhibit hierarchies in competitive ability, fecundity and dispersal ability, which suggests that a competition–colonization trade-off could be producing coexistence. However, we also show that this trade-off is not a sufficient explanation for coexistence. 4 Instead, we provide evidence that a dispersal–fecundity trade-off stabilizes the system by making each genus more dispersal-limited in a different portion of the environment. In this way, dispersal limitation can be seen as a form of environmental niche partitioning. 5 We also find that regeneration niche partitioning and a competition–colonization trade-off may help to bring about local mixing. 6 This study shows that care needs to be taken in identifying the critical mechanisms producing coexistence. Trade-offs between different stages of colonization may be more important for explaining coexistence than any trade-offs between competitive ability and colonization rate.

When applied at the individual patch level, the classic competition-colonization models of species coexistence assume that propagules of superior competitors can displace adults of inferior competitors (displacement competition). But if adults are invulnerable to displacement by propagules (as trees are to seeds), and propagules compete to replace adults that die for reasons independent of the outcome of juvenile competition (a lottery system), a competition-colonization trade-off alone is not able to produce coexistence. However, we show that coexistence is possible if patch density varies spatially, such that it becomes a niche axis. We also show how a dispersal-fecundity trade-off can partition variation in patch density. We discuss the application of these models to empirical systems. An important implication of communities coexisting via variation in patch density is that the amount of habitat loss necessarily interacts with the pattern of loss in affecting extinctions, invasions, and coexistence, in contrast to displacement competition models, for which the spatial pattern of loss is not important or is less important. Finally, with respect to mechanisms promoting coexistence, we suggest that trade-offs between different stages of colonization could be far more common in nature than a trade-off between competitive ability and colonization ability.

Ecological theory has long supported the idea that species coexistence in a homogeneous habitat is promoted by spatial structure, but empirical evidence for this hypothesis has lagged behind theory. Here we describe a Neotropical ant-plant symbiosis that is ideally suited for testing spatial models of coexistence. Two genera of ants, Allomerus cf. demerarae and three species of Azteca are specialized to live on a single species of ant-plant, Cordia nodosa, in a Western Amazonian tropical rain forest. Empirically, using census data from widely separated localities, we show that the relative colonization abilities of the two ant genera are a function of plant density. A parameterized model shows that this pattern alone is sufficiently robust to explain coexistence in the system. Census and experimental data suggest that Azteca queens are better long-distance flyers, but that Allomerus colonies are more fecund. Thus, Azteca can dominate in areas where host-plant densities are low (and parent colony-sapling distances are long), and Allomerus can dominate in areas where host-plant densities are high. Existing spatial heterogeneity in host-plant densities therefore can allow regional coexistence, and intersite dispersal can produce local mixing. In conclusion, a dispersal-fecundity trade-off appears to allow the two genera to treat spatial heterogeneity in patch density as a niche axis. This study further suggests that a spatially structured approach is essential in understanding the persistence of some mutualisms in the presence of parasites.

Host–parasitoid metapopulation models have typically been deterministic models formulated with population numbers as a continuous variable. Spatial heterogeneity in local population abundance is a typical (and often essential) feature of these models and means that, even when average population density is high, some patches have small population sizes. In addition, large temporal population fluctuations are characteristic of many of these models, and this also results in periodically small local population sizes. Whenever population abundances are small, demographic stochasticity can become important in several ways. To investigate this problem, we have reformulated a deterministic, host–parasitoid metapopulation as an integer-based model in which encounters between hosts and parasitoids, and the fecundity of individuals are modelled as stochastic processes. This has a number of important consequences: (1) stochastic fluctuations at small population sizes tend to be amplified by the dynamics to cause massive population variability, i.e. the demographic stochasticity has a destabilizing effect; (2) the spatial patterns of local abundance observed in the deterministic counterpart are largely maintained (although the area of 'spatial chaos' is extended); (3) at small population sizes, dispersal by discrete individuals leads to a smaller fraction of new patches being colonized, so that parasitoids with small dispersal rates have a greater tendency for extinction and higher dispersal rates have a larger competitive advantage; and (4) competing parasitoids that could coexist in the deterministic model due to spatial segregation cannot now coexist for any combination of parameters.

We discuss the question of how to quantify and analyse dynamics and patterns in spatially extended ecologies and introduce several new tools and ideas which use space-time dynamical structure. To illustrate our ideas, we introduce an artificial ecology model of a resource-predator-prey community which is interesting in its own right both ecologically and mathematically. This is a generalized probabilistic cellular automata. The model is stochastic and spatially non-homogeneous. We show how to identify a spatial scale intermediate between the noise dominated microscale and the infinite size limit at which non-trivial determinism is maximized. This is the scale at which to measure the system's dynamics. At this scale the population dynamics are essentially deterministic, low-dimensional and chaotic. This allows us to characterize the complex spatial patterns by a low-dimensional vector. This mapping from spatial patterns to low dimensional vectors provides effective and faithful data compression and is a powerful technique for synthesizing ecological information. It facilitates new analytical techniques. As an application we consider how to distinguish structural change within an ecosystem from natural dynamics. Such change is detected by using our parameterization to construct recurrence plots. Other applications such as the reconstruction of the dynamics of invisible species are discussed elsewhere.

Estimating the abundance of migratory species is difficult because sources of variability differ substantially among species and populations. Recently developed state-space models address this variability issue by directly modeling both environmental and measurement error, although their efficacy in detecting declines is relatively untested for empirical data. We applied state-space modeling, generalized least squares (with autoregression error structure), and standard linear regression to data on abundance of wetland birds (shorebirds and terns) at Moreton Bay in southeast Queensland, Australia. There are internationally significant numbers of 8 species of waterbirds in the bay, and it is a major terminus of the large East Asian-Australasian Flyway. In our analyses, we considered 22 migrant and 8 resident species. State-space models identified abundances of 7 species of migrants as significantly declining and abundance of one species as significantly increasing. Declines in migrant abundance over 15 years were 43-79%. Generalized least squares with an autoregressive error structure showed abundance changes in 11 species, and standard linear regression showed abundance changes in 15 species. The higher power of the regression models meant they detected more declines, but they also were associated with a higher rate of false detections. If the declines in Moreton Bay are consistent with trends from other sites across the flyway as a whole, then a large number of species are in significant decline.

Classifying species according to their risk of extinction is a common practice and underpins much conservation activity. The reliability of such classifications rests on the accuracy of threat categorizations, but very little is known about the magnitude and types of errors that might be expected. The process of risk classification involves combining information from many sources, and understanding the quality of each source is critical to evaluating the overall status of the species. One common criterion used to classify extinction risk is a decline in abundance. Because abundance is a direct measure of conservation status, counts of individuals are generally the preferred method of evaluating whether populations are declining. Using the thresholds from criterion A of the International Union for Conservation of Nature (IUCN) Red List (critically endangered, decline in abundance of80% over 10 years or 3 generations; endangered, decline in abundance of 50-80%; vulnerable, decline in abundance of 30-50%; least concern or near threatened, decline in abundance of 0-30%), we assessed 3 methods used to detect declines solely from estimates of abundance: use of just 2 estimates of abundance; use of linear regression on a time series of abundance; and use of state-space models on a time series of abundance. We generated simulation data from empirical estimates of the typical variability in abundance and assessed the 3 methods for classification errors. The estimates of the proportion of falsely detected declines for linear regression and the state-space models were low (maximum 3-14%), but 33-75% of small declines (30-50% over 15 years) were not detected. Ignoring uncertainty in estimates of abundance (with just 2 estimates of abundance) allowed more power to detect small declines (95%), but there was a high percentage (50%) of false detections. For all 3 methods, the proportion of declines estimated to be80% was higher than the true proportion. Use of abundance data to detect species at risk of extinction may either fail to detect initial declines in abundance or have a high error rate.

The region within which axial loads may be applied to a compression member without inducing tension anywhere in the cross-section, commonly called the ‘kern’, is studied. A general solution is developed for arbitrary polygons. A microcomputer program giving numerical and graphical results is presented. To determine the kern, the program requires only the vertex coordinates which are necessary to describe the polygonal cross-section. Geometries containing curved boundaries can be analyzed by replacing the curved boundary with a suitable set of line segments. Several example geometrics are presented, including standard structural shapes, a cross-section with a hole, a cross-section with disconnected areas, and a cross-section with a curved boundary.

Numerical accuracy considerations for motion of a cable modeled by a chain of rigid links are investigated. Two different systems of equations which are mathematically equivalent are integrated numerically. Effects of small changes in initial conditions, integration tolerance, equation set and integration method are studied. This highly non-linear system exhibits pronounced sensitivity to small parameter changes. Solutions which initially agree closely are found to have differences which grow exponentially with time. The instabilities inherent in numerical solutions of such systems are illustrated using some simple one-degree-of-freedom problems having known exact solutions. Thestrong dependence such systems have to minor changes in physical and numerical parameters suggested that caution should be exercised regarding credibility of results predicted by long-time simulations.

the local dynamics in each patch, reemerges to destabilize the overall system. Extinction occurs when the parasitoid overexploits its host and then goes extinct itself. This is more likely at higher host and parasitoid dispersal rates, for any given lattice size. These theoretical results quali

Coral bleaching characterized by the expulsion of symbiotic algae (zooxanthellae) is an increasing problem worldwide. Global warming has been implicated as one cause, but the phenomenon cannot be fully comprehended without an understanding of the variability of zooxanthellae populations in field conditions. Results from a 6-year field study are presented, providing evidence of density regulation but also of large variability in the zooxanthellae population with regular episodes of very low densities. These bleaching events are likely to be part of a constant variability in zooxanthellae density caused by environmental fluctuations superimposed on a strong seasonal cycle in abundance.

Natural enemy-victim interactions are of major applied importance and of fundamental interest to ecologists. A key question is what stabilizes these interactions, allowing the long-term coexistence of the two species. Three main theoretical explanations have been proposed: behavioral responses, time-dependent factors such as delayed density dependence, and spatial heterogeneity. Here, using the powerful moment-closure technique, we show a fundamental equivalence between these three elements. Limited movement by organisms is a ubiquitous feature of ecological systems, allowing spatial structure to develop; we show that the effects of this can be naturally described in terms of time lags or within-generation functional responses.

Attractor reconstruction using embedding techniques is a widely used tool when analysing data from real systems. It allows reconstruction of the system dynamics from only one observable and is thus extremely powerful. We show here that this reconstruction is also possible from spatially coupled systems. We use a common host–parasitoid model as an example as ecological systems are virtually always spatially extended. Additionally, data from ecological systems has often only one observable, e.g. population density, from a potentially much higher–dimensional system. Singular value decomposition is used to show the existence of a functional relationship mapping the time delayed coordinates of one variable to the full spatially coupled system. We investigate the effects of noise and indicate two important spatial scales. Finally, we illustrate that a reconstruction can be obtained from a system that is only partially sampled.

Methods are developed to compute geometrical and inertial properties for regions of general shape. Formulae are deduced which show the changes occurring in plane or axisymmetric inertia properties when reference axes are subjected to a linear transformation. Various two-dimensional integrals are transformed into line integrals convenient for numerical evaluation. An 1100 statement FORTRAN program determining area and volume properties for regions bounded by contiguous circular :arcs and straight line segments is discussed. More concise exact results applicable in the case of straight line boundaries are obtained. Several numerical examples are presented which illustrate the versatility of the program.

A simple computer method is presented for analysing statically indeterminate beams having sectionally constant EI values and loads consisting of any number of arbitrarily placed concentrated forces and couples as well as any number of uniform and ramp loads. Unknown reactions are treated as parameters which are determined by simulataneous imposition of end conditions and interior constraints. Support locations are specified independently of any discontinuites of load or cross-section. A computer program implementing this method is described which has very concise data input considerably shorter than tupically required in programs based on the stiffness method.

Geometrical and inertial properties of partial volumes of revolution and tapered cylinders are computed by the use of line integrals. A short Fortran program treating cross sections bounded by straight lines and circular arcs is presented. Two simple cross-sections are used to test the program and the corresponding properties are presented in the appendix.

The behavior of a unidirectional fiber-reinforced composite subjected to axial loading is investigated. The elastic analysis of a composite containing a hexagonal array of perfectly bonded circular filaments is formulated to simulate the axial loading of a unidirectional composite. A modified plane strain theory is adopted so that the existing methodology of Muskhelishvili can be utilized. The resulting power series solution along with a point matching technique yields a system of simultaneous equations. Once these equations are solved, the interface, matrix, and filament stresses are found. Graphical presentation of these stresses is made. The conclusions arrived at are that the maximum in-plane stresses are small relative to the applied axial stress and occur at the fiber- matrix interface. These stresses are directly related to the dif ference of the Poisson's ratios of the fiber and matrix. Lastly, the assumption of axial symmetry is valid when considering a unidi rectional composite under axial loading.

An analysis was made of the stresses and displacements in an elastic solid propellant grain perforated internally by a star shaped configuration, bonded peripherally to an elastic motor case, and loaded internally by pressure normal to the perforation. The analysis was performed under the assumption of plane strain using conformal mapping and the complex variable method of N. I. Muskhelishvili. The effects on stress concentration at the star tip owing to changes in star tip radius of curvature and web thickness of the grain were studied. The analysis was made specifically for a four-pointed, star shaped internal perforation but can be generalized to an n-pointed configuration.

A mathematical method is presented for determining stresses in solid propellant rocket grains due to pressurizatio n, steady thermal gradients, and uniform propellant shrinkage. The type of solid propellant grain considered is a long cylinder containing a longitudinal perforation with an arbitrary number of identical star points of general shape. The external boundary of the propellant grain is bonded to a circular-cylindrical motor case. The propellant has constant mechanical and thermal properties and is in a state of plane strain. Linear elasticity theory and complex variable methods are used to formulate a general stress problem for a doubly connected region that has a star-shaped internal boundary and a circular external boundary and is subjected to steady thermal gradients and uniform boundary pressures. This problem is solved approximately by considering a related problem for an infinite plane with a star-shaped hole. Effects of bonding the external boundary to an elastic case are deduced approximately by superposition. A general stress program for a digital computer is described, and example computations testing the validity of the assumed approximations are made. The method is found to provide a practical means of analyzing stresses in solid propellant grains.

Contact stresses in a heavy circular cylinder resting in a smooth rigid cradle of general profile are analyzed for contact zones outside the validity of Hertz theory. Numerical results are presented for various circular cradles having radii different from that of the cylinder and contact angles up to seventy-five degrees. Discrepancies with Hertz theory are discussed.

An approximate analysis is developed for evaluation of stresses and displacements in a plate with a rectangular grid of holes which have symmetry axes directed along the rectangular grid. The holes are either uniformly pressurized or are bonded to rigid inclusions. The plate is loaded in a manner such that the principal stresses at infinity are directed along the rectangular grid. Stress distribution curves are presented for circular and elliptic holes which are load free or contain inclusions. Close agreement is shown with existing literature.

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.