Predator-prey dynamics of bald eagles and glaucous-winged gulls at Protection Island, Washington, USA.

Bald eagle (Haliaeetus leucocephalus) populations in North America rebounded in the latter part of the twentieth century, the result of tightened protection and outlawing of pesticides such as DDT. An unintended consequence of recovery may be a negative impact on seabirds. During the 1980s, few bald eagles disturbed a large glaucous-winged gull (Larus glaucescens) colony on Protection Island, Washington, USA, in the Salish Sea. Breeding gull numbers in this colony rose nearly 50% during the 1980s and early 1990s. Beginning in the 1990s, a dramatic increase in bald eagle activity ensued within the colony, after which began a significant decline in gull numbers.To examine whether trends in the gull colony could be explained by eagle activity, we fit a Lotka-Volterra-type predator-prey model to gull nest count data and Washington State eagle territory data collected in most years between 1980 and 2016. Both species were assumed to grow logistically in the absence of the other.The model fits the data with generalized R 2 = 0.82, supporting the hypothesis that gull dynamics were due largely to eagle population dynamics.Point estimates of the model parameters indicated approach to stable coexistence. Within the 95% confidence intervals for the parameters, however, 11.0% of bootstrapped parameter vectors predicted gull colony extinction.Our results suggest that the effects of bald eagle activity on the dynamics of a large gull colony were explained by a predator-prey relationship that included the possibility of coexistence but also the possibility of gull colony extinction. This study serves as a cautionary exploration of the future, not only for gulls on Protection Island, but for other seabirds in the Salish Sea. Managers should monitor numbers of nests in seabird colonies as well as eagle activity within colonies to document trends that may lead to colony extinction.

Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population.

For structured populations with an annual breeding season, life-stage interactions and behavioral tactics may occur on a faster time scale than that of population dynamics. Motivated by recent field studies of the effect of rising sea surface temperature (SST) on within-breeding-season behaviors in colonial seabirds, we formulate and analyze a general class of discrete-time matrix models designed to account for changes in behavioral tactics within the breeding season and their dynamic consequences at the population level across breeding seasons. As a specific example, we focus on egg cannibalism and the daily reproductive synchrony observed in seabirds. Using the model, we investigate circumstances under which these life history tactics can be beneficial or non-beneficial at the population level in light of the expected continued rise in SST. Using bifurcation theoretic techniques, we study the nature of non-extinction, seasonal cycles as a function of environmental resource availability as they are created upon destabilization of the extinction state. Of particular interest are backward bifurcations in that they typically create strong Allee effects in population models which, in turn, lead to the benefit of possible (initial condition dependent) survival in adverse environments. We find that positive density effects (component Allee effects) due to increased adult survival from cannibalism and the propensity of females to synchronize daily egg laying can produce a strong Allee effect due to a backward bifurcation.

Stable bifurcations in semelparous Leslie models.

In this paper, we consider nonlinear Leslie models for the dynamics of semelparous age-structured populations. We establish stability and instability criteria for positive equilibria that bifurcate from the extinction equilibrium at R (0)=1. When the bifurcation is to the right (forward or super-critical), the criteria consist of inequalities involving the (low-density) between-class and within-class competition intensities. Roughly speaking, stability (respectively, instability) occurs if between-class competition is weaker (respectively, stronger) than within-class competition. When the bifurcation is to the left (backward or sub-critical), the bifurcating equilibria are unstable. We also give criteria that determine whether the boundary of the positive cone is an attractor or a repeller. These general criteria contribute to the study of dynamic dichotomies, known to occur in lower dimensional semelparous Leslie models, between equilibration and age-cohort-synchronized oscillations.

Coping behaviour as an adaptation to stress: post-disturbance preening in colonial seabirds.

In humans, coping behaviour is an action taken to soothe oneself during or after a stressful or threatening situation. Some human behaviours with physiological functions also serve as coping behaviours, for example, comfort sucking in infants and comfort eating in adults. In birds, the behaviour of preening, which has important physiological functions, has been postulated to soothe individuals after stressful situations. We combine two existing modelling approaches - logistic regression and Darwinian dynamics - to explore theoretically how a behaviour with crucial physiological function might evolve into a coping behaviour. We apply the method to preening in colonial seabirds to investigate whether and how preening might be co-opted as a coping behaviour in the presence of predators. We conduct an in-depth study of the environmental correlates of preening in a large gull colony in Washington, USA, and we perform an independent field test for comfort preening by computing the change in frequency of preening in gulls that were alerted to a predator, but did not flee.

Mathematical modeling of appendicular bone growth in glaucous-winged gulls.

Development of locomotor activity is crucial in tetrapods. In birds, this development leads to different functions for hindlimbs and forelimbs. The emergence of walking and flying as very different complex behavior patterns only weeks after hatching provides an interesting case study in animal development. We measured the diaphyseal lengths and midshaft diameters of three wing bones (humerus, ulna, and carpometacarpus) and three leg bones (femur, tibiotarsus, and tarsometatarsus) of 79 juvenile (ages 0-42 days) and 13 adult glaucous-winged gulls (Larus glaucescens), a semiprecocial species. From a suite of nine alternative mathematical models, we used information-theoretic criteria to determine the best model(s) for length and diameter of each bone as a function of age; that is, we determined the model(s) that obtained the best tradeoff between the minimized sum of squared residuals and the number of parameters used to fit the model. The Janoschek and Holling III models best described bone growth, with at least one of these models yielding an R(2) > or = 0.94 for every dimension except tarsometatarsus diameter (R(2) = 0.87). We used the best growth models to construct accurate allometric comparisons of the bones. Early maximal absolute growth rates characterize the humerus, femur, and tarsometatarsus, bones that assume adult-type support functions relatively early during juvenile development. Leg bone lengths exhibit more rapid but less sustained relative growth than wing bone lengths. Wing bone diameters are initially smaller than leg bone diameters, although this relationship is reversed by fledging. Wing bones and the femur approach adult length by fledging but continue to increase in diameter past fledging; the tibiotarsus and tarsometatarsus approach both adult length and diameter by fledging. In short, the pattern of bone growth in this semiprecocial species reflects the changing behavioral needs of the developing organism.

Modeling the daily activities of breeding colonial seabirds: dynamic occupancy patterns in multiple habitat patches.

We constructed differential equation models for the diurnal abundance and distribution of breeding glaucous-winged gulls (Larus glaucescens) as they moved among nesting and non-nesting habitat patches. We used time scale techniques to reduce the differential equations to algebraic equations and connected the models to field data. The models explained the data as a function of abiotic environmental variables with R(2 )=0.57. A primary goal of this study is to demonstrate the utility of a methodology that can be used by ecologists and wildlife managers to understand and predict daily activity patterns in breeding seabirds.

Coexistence of competing juvenile-adult structured populations.

The Leslie-Gower model is a discrete time analog of the competition Lotka-Volterra model and is known to possess the same dynamic scenarios of that famous model. The Leslie-Gower model played a historically significant role in the history of competition theory in its application to classic laboratory experiments of two competing species of flour beetles (carried out by Park in the 1940s-1960s). While these experiments generally supported what became the Competitive Exclusion Principle, Park observed an anomalous coexistence case. Recent literature has discussed Park's 'coexistence case' by means of non-Lotka-Volterra, non-equilibrium dynamics that occur in a high dimensional model with life cycle stages. We study this dynamic possibility in the lowest possible dimension, that is to say, by means of a model involving only two species each with two life cycle stages. We do this by extending the Leslie-Gower model so as to describe the competitive interaction of two species with juvenile and adult classes. We give a complete account of the global dynamics of the resulting model and show that it allows for non-equilibrium competitive coexistence as competition coefficients are increased. We also show that this phenomenon occurs in a general class of models for competing populations structured by juvenile and adult life cycle stages.

Multiple mixed-type attractors in a competition model.

We show that a discrete-time, two-species competition model with Ricker (exponential) nonlinearities can exhibit multiple mixed-type attractors. By this is meant dynamic scenarios in which there are simultaneously present both coexistence attractors (in which both species are present) and exclusion attractors (in which one species is absent). Recent studies have investigated the inclusion of life-cycle stages in competition models as a casual mechanism for the existence of these kinds of multiple attractors. In this paper we investigate the role of nonlinearities in competition models without life-cycle stages.

Modeling territory attendance and preening behavior in a seabird colony as functions of environmental conditions.

In previous studies we developed a general compartmental methodology for modeling animal behavior and applied the methodology to marine birds and mammals. In this study we used the methodology to construct a system of two differential equations to model the dynamics of territory attendance and preening in a gull colony on Protection Island, Strait of Juan de Fuca, Washington. We found that colony occupancy was driven primarily by abiotic environmental conditions, including tide height, time of day, solar elevation, and wind speed over open water. For birds in the colony, preening behavior was driven to some extent by abiotic environmental conditions (including time of day, solar elevation, humidity, and wind speed on the colony), but apparently was driven primarily by local and/or biotic effects not included in the model. In terms of R(2) values, the model explained 65% and 37% of the variability in colony occupancy and preening data, respectively, as a function of these six abiotic environmental factors.

Identifying environmental determinants of diurnal distribution in marine birds and mammals.

Marine birds and mammals move between various habitats during the day as they engage in behaviors related to resting, sleeping, preening, feeding, and breeding. The per capita rates of movement between these habitats, and hence the habitat occupancy dynamics, often are functions of environmental variables such as tide height, solar elevation, wind speed, and temperature. If the system recovers rapidly after disturbance, differential equation models of occupancy dynamics can be reduced to algebraic equations on two time scales. Identification of environmental factors that influence movement between habitats requires time series census data collected in both the absence and presence of disturbance.

Experimental support of the scaling rule for demographic stochasticity.

A scaling rule of ecological theory, accepted but lacking experimental confirmation, is that the magnitude of fluctuations in population densities due to demographic stochasticity scales inversely with the square root of population numbers. This supposition is based on analyses of models exhibiting exponential growth or stable equilibria. Using two quantitative measures, we extend the scaling rule to situations in which population densities fluctuate due to nonlinear deterministic dynamics. These measures are applied to populations of the flour beetle Tribolium castaneum that display chaotic dynamics in both 20-g and 60-g habitats. Populations cultured in the larger habitat exhibit a clarification of the deterministic dynamics, which follows the inverse square root rule. Lattice effects, a deterministic phenomenon caused by the discrete nature of individuals, can cause deviations from the scaling rule when population numbers are small. The scaling rule is robust to the probability distribution used to model demographic variation among individuals.

Anatomy of a chaotic attractor: subtle model-predicted patterns revealed in population data.

Mathematically, chaotic dynamics are not devoid of order but display episodes of near-cyclic temporal patterns. This is illustrated, in interesting ways, in the case of chaotic biological populations. Despite the individual nature of organisms and the noisy nature of biological time series, subtle temporal patterns have been detected. By using data drawn from chaotic insect populations, we show quantitatively that chaos manifests itself as a tapestry of identifiable and predictable patterns woven together by stochasticity. We show too that the mixture of patterns an experimentalist can expect to see depends on the scale of the system under study.

Explaining and predicting patterns in stochastic population systems.

Lattice effects in ecological time-series are patterns that arise because of the inherent discreteness of animal numbers. In this paper, we suggest a systematic approach for predicting lattice effects. We also show that an explanation of all the patterns in a population time-series may require more than one deterministic model, especially when the dynamics are complex.