The importance of sample size in marine megafauna tagging studies.

Telemetry is a key, widely used tool to understand marine megafauna distribution, habitat use, behavior, and physiology; however, a critical question remains: "How many animals should be tracked to acquire meaningful data sets?" This question has wide-ranging implications including considerations of statistical power, animal ethics, logistics, and cost. While power analyses can inform sample sizes needed for statistical significance, they require some initial data inputs that are often unavailable. To inform the planning of telemetry and biologging studies of marine megafauna where few or no data are available or where resources are limited, we reviewed the types of information that have been obtained in previously published studies using different sample sizes. We considered sample sizes from one to >100 individuals and synthesized empirical findings, detailing the information that can be gathered with increasing sample sizes. We complement this review with simulations, using real data, to show the impact of sample size when trying to address various research questions in movement ecology of marine megafauna. We also highlight the value of collaborative, synthetic studies to enhance sample sizes and broaden the range, scale, and scope of questions that can be answered.

Convergence of marine megafauna movement patterns in coastal and open oceans.

The extent of increasing anthropogenic impacts on large marine vertebrates partly depends on the animals' movement patterns. Effective conservation requires identification of the key drivers of movement including intrinsic properties and extrinsic constraints associated with the dynamic nature of the environments the animals inhabit. However, the relative importance of intrinsic versus extrinsic factors remains elusive. We analyze a global dataset of ∼2.8 million locations from >2,600 tracked individuals across 50 marine vertebrates evolutionarily separated by millions of years and using different locomotion modes (fly, swim, walk/paddle). Strikingly, movement patterns show a remarkable convergence, being strongly conserved across species and independent of body length and mass, despite these traits ranging over 10 orders of magnitude among the species studied. This represents a fundamental difference between marine and terrestrial vertebrates not previously identified, likely linked to the reduced costs of locomotion in water. Movement patterns were primarily explained by the interaction between species-specific traits and the habitat(s) they move through, resulting in complex movement patterns when moving close to coasts compared with more predictable patterns when moving in open oceans. This distinct difference may be associated with greater complexity within coastal microhabitats, highlighting a critical role of preferred habitat in shaping marine vertebrate global movements. Efforts to develop understanding of the characteristics of vertebrate movement should consider the habitat(s) through which they move to identify how movement patterns will alter with forecasted severe ocean changes, such as reduced Arctic sea ice cover, sea level rise, and declining oxygen content.

Dynamics of link states in complex networks: the case of a majority rule.

Motivated by the idea that some characteristics are specific to the relations between individuals and not to the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have a link in one of the two states. We consider this link-dynamics model in fully connected networks, square lattices, and Erdös-Renyi random networks. In each case we find and characterize a number of nontrivial asymptotic configurations, as well as some of the mechanisms leading to them and the time evolution of the link heterogeneity index distribution. For a fully connected network and random networks there is a broad distribution of possible asymptotic configurations. Most asymptotic configurations that result from link dynamics have no counterpart under traditional node dynamics in the same topologies.

Update rules and interevent time distributions: slow ordering versus no ordering in the voter model.

We introduce a general methodology of update rules accounting for arbitrary interevent time (IET) distributions in simulations of interacting agents. We consider in particular update rules that depend on the state of the agent, so that the update becomes part of the dynamical model. As an illustration we consider the voter model in fully connected, random, and scale-free networks with an activation probability inversely proportional to the time since the last action, where an action can be an update attempt (an exogenous update) or a change of state (an endogenous update). We find that in the thermodynamic limit, at variance with standard updates and the exogenous update, the system orders slowly for the endogenous update. The approach to the absorbing state is characterized by a power-law decay of the density of interfaces, observing that the mean time to reach the absorbing state might be not well defined. The IET distributions resulting from both update schemes show power-law tails.

Extracting directed information flow networks: an application to genetics and semantics.

We introduce a general method to infer the directional information flow between populations whose elements are described by n-dimensional vectors of symbolic attributes. The method is based on the Jensen-Shannon divergence and on the Shannon entropy and has a wide range of application. We show here the results of two applications: first we extract the network of genetic flow between meadows of the seagrass Poseidonia oceanica, where the meadow elements are specified by sets of microsatellite markers, and then we extract the semantic flow network from a set of Wikipedia pages, showing the semantic channels between different areas of knowledge.

Broad lifetime distributions for ordering dynamics in complex networks.

We search for conditions under which a characteristic time scale for ordering dynamics toward either of two absorbing states in a finite complex network of interactions does not exist. With this aim, we study random networks and networks with mesoscale community structure built up from randomly connected cliques. We find that large heterogeneity at the mesoscale level of the network appears to be a sufficient mechanism for the absence of a characteristic time for the dynamics. Such heterogeneity results in dynamical metastable states that survive at any time scale.

Local versus global interactions in nonequilibrium transitions: A model of social dynamics.

A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod's model for cultural dissemination.

Quasiperiodic patterns in boundary-modulated excitable waves.

We investigate the impact of domain shape on wave propagation in excitable media. Channeled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration that repeats periodically in time. The phenomenon is numerically studied in a model for a photosensitive Belousov-Zabotinsky reaction. Spatial return maps for the height and position of the successive fronts are analytically obtained, and reveal the similarity between this spatial quasiperiodicity and the temporal quasiperiodicity appearing in forced oscillators.

Complex Ginzburg-Landau equation in the presence of walls and corners.

We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of two-dimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and arguments provided, to show that Dirichlet walls introduce strong selection mechanisms for the wave pattern. Corners between walls provide additional synchronization mechanisms and associated selection criteria. The numerical results fit well with the theoretical predictions in the parameter range studied.

Evidence of a Hopf bifurcation in frog hair cells.

The membrane potential of hair cells in the low-frequency hearing organ of the bullfrog, the amphibian papilla, sinusoidally oscillates at small amplitude in the absence of acoustical input. We stimulate the cell with a series of periodic currents close to this natural frequency and observe that its current-to-voltage transfer function is compressively nonlinear, having a large gain for small stimuli and a smaller gain for larger currents. Along with the spontaneous oscillation, this implies that the cell is poised close to a dynamical instability such as a Hopf bifurcation, because distant from the instability the transfer function becomes linear. The cell's frequency selectivity is enhanced for small stimuli. Simulations show that the cell's membrane capacitance is effectively reduced due to a current gain provided by this dynamical instability. We propose that the Hopf resonance is widely used by transducer cells on the sensory periphery to achieve small-signal amplification.

Essential nonlinearities in hearing.

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely sharp tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.

Transmission of information and herd Behavior: an application to financial markets.

We propose a model for stochastic formation of opinion clusters, modeled by an evolving network, and herd behavior to account for the observed fat-tail distribution in returns of financial-price data. The only parameter of the model is h, the rate of information dispersion per trade, which is a measure of herding behavior. For h below a critical h(*) the system displays a power-law distribution of the returns with exponential cutoff. However, for h>h(*) an increase in the probability of large returns is found and may be associated with the occurrence of large crashes.

Frozen spatial chaos induced by boundaries.

We show that rather simple but nontrivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.