Multiple behaviors for turning performance of Pacific bluefin tuna (Thunnus orientalis).

Tuna are known for exceptional swimming speeds, which are possible because of their thunniform lift-based propulsion, large muscle mass and rigid fusiform body. A rigid body should restrict maneuverability with regard to turn radius and turn rate. To test if turning maneuvers by the Pacific bluefin tuna (Thunnus orientalis) are constrained by rigidity, captive animals were videorecorded overhead as the animals routinely swam around a large circular tank or during feeding bouts. Turning performance was classified into three different types: (1) glide turns, where the tuna uses the caudal fin as a rudder; (2) powered turns, where the animal uses continuous near symmetrical strokes of the caudal fin through the turn; and (3) ratchet turns, where the overall global turn is completed by a series of small local turns by asymmetrical stokes of the caudal fin. Individual points of the rostrum, peduncle and tip of the caudal fin were tracked and analyzed. Frame-by-frame analysis showed that the ratchet turn had the fastest turn rate for all points with a maximum of 302 deg s-1. During the ratchet turn, the rostrum exhibited a minimum global 0.38 body length turn radius. The local turn radii were only 18.6% of the global ratchet turn. The minimum turn radii ranged from 0.4 to 1.7 body lengths. Compared with the performance of other swimmers, the increased flexion of the peduncle and tail and the mechanics of turning behaviors used by tuna overcomes any constraints to turning performance from the rigidity of the anterior body morphology.

Kinematics of swimming of the manta ray: three-dimensional analysis of open-water maneuverability.

For aquatic animals, turning maneuvers represent a locomotor activity that may not be confined to a single coordinate plane, making analysis difficult, particularly in the field. To measure turning performance in a three-dimensional space for the manta ray (Mobula birostris), a large open-water swimmer, scaled stereo video recordings were collected. Movements of the cephalic lobes, eye and tail base were tracked to obtain three-dimensional coordinates. A mathematical analysis was performed on the coordinate data to calculate the turning rate and curvature (1/turning radius) as a function of time by numerically estimating the derivative of manta trajectories through three-dimensional space. Principal component analysis was used to project the three-dimensional trajectory onto the two-dimensional turn. Smoothing splines were applied to these turns. These are flexible models that minimize a cost function with a parameter controlling the balance between data fidelity and regularity of the derivative. Data for 30 sequences of rays performing slow, steady turns showed the highest 20% of values for the turning rate and smallest 20% of turn radii were 42.65±16.66 deg s-1 and 2.05±1.26 m, respectively. Such turning maneuvers fall within the range of performance exhibited by swimmers with rigid bodies.

Optimal Mating Strategies for Preferentially Outcrossing Simultaneous Hermaphrodites in the Presence of Predators.

The optimal timing for initiating reproduction (i.e., the age at first reproduction) is a critical life history trait describing aspects of an individual's resource-allocation strategy. Recent theoretical and empirical work has demonstrated that this trait is also tied to mating system expression when individuals have the opportunity to reproduce via both self-fertilization and cross-fertilization. A strategy of "delayed selfing" has emerged as a "best of both worlds" arrangement where, in the absence of a mate, an individual will delay reproduction (selfing) to "wait" for a mate. Herein, we extend previously developed predictive optimization models for the timing of reproduction to a situation where organisms can allocate their resources to size-dependent and size-independent defensive strategies to counter the threat of predation. By incorporating inducible defenses into a predictive framework for analyzing life history expression and evolution, we can more accurately evaluate the role that allocation strategy plays in altering the optimal waiting time. We compare our model to previous models and empirical results highlighting that incorporation of inducible defenses into the model broadens the parameter space in which a waiting time is expected and often leads to a predicted waiting time that is longer than in the situation without inducible defenses. In particular, a waiting time is predicted to exist regardless of the strength of inbreeding depression in the population.

A continuum three-zone model for swarms.

We present a progression of three distinct three-zone, continuum models for swarm behavior based on social interactions with neighbors in order to explain simple coherent structures in popular biological models of aggregations. In continuum models, individuals are replaced with density and velocity functions. Individual behavior is modeled with convolutions acting within three interaction zones corresponding to repulsion, orientation, and attraction, respectively. We begin with a variable-speed first-order model in which the velocity depends directly on the interactions. Next, we present a variable-speed second-order model. Finally, we present a constant-speed second-order model that is coordinated with popular individual-based models. For all three models, linear stability analysis shows that the growth or decay of perturbations in an infinite, uniform swarm depends on the strength of attraction relative to repulsion and orientation. We verify that the continuum models predict the behavior of a swarm of individuals by comparing the linear stability results with an individual-based model that uses the same social interaction kernels. In some unstable regimes, we observe that the uniform state will evolve toward a radially symmetric attractor with a variable density. In other unstable regimes, we observe an incoherent swarming state.

Effects of demographic stochasticity on population persistence in advective media.

Many populations live and disperse in advective media. A fundamental question, known as the "drift paradox" in stream ecology, is how a closed population can survive when it is constantly being transported downstream by the flow. Recent population-level models have focused on the role of diffusive movement in balancing the effects of advection, predicting critical conditions for persistence. Here, we formulate an individual-based stochastic analog of the model described in (Lutscher et al., SIAM Rev. 47(4):749-772, 2005) to quantify the effects of demographic stochasticity on persistence. Population dynamics are modeled as a logistic growth process and dispersal as a position-jump process on a finite domain divided into patches. When there is no correlation in the interpatch movement of residents, stochasticity simply smooths the persistence-extinction boundary. However, when individuals disperse in "packets" from one patch to another and the flow field is memoryless on the timescale of packet transport, the probability of persistence is greatly enhanced. The latter transport mechanism may be characteristic of larval dispersal in the coastal ocean or wind-dispersed seed pods.

Coarse analysis of collective motion with different communication mechanisms.

We study the effects of a signalling constraint on an individual-based model of self-organizing group formation using a coarse analysis framework. This involves using an automated data-driven technique which defines a diffusion process on the graph of a sample dataset formed from a representative stationary simulation. The eigenvectors of the graph Laplacian are used to construct 'diffusion-map' coordinates which provide a geometrically meaningful low-dimensional representation of the dataset. We show that, for the parameter regime studied, the second principal eigenvector provides a sufficient representation of the dataset and use it as a coarse observable. This allows the computation of coarse bifurcation diagrams, which are used to compare the effects of the signalling constraint on the population-level behavior of the model.

How the spatial position of individuals affects their influence on swarms: a numerical comparison of two popular swarm dynamics models.

Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual's Voronoi neighbors. The models include a tunable parameter that controls an individual's relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.

Coarse-grained analysis of stochasticity-induced switching between collective motion states.

A single animal group can display different types of collective motion at different times. For a one-dimensional individual-based model of self-organizing group formation, we show that repeated switching between distinct ordered collective states can occur entirely because of stochastic effects. We introduce a framework for the coarse-grained, computer-assisted analysis of such stochasticity-induced switching in animal groups. This involves the characterization of the behavior of the system with a single dynamically meaningful "coarse observable" whose dynamics are described by an effective Fokker-Planck equation. A "lifting" procedure is presented, which enables efficient estimation of the necessary macroscopic quantities for this description through short bursts of appropriately initialized computations. This leads to the construction of an effective potential, which is used to locate metastable collective states, and their parametric dependence, as well as estimate mean switching times.