### Modeling Predation Behaviors of Anelosimus Studiosus

**A short summary of the paper by Quijano et. al. 2016, Journal of Theoretical Biology.**

**Project Collaborators. **Alex John Quijano, Michele L. Joyner, Chelsea Ross, J. Colton Watts, Nathaniel Hancock, Michael Largent, Edith Seier, and Thomas C. Jones

*An Anelosimus studiosus spider taking a prey (left) and the digitized trajectory of the spider and prey (right). The objective of the paper by Joyner et. al. and Quijano et. al. is to model the movement of the spider.*

## Introduction.

Among predators, cooperative hunting grants better chances in covering ground and consolidating the capture of prey; more so with those of a larger size (Clark and Mangel 1986).

The Anelosimus studiosus is a species of spiders noted for such behavior, living in communal webs for which they are able to intercept and capture more prey. Their large webs allow them to hunt in an efficient manner and care for broods (Jones 2007). The spider colonies vary along with their levels of sociality, either as a colony consisting of a mother and her offspring or as males and females cooperating in colony work (including prey capture, brood care, habitat building, and maintenance).

This study sheds light on the predation movements of the A. studiosus, on how they are positioned in their webs and their spatial configurations to determine optimal spacing for successful predation. To determine this, the stochastic simulation model by Joyner et. al. (Joyner 2014) and Quijano et. al. (Quijano 2015) was fashioned to determine these behavior algorithms.

The focus of the paper by Quijano et al. (Quijano 2016) is to develop and install an extended stochastic model, which includes spider interactions and the incorporation of latency periods. The model uses different initial spatial configurations and different levels of influence. Surrounding spiders and prey determine the effects on the probability of foraging success.

## The Spatio-Temporal Model.

The previous existing stochastic models use differential equations and computational algorithms. In the model, the spider changes position, speed, and velocity when the time iterates. The spider does this until a prey is within capture distance and the prey gets caught. Otherwise, the spider changes its position. The computational algorithm iterates the spider’s search distance from 1 cm to 12 cm. Once the distance reaches a number greater than 12 cm, an error function sets the distance radian back to 1 cm. Looping the distance prevents the simulation from increasing the distance more than needed.

A common sub-social spider colony is comprised of a mother and her juveniles. The extended model makes it necessary to consider both the adult and juvenile spiders. One assumption it has is that the juvenile is slower than the adult mother. A minor change in the algorithm reflects this by reducing the juvenile’s velocity to a quarter of the adult’s. Another assumption is that the mother immediately captures the prey within capture distance. The juvenile needs at least three juveniles within capture distance to subdue a prey. This simulates the juvenile’s small size and inexperience compared to the adult.

Studies about the movement of a prey when hunted by A. studiosus have no records. In theory, the prey moves depending on their awareness of the predator. The extended model considers two types of prey: perceptive prey and careless prey. The perceptive prey is aware of predation as soon as it intercepts the web. This type locates the nearest edge of the web and walks away to escape. The model by Joyner et al. (Joyner 2014) makes use of careless prey. Said prey is unaware of the predation and moves in any desired direction.

The extended model incorporates aspects of the model developed by Heppner and Grenander (Heppner and Grenander 1990). They investigated the movement of coordinated bird flocks flying back home. Since A. studiosus share the same nest, the extended model assumes interactivity. The interactions of these spiders change their direction depending on surrounding spiders. A colony of subsocial spiders could coordinate in the same manner as the bird flocks.

*The extended model and algorithm (above figure) was developed by Quijano and Joyner et. al.. The term [X[t],Y[t]] is the 2-dimensional position of a single spider. See (Quijano 2016) for more details.*

A large number of spiders in the web add two important aspects: homing (when the spiders travel towards the perceived location of the prey) and interaction. The basis of perceived locations is from vibration-caused entities in the web. These include the prey and other spiders that give off directional cues. With this, spiders are able to differentiate vibrations from a prey and a fellow spider.

Interaction changes a spider's level of influence. Each moving spider in the web has a level of influence from 0 < ωp < 1 with step increments of 0.1. The level of influence changes the movement and direction of other moving spiders. A spider’s level of influence changes depending on its distance from other spiders. The farther a moving spider is from another spider, the lower its level of influence is. This also means that two spiders close to each other have a higher level of influence.

*The above figures show how the spiders locate the prey with information given from other spiders.*

A latency period adds a buffer time to the stochastic model (the amount of time the spider waits until it decides to pursue a prey that lands on the web). The amount of spiders within capture distance determines when a spider pursues prey. Each spider has a different latency period and will wait until it moves. If more than one spider is moving, then other spiders start to move in the same direction.

*Example simulation video with 16 juvenile spiders (in black), one mother (in red), and one prey (in blue).*

## Simulations.

The main purpose of the model is to determine optimal spatial distribution by conducting tests of different models. This tells how to subdue the most prey and avoid predators. Combinations of different classifications characterize each spatial distribution. There exist different distribution models labeled for their characteristic: random, clustered, uniform, grouped, and their edge counterparts.

*Random Distribution*

*Edge Grouped*

*Clustered*

*Edge Random*

*Uniform*

*Edge Clustered*

*Edge Uniform*

Using the spatial distribution models, one can determine the prey capture success rate. Consider four colony sizes consisting of 4, 9, 16, and 25 spiders for each web dimension. Also, consider both perceptive and careless prey with varying levels of influence. There are 4 different colony sizes distributed in 7 different spatial distributions. There are also 2 prey phenotypes with 11 levels of influences. There are a total of 616 combinations of these parameters.

They performed one thousand simulations for each combination. They record the successes in capturing prey, failures where the prey escapes, and when the spiders are unable to find prey within 2 minutes. In total, there are 616,000 simulations to perform.

*Proportion of spider wins with careless prey. Results from Quijano et. al. 2016.*

*Proportion of spider wins with perceptive prey. Results from Quijano et. al. 2016.*

The proportion of success increases as the level of influence gets closer to 1. The level of influence determines how strong the spiders sense the prey. Regardless of type, the prey gets caught with a high influence level. The prey’s escape rate decreases to zero the closer the level of influence is to 1. With 0 influence, the spiders found and caught the prey by random chance. In almost all cases, the chances of winning increases as the colony size increases.

Edge spatial distribution has a 30% chance of success given the largest colony size, 0 level of influence, and the prey being perceptive. The percentage is higher than other spatial distributions, which have a common prey capture chance of less than 10%. Exceptions are when the spiders group along the edge.

Random edge distribution takes only 30 to 50 seconds to catch the prey by chance. This range is lower than other spatial distributions indicating they capture prey faster. Both the mean time elapsed and proportions of wins are more equal as the influence approaches 1.

There are benefits from better sensing the prey when influence level is less than 0.6. Increasing level of influence further has less impact on capture success. The time elapsed increases at 0 level of influence while decreasing at around 0.2. This should be the case thus there is uncertainty for the discernible pattern.

The main goal was to determine which spatial distribution works best for the spiders. When faced with perceptive prey, spiders have a lower win rate than with careless prey. Regardless of prey type, it is important that the spiders catch as many preys to determine the best model.

When focusing on a level of influence, the edge uniform model has the best success rate. The edge random model comes close after. This result is due to the fact that the given prey has inhibited flight and the prey needs to move to the edge to escape, intercepting the spiders on the edge.

## Conclusion.

In conclusion, the extended model adapts the effects of interaction among subsocial spiders. The interaction takes into account levels of influence from prey as well as spiders in the web. The extended model adapted to include a latency period exhibited by A. studiosus. The model takes into account different spatial configurations. This is to determine the most efficient method of hunting for food.

The spatial distribution most efficient for coordinated hunting is the edge uniform distribution. For optimal cooperative hunting, spiders should surround and close in on the prey. Surrounding the prey closes any exits and decreases the chance of escape. Cooperative hunting is best when individual entities signal each other to join hunting. In the case of A. studiosus, the signal may not be an alert but instead draws attention to the prey. Unable to know the type of vibration, spiders confuse vibrations and follow a general location. Increased vibrations make it difficult to differentiate spider from prey.

The simulations find that large groups have high success rates for prey capture. In future work, they will extend the current model to include changes in web size. This takes into account the A. studiosus web correlating with the colony size. Extended models could suggest that cooperative hunting enhances without complex or specific communication. Increasing prey perception of the group may be one solution to less communication.

## References.

- Quijano, Alex John, et al. "Spatio-temporal analysis of foraging behaviors of Anelosimus studiosus utilizing mathematical modeling of multiple spider interaction on a cooperative web." Journal of theoretical biology 408 (2016): 243-259.
- Quijano, Alex John, et al. "An aggregate stochastic model incorporating individual dynamics for predation movements of anelosimus studiosus." Mathematical biosciences and engineering: MBE 12.3 (2015): 585-607.
- Joyner, Michele L., et al. "A stochastic simulation model for anelosimus studiosus during prey capture: A case study for determination of optimal spacing." Mathematical Biosciences and Engineering 11.9 (2014).
- Jones, Thomas C., et al. "Fostering model explains variation in levels of sociality in a spider system." Animal Behaviour 73.1 (2007): 195-204.
- Heppner, Frank, and Ulf Grenander. "A stochastic nonlinear model for coordinated bird flocks."
*The ubiquity of chaos*233 (1990): 238. - Clark, Colin W., and Marc Mangel. "The evolutionary advantages of group foraging." Theoretical population biology 30.1 (1986): 45-75.