Division of Labor and Task Allocation Robert Herbig Peter Fine

Overview Division of Labor Response Thresholds Models One Task Several Tasks “Emergent” Task Succession Model 1 Model 2

Division of Labor Simultaneous task performance by specialized workers Better than sequential task performance by unspecialized workers Examples: Reproduction Foraging Hive defense Cleaning of the nest

Division of Labor Temporal polyethism (Age castes) Individuals of the same age tend to perform identical tasks Worker polymorphism (Morphological or physical castes) Workers have different morphologies Individual variability (Behavioral castes) Differences among individuals in the frequency and sequence of task performance

Division of Labor Specialization Plasticity Resilience Division of labor is rarely rigid Ratio of workers performing different tasks varies in response to changes Resilience How much the colony responds to alterations Determined by elasticity at the individual level

Response Thresholds Individuals perform a task when their threshold is met When a task is performed, the threshold for that worker for that task is lowered Honey Bee

Response Thresholds Pheidole pallidula ant species: Major workers have higher thresholds for foraging and nest defense than minors

Response Thresholds Ectatomma ruidum ant species: Specialized “stinger ants” retrieve prey if necessary

Models with One Task Inactive individual performs tasks with probability P: P(Xi=0 -> Xi=1)=Tθi(s)=s²/(s²+ θi²) Active individual gives up task and becomes inactive with probability p: P(Xi=1 -> Xi=0)= p Average time spent on a task: 1/p Stimulus intensity: s(t+1)=s(t)+δ-αNact/N

Models with Several Tasks Given m tasks with Nij the # of workers of type i engaged in task j Two equations govern this complex model:

Models with “Emergent” Task Succession Individuals have identical response thresholds Thresholds vary for each task Success rate varies for each task In general, heavy items are “carried” (processed) after lighter items Examples: Brood sorting of Leptothorax ants Carrying leaf fragments to their appropriate location

Models with “Emergent” Task Succession Performing a task increases the demand for another task One task will generally be followed by another Examples: Creating a pile of refuse at the entrance to the nest generates a need for cleaning Killer ants kill prey, which increases the need for transportation of the corpses

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