Stephen Wrecsics
GEOG490, Bone
June 4, 2015
Final Project
An Agent Based Model of Spatial Patterns seen in Insular Biogeography
1. Introduction
In the 1960’s Robert H. MacArthur and E. O. Wilson developed a theory to try and understand the spatial and richness distribution of species within insular geographies. A fairly obvious characteristic of insular geography is that the degree of diversity of island biota as a direct result of the isolation level of the island from the mainland, and that this rate of isolation (no matter the amount of habitat diversity an island can offer biota) is the leading factor of species richness on islands.
Species richness of any island depends on (at least in the short term) the rate of colonization of plant and animal species to an island from the mainland. MacArthur and Wilson argue that this colonization rate is not just dependent on the distance of an island from the mainland species pool, but also on the rate of immigration and extinction events related to the colonizing species, MacArthur and Wilson called this rate of replacement a “turnover rate”. MacArthur and Wilson also suggested that over time these interrelated immigration and extinction events would eventually lead to a state of equilibrium between the number of colonizing species not already on the island, and the number of extinction events of resident species already occupying the island. (Figure 1)
MacArthur and Wilson explain their theory and its relationship between colonization and immigration by looking at a single type of island (large-far/near or small-far/near) that has become available for colonization. MacArthur and Wilson explain that the rate of colonization will initially be high due to all immigrant species being new to the island. As time progresses these immigrant species become resident to the island, and the number of new species populating the island appears to drop. The rate of immigration to the island is also a product of the distance from the mainland species pool.
However, the rate of extinction (locally, not globally) will start at a lower level and gradually rise. This is because as more and more species populate the island, the amount of competition among the residents of the island increases and begins to push less adaptive species off the island, smaller communities of species are more susceptible to extinction events.
Eric and I initially chose this model because of the obvious spatial and temporal components of the theory, we also chose this model because of its non-linear behavior. Insular Biogeography is an extremely complex system with numerous relationships and interactions between its components (distance, area, species diversity, environmental niches, competition, topography, and climate). However, as we read further into the theory, we noticed that MacArthur and Wilson theorized that these two interrelated processes will eventually come to an equilibrium point and remain constant, as in, for every immigration event that occurred eventually another species would be forced off the island and create an extinction event. Since nature is intrinsically stochastic, this quickly became the objective of our research project. Nature is not a consistent, orderly package like MacArthur and Wilson seem to suggest. And if nature is not predictable in this case, how do we code that stochasticity into our model? What was leading to the outer island becoming populated in our model if not directly from the mainland as the theory suggests?
An agent-based simulation model became necessary to achieve our objective. It became necessary because of the temporal requirements to see changes in the species richness of insular environments is realistically beyond that of a human lifetime. The model is initiated with 14 species on the continent; this number is a result of the number of clearly distinct colors that can be modeled in NetLogo. Stochasticity is coded into the agent movements, and breeding at each time step. If an agent is over land, the agents move in a random direction determined by a random number generator. Individuals that find themselves in the sea initiate a random walk at a higher pace than on land, but at a higher energy cost. Only species that have reached the coastline are allowed to emigrate to islands. This higher cost of oceanic movement is coded in to simulate the lack of resources during an oceanic migration. If the agent does not reach the island their energy is exhausted and the agent dies. Those that do manage to colonize the island can begin to replicate and form a metapopulation. Breeding of agents is determined by r/K selection theory. Agents that are r-selected (prey agents) breed twice a year, where agents that are K-selected (predator agents) breed once a year. Mortality during breeding is modeled using a random assignment of initial energy, if the energy of either species is lower than the amount to sustain life, the agents offspring will not survive to the next time step. Completion between species is modeled by using simple rules that remove individuals through crowding, more than 3 of the same agents occupying the same patch will die at the next time step. Similar rules are applied to both the continental populations, and island populations. New individuals reaching the island may colonize, but lack of space leads to faster extinction (turnover) rates as time goes on.
- Methods
2.1 Overview
2.1.1 Purpose of the model
This model was built to help understand the level of uncertainty in the spatial movements and emerging patterns involved in insular biogeography. To explore those emergent patterns, and try to understand the discrepancy between what MacArthur and Wilson describe vs. what patterns are seen in the model: how do outer islands in an island chain become populated if not by the mainland species pool?
2.1.2 Entities, State Variables and Scales
Entities involved are two main agents that represent eight prey species, and two predator species. Each species are assigned a distinct color, shape, initial energy level, individualized life-span, and K or R type. The scale of the model is not defined other than temporal. Each time step represents a month, and twelve time steps equal one year.
2.1.3 Process Overview and Scheduling
One model time step will represent one month, and twelve time steps equal one year. At Set-Up, each species is assigned their individualized characteristics, islands are randomly placed, and food is grown. At Go, agents initiate a random walk, check energy levels, life span, if predator energy level drops below “prey energy” they begin to hunt prey.
2.2 Design Concepts
2.2.1 Basic Principles
Agents along the cost have a preference to emigrate away from the mainland. Once over a patch defined as an island, the agent will colonize, reproduce, and feed.
2.2.2 Emergence
Early initial dominance of one or two species along the coast of the mainland leads to those species becoming the dominant resident species of the islands.
2.2.3 Adaptation
Adaptation occurs when competition among species is simulated. If more than 3 of the same species is occupying a patch, the agent with the lowest amount of energy dies off.
2.2.4 Objectives
Agent objectives are to breed, and maintain their level of energy above the minimum level.
2.2.5 Learning
No learning is modeled in this version.
2.2.6 Prediction
No prediction is modeled in this version.
2.2.7 Sensing
Agents are aware of their current energy levels, food availability, predator agents are aware of their need to hunt, r/K selected seasonal breeding cycles, and what type of patch they currently occupy.
2.2.8 Interaction
If a patch is coastal all agent types will emigrate away from the mainland. During movement over ocean patches, all agent types will colonize island patches. Interaction of predator and prey agents are limited to predation when energy conditions (below initial prey energy level) are met.
2.2.9 Stochasticity
Stochasticity is modeled into the agent movements, number of total agents at set-up, hunting outcome, reproduction outcome, and mortality at birth.
2.2.10 Collectives
Agents form metapopulations on the islands if predator escape is achieved. (Populations on islands without any predators). Prey agents form clusters on mainland due to their r-type selection breeding.
2.2.11 Observation
We were not able to collect statistical data due to unforeseen circumstances of one team member. However visual outcomes are included.
Results
The first image shows the initial population of orange and blue species from the coast to the large island.
The second image shows the immigration of three species to the northern island, one predator and two prey species. The southern island is now populated with two species of predator (white and black), and five species of prey. (Light blue, orange, purple, dark blue, magenta).
The third image shows one species of prey who has achieved predator escape and is dominating one island.
The fourth image shows ten species resident on the continent, two on a nearby small island, four on a large close island, two on a small far island, and one species on a small distant island.
Discussion
Being limited to a narrative approach it is difficult to determine if MacArthur and Wilson’s theory of a equilibrium state is one of a static nature or dynamic. From running the model with a narrative approach I begin to see that equilibrium is indeed dynamic with stochastic elements modeled. Again, that is the benefit of agent-based spatial simulation, the ability to condense large amounts of time into a short period over and over again. This model allows for nonlinearities of the complex system of Insular Biogeography to emerge. Through the positive feedbacks of emigration, predation, food growth, and reproduction a larger emergent pattern begins to form that does not support MacArthur and Wilson’s theory.
Conclusion
Early initial dominance of one or two species along the coast of the mainland leads to those species becoming the resident species of the islands. Contrary to what MacArthur and Wilson. Hopscotch emigration from island to island, and not a turnover rate of resident species from the mainland appears to be the reason for the population spreading from island to island. Species richness does not mimic that of the mainland, rather it mimics the closest island neighbors and tapers off as the distance from the mainland grows.
