Interspecific mutualistic interactions are widespread in nature, from geographic and evolutionary perspectives
(Hoeksema and Bruna 2000). These interactions are beneficial to both species involved and can be categorized as facultative or obligatory. Obligatory mutualistic species require interspecific interaction for survival while facultative mutualistic species can survive on their own but benefit from interspecific interactions. Although widespread in nature, mutualistic interactions are not well understood in the theoretical realm of biology. Although models exploring these interactions date as far back as competition and predator-prey models, mutualistic models are often not included in ecology textbooks, and they have a history of being forgotten and rediscovered (Morin 1999, Stadler and
Dixon 2008).
The goal of this project is to explore some of the models that have been developed to model facultative and obligatory mutualistic interactions.
Two models were explored in this project:
1)A simplistic model - based on the Lotka-
Volterra model for competing species,
2)Dean ’s model of mutualistic relationships
Although widespread in nature, mutualistic interactions are not well understood in theoretical ecology. My goal was to explore some of the well-studied models of mutualism.
I simulated population trajectories over time and plotted zero-growth isoclines for facultative mutualists using two models: the simplistic model based on the Lotka-Volterra model for competing species and Dean ’s model of mutualistic relationships.
Dean ’s model incorporates the biological concept of species’ carrying capacity providing a more elaborate model to simulate mutualistic interactions.
Simplistic model Dean ’s model
Population trajectories over time for a facultative mutualistic species as predicted by Dean ’s model. Parameters
: r
1
= 1, α
12
= 0.75, K
1
= 1000. Note how population grows beyond carrying capacity (dashed line).
Population trajectories over time for two facultative mutualistic species as predicted by Dean ’s model. Variables used: r
1
K
2
= 100, C
1
= 20 and C
2 and r
= 20.
2
= 1.22, a = 2, b = 3, K
1 and
. Zero-growth isoclines for species 1 (red) and species 2
Zero-growth isoclines for species 1 (red) and species 2
(blue) in phase space. Arrows indicate expected direction of
(blue) in phase space. Arrows indicate expected direction of trajectories if initial population size falls to either side of the species ’ isocline. Grey dot represents equilibrium point. Note trajectories if initial population size falls to either side of the species ’ isocline.
how equilibrium point is beyond K1 and K2.