Effects of tunnel structures of two termite species on territorial competition and territory size
수학원리응용센터

Wonju Jeon, Lee, S.H.

Journal of AsiaPacific entomology
17(3), 199205
(2014)
The foraging territories of 2 subterranean termites, Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar), were simulated using a model to explore how territorial intraspecific competition changes with 4 variables characterizing the formation of territory: the number of primary tunnels, $N_0$; the branching probability, $P_{branch}$; the number of territories, $N$; and the blocking probability, $P_{block}$. The blocking probability $P_{block}$ quantitatively describes the probability that a tunnel will be terminated when another tunnel is encountered; higher $P_{block}$ values indicate more likely termination. Higher tunneltunnel encounters led to denser tunnel networks. We defined a territory as a convex polygon containing a tunnel pattern and explored the effects of competition among termite colonies on territory size distribution at steady state attained after sufficient simulation time. At the beginning of the simulation, $N = 10, 20, \cdots, 100$ initial territory seeds were randomly distributed within a square area. In our previous study, we introduced an interference coefficient $\gamma$; to characterize territorial competition. Higher $\gamma$; values imply higher limitations on network growth. We theoretically derived $\gamma$; as a function of $P_{block}$ and $N$. In this study, we considered the constants in $\gamma$; as functions of $N_0$ and $P_{branch}$ so as to quantitatively examine the effect of tunnel structure on territorial competition. By applying statistical regression to the simulation data, we determined the generalized $\gamma$; functions for both species. Under competitive conditions, territory size is most strongly affected by $N_0$, while the outcome of territorial competition is most strongly affected by $N$, followed by $P_{block}$ and $N_0$.
 초록
The foraging territories of 2 subterranean termites, Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar), were simulated using a model to explore how territorial intraspecific competition changes with 4 variables characterizing the formation of territory: the number of primary tunnels, $N_0$; the branching probability, $P_{branch}$; the number of territories, $N$; and the blocking probability, $P_{block}$. The blocking probability $P_{block}$ quantitatively describes the probability that a tunnel will be terminated when another tunnel is encountered; higher $P_{block}$ values indicate more likely termination. Higher tunneltunnel encounters led to denser tunnel networks. We defined a territory as a convex polygon containing a tunnel pattern and explored the effects of competition among termite colonies on territory size distribution at steady state attained after sufficient simulation time. At the beginning of the simulation, $N = 10, 20, \cdots, 100$ initial territory seeds were randomly distributed within a square area. In our previous study, we introduced an interference coefficient $\gamma$; to characterize territorial competition. Higher $\gamma$; values imply higher limitations on network growth. We theoretically derived $\gamma$; as a function of $P_{block}$ and $N$. In this study, we considered the constants in $\gamma$; as functions of $N_0$ and $P_{branch}$ so as to quantitatively examine the effect of tunnel structure on territorial competition. By applying statistical regression to the simulation data, we determined the generalized $\gamma$; functions for both species. Under competitive conditions, territory size is most strongly affected by $N_0$, while the outcome of territorial competition is most strongly affected by $N$, followed by $P_{block}$ and $N_0$.
 초록
The foraging territories of 2 subterranean termites, Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar), were simulated using a model to explore how territorial intraspecific competition changes with 4 variables characterizing the formation of territory: the number of primary tunnels, $N_0$; the branching probability, $P_{branch}$; the number of territories, $N$; and the blocking probability, $P_{block}$. The blocking probability $P_{block}$ quantitatively describes the probability that a tunnel will be terminated when another tunnel is encountered; higher $P_{block}$ values indicate more likely termination. Higher tunneltunnel encounters led to denser tunnel networks. We defined a territory as a convex polygon containing a tunnel pattern and explored the effects of competition among termite colonies on territory size distribution at steady state attained after sufficient simulation time. At the beginning of the simulation, $N = 10, 20, \cdots, 100$ initial territory seeds were randomly distributed within a square area. In our previous study, we introduced an interference coefficient $\gamma$; to characterize territorial competition. Higher $\gamma$; values imply higher limitations on network growth. We theoretically derived $\gamma$; as a function of $P_{block}$ and $N$. In this study, we considered the constants in $\gamma$; as functions of $N_0$ and $P_{branch}$ so as to quantitatively examine the effect of tunnel structure on territorial competition. By applying statistical regression to the simulation data, we determined the generalized $\gamma$; functions for both species. Under competitive conditions, territory size is most strongly affected by $N_0$, while the outcome of territorial competition is most strongly affected by $N$, followed by $P_{block}$ and $N_0$.
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