Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction

Abstract

Organisms often exhibit behavioral or phenotypic diversity to improve population fitness in the face of environmental variability. When each behavior or phenotype is individually maladaptive, alternating between these losing strategies can counter-intuitively result in population persistence-an outcome similar to the Parrondo's paradox. Instead of the capital or history dependence that characterize traditional Parrondo games, most ecological models which exhibit such paradoxical behavior depend on the presence of exogenous environmental variation. Here we present a population model that exhibits Parrondo's paradox through capital and history-dependent dynamics. Two sub-populations comprise our model: nomads, who live independently without competition or cooperation, and colonists, who engage in competition, cooperation, and long-term habitat destruction. Nomads and colonists may alternate behaviors in response to changes in the colonial habitat. Even when nomadism and colonialism individually lead to extinction, switching between these strategies at the appropriate moments can paradoxically enable both population persistence and long-term growth.

Keywords: Ecology; Evolutionary Biology; Parrondo's paradox; computational biology; ecology; none; systems biology.

Figure 1.. In the absence of switching, (a) eventual extinction for both strategies vs (b) survival for the colonial strategy.

Initial conditions for both are $n_1=2$, $n_2=2$, $K=5$. Shared parameters are $r_s=0$, $r_1=1$, $r_2=10$. For (a), $A=1.001$. For (b), $A=0.5$.

Figure 2.. Behavioral switching which results in (a) extinction vs (b) survival.

Initial conditions for both are $n_1=2$, $n_2=2$, $K=5$. Shared parameters are $r_s=1000$, $r_1=1$, $r_2=10$. For (a), $L_1=3$, $L_2=4.5$. For (b), $L_1=3$, $L_2=4$.

Figure 3.. Long-term growth through strategic alternation.

Initial conditions are $n_1=0$, $n_2=2$, $K=5$. Parameters are $A=1.001$, $L_1=3$, $L_2=4$, $r_s=1000$, $r_1=1$, $r_2=10$.

Figure 4.. Zoomed-in portion of Figure 5 that shows the mechanism behind the spikes in n1.

When $n_2$ is large, switching takes longer, causing a drop in $K$, and a large increase in $n_1$.

Figure 5.. Long-term growth through strategic alternation, up to t=1000.

Initial conditions are $n_1=0$, $n_2=2$, $K=5$. Parameters are $A=1.001$, $r_s=1000$, $r_1=1$, $r_2=10$.

Figure 6.. Survival through periodic alternation under slow habitat change.

Parameters for (a) are $r_s=10000$, $r_1=10$, $r_2=100,L_1=3$, $L_2=3.083$. For (b), $r_s=100000$, $r_1=100$, $r_2=1000,L_1=3$, $L_2=3.008$. Shared parameters are $K_{\max }=20$, $A=1.001$.

Figure 7.. Long-term growth through strategic alternation with a bounded carrying capacity.

Initial conditions are $n_1=0$, $n_2=2$, $K=5$, shared parameters are $A=1.001$. For (a), $K_{\max }=20$, $r_s=1000$, $r_1=1$, $r_2=10$ (fast habitat change). For (b), $K_{\max }=7.5$, $r_s=10000$, $r_1=10$, $r_2=100$ (slow habitat change).

Appendix 1—figure 1.. An example of switching from colonialism to nomadism.

$t_1$ marks the start of the switch, $t_2$ marks the end. Other parameters are $A=1.001$, $r_s=1000$, $r_1=1$, $r_2=10$.

Appendix 1—figure 2.. An example of switching from nomadism to colonialism.

$t_1$ marks the start of the switch, $t_2$ marks the end. Other parameters are $A=1.001$, $r_s=1000$, $r_1=1$, $r_2=10$.