Varieties of mutualistic interaction in population models

Evolutionary origins and diversification of proteobacterial mutualists

“…Classic mutualism models predict evolutionary instability of mutualist phenotypes, either because mutualists experience increased extinction risk [10,[17][18][19] or because cheater mutants can invade mutualist populations and drive transitions from mutualism to parasitism [14,15]. Yet, our data are inconsistent with these models.…”

“…Yet, the latter comparisons were sensitive to taxon sampling and were significant in only approximately 60% of the sampling schemes (see the electronic supplementary material, S6), so these conclusions are preliminary. Finally, classic theory predicted that mutualists are particularly vulnerable to extinction [17,18], but MuSSE inferred that both mutualists and parasites exhibit similarly elevated extinction rates compared to free-living taxa (figure 3; electronic supplementary material, S6). We recognize the uncertainty in estimating extinction rates from phylogenies [30], so we treat this conclusion with some caution.…”

“…There is also intense debate about the evolutionary stability of mutualism [1,5,[10][11][12][13][14][15], and in particular the degree to which mutualist phenotypes drive or hinder lineage diversification [2,[16][17][18][19]. Early population-based models predicted that mutualist taxa are more vulnerable to extinction than other lifestyles [17,18] but few empirical data have supported these ideas [19].…”

“…Early population-based models predicted that mutualist taxa are more vulnerable to extinction than other lifestyles [17,18] but few empirical data have supported these ideas [19]. In parallel, models of interspecific cooperation predict that bacteria-which often evolve rapidly-generate mutants that exploit or abandon their more slowly evolving eukaryotic hosts [14,15], thus predicting that mutualists commonly transition into other lifestyles [1,10].…”

Dynamics of an almost periodic facultative mutualism model with time delays

“…Obvious examples include the algal-fungal associations of lichens [8], plant-pollinator interactions [12], seed dispersal systems that rely on animal vectors [19], the legume nitrogen-fixing bacteria interactions [1,13], and damselfish-sea anemone interactions [23]. Mutualism may be obligate or facultative, but models of obligate mutualism have qualitatively different stability properties from those of facultative ones (see [24]). An obligate mutualist is a species which requires the presence of another species for its survival, e.g., some species of Acacia require the ant P seudomyrmex in order to survive (see [11]).…”