Ecosystems with alternative stable states (ASS) may shift discontinuously from one stable state to another as environmental parameters cross a threshold. Reversal can then be difficult due to hysteresis effects. This contrasts with continuous state changes in response to changing environmental parameters, which are less difficult to reverse. Worldwide degradation of coral reefs, involving "phase shifts" from coral to algal dominance, highlights the pressing need to determine the likelihood of discontinuous phase shifts in coral reefs, in contrast to continuous shifts with no ASS. However, there is little evidence either for or against the existence of ASS for coral reefs. We use dynamic models to investigate the likelihood of continuous and discontinuous phase shifts in coral reefs subject to sustained environmental perturbation by fishing, nutrification, and sedimentation. Our modeling results suggest that coral reefs with or without anthropogenic stress can exhibit ASS, such that discontinuous phase shifts can occur. We also find evidence to support the view that high macroalgal growth rates and low grazing rates on macroalgae favor ASS in coral reefs. Further, our results suggest that the three stressors studied, either alone or in combination, can increase the likelihood of both continuous and discontinuous phase shifts by altering the competitive balance between corals and algae. However, in contrast to continuous phase shifts, we find that discontinuous shifts occur only in model coral reefs with parameter values near the extremes of their empirically determined ranges. This suggests that continuous shifts are more likely than discontinuous shifts in coral reefs. Our results also suggest that, for ecosystems in general, tackling multiple human stressors simultaneously maximizes resilience to phase shifts, ASS, and hysteresis, leading to improvements in ecosystem health and functioning.

The uniparental inheritance (UPI) of mitochondria is thought to explain the evolution of two mating types or even true sexes with anisogametes. However, the exact role of UPI is not clearly understood. Here, we develop a new model, which considers the spread of UPI mutants within a biparental inheritance (BPI) population. Our model explicitly considers mitochondrial mutation and selection in parallel with the spread of UPI mutants and self-incompatible mating types. In line with earlier work, we find that UPI improves fitness under mitochondrial mutation accumulation, selfish conflict and mitonuclear coadaptation. However, we find that as UPI increases in the population its relative fitness advantage diminishes in a frequency-dependent manner. The fitness benefits of UPI ‘leak’ into the biparentally reproducing part of the population through successive matings, limiting the spread of UPI. Critically, while this process favours some degree of UPI, it neither leads to the establishment of linked mating types nor the collapse of multiple mating types to two. Only when two mating types exist beforehand can associated UPI mutants spread to fixation under the pressure of high mitochondrial mutation rate, large mitochondrial population size and selfish mutants. Variation in these parameters could account for the range of UPI actually observed in nature, from strict UPI in some Chlamydomonas species to BPI in yeast. We conclude that UPI of mitochondria alone is unlikely to have driven the evolution of two mating types in unicellular eukaryotes.

Sperm competition theory has largely focused on the evolution of ejaculate expenditure strategies across different species or populations or across discrete mating roles on which sperm competition operates differentially. Few studies have considered the extent to which male ejaculate expenditure is influenced by continuous change in male phenotype within a population. Here we model how optimal ejaculate expenditure responds to two sources of continuous variation: (1) the quantity of resources allocated by a male to mating within a breeding season and (2) the resource cost of obtaining a mate. We find that variation in the amount of resources available for mating does not alone produce selection for differing ejaculate investment strategies. However, when there is variation in the cost of obtaining a mate, males with a lower cost will be selected to invest fewer sperm per mating than males whose cost is higher. Any parameter decreasing this cost will also select for decreased ejaculate investment per mating. These results provide a novel insight into the evolution of male ejaculate expenditure strategies, revealing that individual constraints on the ability to secure matings can lead to variation in ejaculate expenditure even when the risk of sperm competition is the same for all males.

Discounting occurs when an immediate benefit is systematically valued more highly than a delayed benefit of the same magnitude. It is manifested in physiological and behavioural strategies of organisms. This study brings together life-history theory and time-preference theory within a single modelling framework. We consider an animal encountering reproductive opportunities as a random process. Under an external hazard, optimal life-history strategy typically prioritizes immediate reproduction at the cost of declining fertility and increasing mortality with age. Given such ageing, an immediate reproductive reward should be preferred to a delayed reward because of both the risk of death and declining fertility. By this analysis, ageing is both a consequence of discounting by the body and a cause of behavioural discounting. A series of models is developed, making different assumptions about external hazards and biological ageing. With realistic ageing assumptions (increasing mortality and an accelerating rate of fertility decline) the timepreference rate increases in old age. Under an uncertain external hazard rate, young adults should also have relatively high time-preference rates because their (Bayesian) estimate of the external hazard is high. Middle-aged animals may therefore be the most long term in their outlook.

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