Population-Level Density Dependence Influences the Origin and Maintenance of Parental Care

Abstract

Parental care is a defining feature of animal breeding systems. We now know that both basic life-history characteristics and ecological factors influence the evolution of care. However, relatively little is known about how these factors interact to influence the origin and maintenance of care. Here, we expand upon previous work and explore the relationship between basic life-history characteristics (stage-specific rates of mortality and maturation) and the fitness benefits associated with the origin and the maintenance of parental care for two broad ecological scenarios: the scenario in which egg survival is density dependent and the case in which adult survival is density dependent. Our findings suggest that high offspring need is likely critical in driving the origin, but not the maintenance, of parental care regardless of whether density dependence acts on egg or adult survival. In general, parental care is more likely to result in greater fitness benefits when baseline adult mortality is low if 1) egg survival is density dependent or 2) adult mortality is density dependent and mutant density is relatively high. When density dependence acts on egg mortality, low rates of egg maturation and high egg densities are less likely to lead to strong fitness benefits of care. However, when density dependence acts on adult mortality, high levels of egg maturation and increasing adult densities are less likely to maintain care. Juvenile survival has relatively little, if any, effect on the origin and maintenance of egg-only care. More generally, our results suggest that the evolution of parental care will be influenced by an organism's entire life history characteristics, the stage at which density dependence acts, and whether care is originating or being maintained.

Fig 1. The origin of parental care in relation to egg, adult, and juvenile survival.

When egg death rate is density-dependent (A) and when adult death rate is density dependent (B) the fitness benefit associated with care is greatest when baseline egg death rate (i.e. egg death rate before any care is accounted for) is relatively high. When egg death rate is density dependent (C), the fitness benefit associated with care is greatest when baseline adult death rate is relatively low. However, when the adult death rate is density dependent (D), there is no relationship between the fitness of care and baseline adult death rate. When egg death rate is density-dependent (E) and when adult death rate is density-dependent (F), the fitness benefit associated with care is unrelated to juvenile survival. Unless otherwise noted, d_{E 0} = d_{E m0} = 10, m_E = m_{E m} = 0.1, r₀ = r_m0 = 10,000, d_A0 = d_Am0 = 10, σ_J0 = σ_Jm0 = 0.01, τ = 0.1, c = 0.9.

Fig 2. The maintenance of parental care in relation to egg, adult, and juvenile survival and the density of mutant individuals.

When egg death rate (A) and when adult death rate (B) are density dependent, the fitness benefit associated with care is greatest at higher levels of baseline egg death rate when mutant density is relatively low. As density increases, the fitness benefits associated with care decrease and the fitness benefits of care become insensitive to baseline egg death rate (A-B). When density dependence acts on egg death rate, the fitness benefits associated with the maintenance of care are highest when adult death rate is relatively low (C). When density dependence acts on adult death rate, the fitness benefits associated with the maintenance of care are relatively insensitive to baseline adult death rate at low mutant densities (D). When density dependence acts on adult mortality and mutant density is high, the maintenance of parental care is most strongly favored at lower baseline adult death rates high (D). When mutant density is relatively high, the fitness benefits associated with the maintenance of care are greatest when juvenile survival is intermediate or relatively high regardless of whether density dependence acts on egg death rate (E) or adult mortality (F). Unless otherwise noted, d_{E 0} = d_{E m0} = 10, m_E = m_{E m} = 0.1, r₀ = r_m0 = 10,000, d_A0 = d_Am0 = 10, σ_J0 = σ_Jm0 = 0.01, τ = 0.1, c = 0.9.

Fig 3. Fitness benefits of the origin of parental care in relation to egg and juvenile development.

When egg death rate is density dependent (A), the fitness benefit associated with care is highest when egg maturation rate is relatively high, whereas when adult death rate is density dependent (B), the fitness benefit of care is highest when egg maturation rate is relatively low. However, in both cases (A-B) the slope of this relationship is close to zero, and as such, egg maturation rate has minimal effects on the fitness benefits of care. When egg death rate (C) and adult death rate (D) are density dependent, the fitness benefit associated with care is highest when the juvenile stage is relatively short. Unless otherwise noted, d_{E 0} = d_{E m0} = 10, m_E = m_{E m} = 0.1, r₀ = r_m0 = 10,000, d_A0 = d_Am0 = 10, σ_J0 = σ_Jm0 = 0.01, τ = 0.1, c = 0.9.

Fig 4. Fitness benefits of the maintenance of parental care in relation to egg and juvenile development and the population density of mutant individuals.

When density dependence is acting upon the egg death rate, (A) the fitness benefit associated with the maintenance of care is highest when egg maturation rate is lowest and mutant density is low. When adult mortality is density dependent, the fitness benefits associated with the maintenance of care are greatest when egg maturation rate is low and mutant density is low. When egg death rate (C) and when adult death rate (D) are density dependent, the fitness benefits associated with the maintenance of care are greatest when the duration of the juvenile stage is relatively long if mutant density is relatively high. Unless otherwise noted, d_{E 0} = d_{E m0} = 10, m_E = m_{E m} = 0.1, r₀ = r_m0 = 10,000, d_A0 = d_Am0 = 10, σ_J0 = σ_Jm0 = 0.01, τ = 0.1, c = 0.9.

Fig 5. Fitness benefits of varying levels of parental care.

Intermediate levels of care are favoured for the origin of parental care when (A) egg death rate and (B) adult death rate are density dependent. Intermediate levels of care are favoured for the maintenance of care when (A) egg death rate and (B) adult death rate are density dependent. d_{E 0} = d_{E m0} = 10, m_E = m_{E m} = 0.1, r₀ = r_m0 = 10,000, d_A0 = d_Am0 = 10, σ_J0 = σ_Jm0 = 0.01, τ = 0.1, A_m = 0–1.