Dynamical Adaptation of Parental Care

Abstract

Two models are proposed to simulate population growth of species with mature stage and immature stage in which there are parental cares for immature. It is assumed that the protection of mature to their immature reduces mortality of immature at the cost of reduction of reproduction. Dynamical adaptation of parental care is incorporated into the models, one of which is described with the proportional transition rate from immature to mature (ODE model) and the other one is described with a transition rate from immature to mature according to a fixed age (DDE model). For the ODE model, it is shown that the adaptation of parental care enlarges the possibility of species survival in the sense that population is permanent under the influences of the adaptation, but becomes extinct in the absence of adaptation. It is proved that the outcome of the adaptation makes the population in an optimal state. It is also observed that there are parental care switches, from noncare strategy to care strategy, as the natural death rate of immature individuals increases. The analysis of the DDE model indicates that the adaptation also enlarges the opportunity of population persistence, but the stage delay has the tendency to hinder the movement of population evolution to the optimal state. It is found that the loss rate of immature in the absence of parental care can induce different patterns to disturb the adaptation of population to optimal state. However, it is shown that the adaptation of parental care approaches to the optimal state when parental care is required for the survival of the population, for example, when the loss rate of immature or competition among mature increases or the fecundity decreases.

Chaotic Dynamics of a Tri-Topic Food Chain Model with Beddington-DeAngelis Functional Response in Presence of Fear Effect

“…Those models are constructed with only prey dependent, both monotone and non-monotone functional responses [15,16,20,24,25], both prey and predator dependent functional response like Cowley-Martin type functional response [17], Beddington-DeAngelis type functional response [26,27], Monod-Haldane type functional response [28] and ratio-dependent functional response [20,29]. In 2009, Takeuchi et al studied the dissension along with investing time on taking care of juvenile and searching for food/nutrients of mature prey in absence of direct predation, while they assumed that matures accommodate their parental care time via learning [30]. Krivan (2007) investigated that exchange among foraging and predation based on classical Lotka-Volterra prey-predator system where either prey or predator or both species were adaptive to maximize their independent sturdiness [31].…”

Chaotic dynamics of a tri-topic food chain model with Beddington–DeAngelis functional response in presence of fear effect

“…Those models are constructed with only prey dependent, both monotone and non-monotone functional responses [15,16,20,24,25], both prey and predator dependent functional response like Cowley-Martin type functional response [17], Beddington-DeAngelis type functional response [26,27], Monod-Haldane type functional response [28] and ratio-dependent functional response [20,29]. In 2009, Takeuchi et al studied the dissension along with investing time on taking care of juvenile and searching for food/nutrients of mature prey in absence of direct predation, while they assumed that matures accommodate their parental care time via learning [30]. Krivan (2007) investigated that exchange among foraging and predation based on classical Lotka-Volterra prey-predator system where either prey or predator or both species were adaptive to maximize their independent sturdiness [31].…”

E‐cigarette smoking with peer pressure

“…Our objective here is to present and analyse an SIR or SI like ODE model for non-smokers, tobacco smokers, and those who smoke e-cigarettes, incorporating peer pressure in the switch from tobacco to e-cigarette smoking. We note that differential equation models have been used extensively in modelling social problems and related issues, including the spread of infections; see, eg, Bissell,7,8 Bissell et al, 9 Buonomo et al, 10 Caiado, 11 Ciarcia et al, 12 Giacobbe and Mulone, 13 Giacobbe et al, 14 Gonzalez et al, 15 Guo et al, 16 Hethcote et al, 17 Huo and Song, 18 Huo and Wang, 19 Jung et al, 20 Mulone and Straughan, 21,22 Mulone et al, 23 Mushanyu et al, 24 Nyabadza et al, 25 Pomeroy, 26 Sharomi and Gumel, 27 Srivastava and Günerhan, 28 Straughan, 29 Takeuchi et al, 30 Usaini et al, 31 Walters, 32 Walters and Kendal, 33 Wang, 34 Wang et al, 35 Wang and Mulone, 36 Wang and Zhao, 37,38 Wang and Zou, 39 and Zhou et al 40 In particular, SIR models and ramifications thereof, such as those involving conformity bias (Walters, 32 Walters and Kendal, 33 and Bissell 8 ), incorporating external information (Buonomo et al 10 and Giacobbe et al 14 ), and allowing for multi-patch models (Wang and Mulone 36 ), have been employed in...…”

“…Our objective here is to present and analyse an SIR or SI like ODE model for non‐smokers, tobacco smokers, and those who smoke e‐cigarettes, incorporating peer pressure in the switch from tobacco to e‐cigarette smoking. We note that differential equation models have been used extensively in modelling social problems and related issues, including the spread of infections; see, eg, Bissell, Bissell et al, Buonomo et al, Caiado, Ciarcia et al, Giacobbe and Mulone, Giacobbe et al, Gonzalez et al, Guo et al, Hethcote et al, Huo and Song, Huo and Wang, Jung et al, Mulone and Straughan, Mulone et al, Mushanyu et al, Nyabadza et al, Pomeroy, Sharomi and Gumel, Srivastava and Günerhan, Straughan, Takeuchi et al, Usaini et al, Walters, Walters and Kendal, Wang, Wang et al, Wang and Mulone, Wang and Zhao, Wang and Zou, and Zhou et al …”