Production of offspring using current income and reserves: size-number trade-off and optimal offspring size

To analyse the effects of current income on the nature of size-number trade-off and optimal offspring size, we developed a model in which offspring grow by absorbing current income and reserves. The offspring continue to grow while the current income is available or the reserves exist, and they cease to grow when the reserves are depleted and the current income ceases. We showed that the size-number trade-off is nonlinear in the region where the number of offspring is smaller than the critical number and linear in the region where the number of offspring is greater than the critical number. In the former region, the reserves are not depleted by the time the current income ceases and the offspring cease to grow when the reserves are depleted, whereas in the latter region, the reserves are depleted before the current income ceases and the offspring production is completed when the current income ceases. The optimal offspring size is the same as that shown in Sakai and Harada (Evolution 55 (2001) 467) if this optimal size is realized in the region of nonlinear trade-off, whereas the optimal offspring size is the same as that shown in Smith and Fretwell (Am. Natur. 108 (1974) 499) if this optimal size is realized in the region of linear trade-off.     

Size-number trade-off and optimal offspring size for offspring produced sequentially using a fixed amount of reserves

We analysed the nature of size-number trade-off of offspring when multiple cohorts of such offspring are produced sequentially using a fixed amount of reserves. In the model, we incorporated sink-limitation in the resource absorption rate of offspring from the mother tissue and the loss of resources by maintenance respiration. We found that the later the initiation of a cohort, the greater the cost of producing a cohort with the same size and number of offspring. This is due to the loss of resources by maintenance respiration during the period from the beginning of reproduction to the initiation of the cohort. Also, the extra cost increases with an increase in the specific maintenance respiration rate. Thus, resources lost to respiration over time reduces the fitness value of producing late cohorts. Hence, it is advantageous to produce all offspring simultaneously unless there are fitness advantages of producing offspring sequential which overcome this cost or constraints preventing simultaneous production. Sequentially offspring production evolves if there is a constraint on the number of offspring of each cohort. With this constraint, the optimal offspring size decreases with the production sequence of cohorts.