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.