An individual-based approach is used to describe population dynamics. Two kinds of models have been constructed with different distributions illustrating individual variability. In both models, the growth rate of an individual and its final body weight at the end of the growth period, which determines the number of offspring, are functions of the amount of resources assimilated by an individual. In the model with a symmetric distribution, the half saturation constant in the Michaelis–Menten function describing the relationship between the growth of individuals and the amount of resources has a normal distribution. In the model with an asymmetric distribution, resources are not equally partitioned among individuals. The individual who acquired more resources in the past, will acquire more resources in the future. A single population comprising identical individuals has a very short extinction time. If individuals differ in the amount of food assimilated, this time significantly increases irrespectively of the type of model describing population dynamics. Individuals of two populations of competing species use common resources. For larger differences in individual variability, the more variable species will have a longer extinction time and will exclude less variable species. Both populations can also coexist when their variabilities are equal or even when they are slightly different, in the latter case under the condition of high variability of both species. These conclusions have a deterministic nature in the case of the model with the asymmetric distribution—repeated simulations give the same results. In the case of the model with the symmetric distribution, these conclusions are of a statistical nature—if we repeat the simulation many times, then the more variable species will have a longer extinction time more frequently, but some results will happen (although less often) when the less variable species has a longer extinction time. Additionally, in the model with the asymmetric distribution, the result of competition will depend on the way of the introduction of variability into the model. If the higher variability is due to an increase in the proportion of individuals with a low assimilation of resources, it can produce a longer extinction time of the less variable species.

基于个体的方法用于描述人口动态。已经构建了两种具有不同分布的模型来说明个体变异性。在这两种模型中，个体的生长速度及其在生长期结束时的最终体重，决定了后代的数量，是个体同化资源量的函数。在具有对称分布的模型中，描述个体成长与资源量之间关系的 Michaelis-Menten 函数中的半饱和常数呈正态分布。在具有不对称分布的模型中，资源在个体之间分配不均。过去获得更多资源的个人，将来会获得更多资源。由相同个体组成的单一种群具有非常短的灭绝时间。如果个体同化的食物量不同，则无论描述人口动态的模型类型如何，这个时间都会显着增加。两个竞争物种种群的个体使用共同的资源。对于个体变异性的较大差异，变异性较大的物种将具有较长的灭绝时间，并将排除变异性较小的物种。当它们的变异性相等或什至它们略有不同时，两个种群也可以共存，在后一种情况下，在两个物种的高度变异性的条件下。在具有不对称分布的模型的情况下，这些结论具有确定性——重复模拟给出了相同的结果。在具有对称分布的模型的情况下，这些结论是统计性质的——如果我们多次重复模拟，那么变量越多的物种会更频繁地出现更长的灭绝时间，但会出现一些结果（虽然不那么频繁) 当变化较小的物种具有较长的灭绝时间时。此外，在具有不对称分布的模型中，竞争的结果将取决于将可变性引入模型的方式。如果较高的变异性是由于资源同化程度低的个体比例增加，则可能导致变异性较小的物种的灭绝时间更长。那么变异越多的物种灭绝时间越长，但当变异较少的物种具有更长的灭绝时间时，会发生一些结果（尽管频率较低）。此外，在具有不对称分布的模型中，竞争的结果将取决于将可变性引入模型的方式。如果较高的变异性是由于资源同化程度低的个体比例增加，则可能导致变异性较小的物种的灭绝时间更长。那么变异越多的物种灭绝时间越长，但当变异较少的物种具有更长的灭绝时间时，会发生一些结果（尽管频率较低）。此外，在具有不对称分布的模型中，竞争的结果将取决于将可变性引入模型的方式。如果较高的变异性是由于资源同化程度低的个体比例增加，则可能导致变异性较小的物种的灭绝时间更长。