Plants exchange a variety of information intra- and interspecifically by using various mediating cues. For example, plant individuals that are injured by herbivores release volatile chemicals, which induce receiver plants to express anti-herbivore resistance. Remarkably, some plant species were known to represent kin specificity in the response, where cues from a damaged individual induce a higher level of resistance in a kin receiver than in a non-kin receiver. Such higher sensitivity to warning cues from kin could be advantageous via two mechanisms. If each herbivore tends to attack plants with a certain genotype, plants should be more sensitive to warning cues from kin that share genetic properties. In addition, if herbivores successively attack the neighboring plant with a high probability, and if related plants tend to grow in close proximity, plants may be more sensitive to warning cues from neighboring kin under the presence of a trade-off between sensitivity to kin and non-kin. In the present study, we constructed a mathematical model including those mechanisms to investigate the evolutionary process of the higher sensitivity to warning cues from kin than sensitivities to cues from non-kin. According to the analysis of evolutionary dynamics, we revealed that both mechanisms could contribute, although higher sensitivity to cues from kin is more likely to evolve when the spatial range of competition is greater than the range of effective alarm cues. This result highlights the importance of the competition regime in the evolution of signaling among kin.