The role of respiration in the genesis of heart rate variability (HRV) has been the subject matter of many experimental and modeling studies. It is widely accepted that the high frequency (HF) peak of a HRV power spectrum, which is centered at the average respiratory frequency, is caused by mechanisms activated by respiration. On the other hand, there is a debate on the possible role of respiration in the genesis of the low frequency (LF) peak which is usually centered around 0.1 Hz. In this study, a comprehensive cardiorespiratory interaction model is used to test various hypotheses regarding the role of respiration in the LF peak of HRV. In this model, chest and abdomen circumference signals and lung volume signal are used as respiratory inputs. Simulations are made for periodic, spontaneous and slightly irregular respiratory patterns, and it is observed that the more low frequency (LF) power there in the respiratory signals, the more LF power there in the model-predicted HRV. Experiments on nine volunteers are also performed for the same respiratory patterns and similar results are observed. Furthermore, the actual measured respiratory signals are input to the model and the model predicted and the actual HRVs are compared both in time domain and also with respect to their power spectra. It is concluded in general that respiration not only is the major contributor to the genesis of the HF peak in the HRV power spectrum, but also plays an important role in the genesis of its LF peak. Thus, the LF/HF ratio, which is used to assess sympathovagal balance, cannot be correctly utilized in the absence of simultaneous monitoring of respiration during an HRV test.