  Parameters of a special kind of \alpha-effect known in dynamo theory as the
Babcock-Leighton mechanism are estimated using the data of sunspot catalogs.
The estimates evidence the presence of the Babcock-Leighton \alpha-effect on
the Sun. Fluctuations of the \alpha-effect are also estimated. The fluctuation
amplitude appreciably exceeds the mean value, and the characteristic time for
the fluctuations is comparable to the period of the solar rotation.
Fluctuations with the parameters found are included in a numerical model for
the solar dynamo. Computations show irregular changes in the amplitudes of the
magnetic cycles on time scales of centuries and millennia. The calculated
statistical characteristics of the grand solar minima and maxima agree with the
data on solar activity over the Holocene.
