  Future weak lensing surveys will directly probe the density fluctuation in
the universe. Recent studies have shown how the statistics of the weak lensing
convergence field is related to the statistics of collapsed objects. Extending
earlier analytical results on the probability distribution function of the
convergence field we show that the bias associated with the convergence field
can directly be related to the bias associated with the statistics of
underlying over-dense objects. This will provide us a direct method to study
the gravity induced bias in galaxy clustering. Based on our analytical results
which use the hierarchical {\em ansatz} for non-linear clustering, we study how
such a bias depends on the smoothing angle and the source red-shift. We compare
our analytical results against ray tracing experiments through N-body
simulations of four different realistic cosmological scenarios and found a very
good match. Our study shows that the bias in the convergence map strongly
depends on the background geometry and hence can help us in distinguishing
different cosmological models in addition to improving our understanding of the
gravity induced bias in galaxy clustering.
