Each of us is unique in how our personality, education, and professional and life experiences have shaped us. As a result, we do not have much actual head-to-head competition. No one else knows exactly what you know. No one else has experienced what you have. Certainly, no one else explains the same set of facts exactly as you do. I believe that a healthy attitude of regarding supposed "competitors" as quasi-associates will benefit you in several ways.
Think of your prospective clients as a large and ever expanding pie, of which there are plenty of slices for everyone. Fortunately and unfortunately, there is a plethora of litigation. This viewpoint should prevent you from feeling, sounding, and acting desperate. Another case is always out there.
When you cannot accept a case because of a disagreement with the premise or a conflict with the attorney, litigant, or schedule, consider referring the case to another expert in your field. The attorney will remember your helpfulness and openness, and the associate will owe you. Contact the expert and let him know that you sent one his way. By the law of reciprocation, it is likely that in the future he will send you a case (or two) in return.
Do not wait for an associate to refer business to you and then reciprocate. Cast your bread upon the waters. Give and it shall be given unto you. Trite? Perhaps. But true. One principle of networking is to look for ways to help as many people as you can, regardless of whether or how they can help you. As stated by Ralph Waldo Emerson in his essay entitled, "Compensation," the longer you put in without getting out, the better your result when it finally comes. It is a truism that you can have anything you want in life as long as you help others get what they want. The goodwill is certain to come back to you.
Another time you really should refer a case to an associate is when you are asked to consult and possibly testify in an area or subtopic of your profession in which you are not totally competent. Again, let the expert whom you referred know of your good deed.