There is a persistent debate in economics about the effects of migration of the highly-skilled workers on employment prospects and careers of the natives. Here is one interesting study looking at such effects within the context of the targeted immigration programme based on skills within the particular set of sectors - the STEM, or more commonly, Science and Technology.
Kerr, Sari Pekkala and Kerr, William R. and Lincoln, William Fabius, Skilled Immigration and the Employment Structures of U.S. Firms (see arvard Business School Entrepreneurial Management Working Paper No. 14-040: http://ssrn.com/abstract=2354963) "study the impact of skilled immigrants on the employment structures of U.S. firms … [accounting for] the fact that many skilled immigrant admissions are driven by firms themselves (e.g., the H-1B visa)." The authors "find rising overall employment of skilled workers with increased skilled immigrant employment by firm. Employment expansion is greater for younger natives than their older counterparts, and departure rates for older workers appear higher for those in STEM occupations compared to younger worker."
From the point of view of countries, like Ireland, relatively open to immigration of skilled workers, but without a specific skills-based 'filter' (Irish system is open to migrants on the basis of nationality, rather than skills, but has strong selection biases into skills-based immigration due to lack of jobs creation outside the STEM categories of jobs), the above suggests that skills depreciation in the STEM sector can be a problem for the natives. As supply of younger STEM employees from abroad rises, there can be a tendency for displacement of older workers, premature termination or flattening out of careers and, subsequently, lower supply of pensions and income provisions in later years of life.