African Journal of Agricultural Research Vol. 7(24), pp. 3506-3512, 26 June, 2012 Available online at http://www.academicjournals.org/AJAR DOI: 10.5897/AJAR11.1704 ISSN 1991-637X ©2012 Academic Journals Full Length Research Paper Reproduction and culling effect on the number of ewes and lambs in two types of breeding − Mathematical model Milan Krajinović 1 , Snežana Matić-Kekić 2 , Nebojša Dedović 2* , Ivan Pihler 1 , Mirko Simikić 2 , Vladislav Simin 1 and Lazar Savin 2 1 Department of Animal Husbandry, University of Novi Sad, Faculty of Agriculture, 21000 Novi Sad, Republic of Serbia. 2 Department of Agricultural Engineering, University of Novi Sad, Faculty of Agriculture, 21000 Novi Sad, Republic of Serbia. Accepted 18 May, 2012 This study presents the development of mathematical model for determining the potential number of sheep and lambs in a ten-year period. The model enables prediction of the number of female sheep and lambs, plans for future feeding, care and breeding costs. Two types of sheep breeding (traditional and intensive) were considered, assuming the following: 1) the initial herd contained S pregnant ewes; 2) new ewes or female lambs were not bought; 3) female lambs obtained by reproduction of the livestock unit were not sold; 4) male and female lambs and ewes which did not satisfy the selection and health criteria for further reproduction, were sold. Considering the reproductive cycles of Württemberg, Ile d’ France, Suffolk and domestic Tsigai (from Serbia) sheep breeds, we established the number of ewes and lambs for sale, after n years from the herd establishment. It depends on the following parameters: the initial size of herd S, average percentage p of new, two year old ewes reproduced from the herd, and average percentage r of non culled sheep. A recursive formula for the number of ewes is given, as well as the number of lambs for sale after n years. Proposed formulas could be used for numerous additional financial analyses of sheep breeding. General model for evaluation of yearly and cumulative income for both types of sheep breeding has been presented. The obtained results represent the first step in deciding which breed and which type of breeding should be accepted in order to gain the highest possible profit. Key words: Culling and reproductive, mathematical model, sheep breeding. INTRODUCTION Reproductive parameters such as fertility index (number of lambs per ewe per year), sex ratio (proportion of male to female offspring born) and percentage of lambing have important influence on herd size increasing speed as well as quantity and quality of meat and milk (Janssens et al., 2004; Ochoa-Cordero et al., 2007). Population studies for sheep breeding have generally been based on an *Corresponding author. E-mail: dedovicn@polj.uns.ac.rs. Tel: +381 21 485 3 292. expected sex ratio 0.5: 0.5, which is accepted in this study. This ratio is rarely different for sheep breeding (Napier and Mullaney, 1974; Lindström et al., 2002), but not for cattle-breeding (Demiral et al., 2007; Silva et al., 2007), otherwise, other reproductive parameters will not be fixed and their variability can affect meat or milk quality and quantity. For example, heat stress has affected the reproductive function of Suffolk ewes (Tabarez-Rojas et al., 2009), while the number of lambs per ewe has effect on sheep milk composition (Ochoa- Cordero et al., 2007). Shearing at housing, grass silage feed value and extended grazing during pregnancy also