Linear selection indices for non-linear profit functions

1988 ◽  
Vol 75 (4) ◽  
pp. 553-560 ◽  
Author(s):  
Y. Itoh ◽  
Y. Yamada
Keyword(s):  
Selection Indices ◽  
Linear Selection ◽  
Non Linear ◽  
Profit Functions

Optimum linear selection indexes for multiple generation objectives with non-linear profit functions

1995 ◽  
Vol 61 (1) ◽  
pp. 165-175 ◽  
Author(s):  
J. C. M. Dekkers ◽  
P. V. Birke ◽  
J. P. Gibson
Keyword(s):  
Optimal Control ◽  
Net Present Value ◽  
Selection Index ◽  
Index Theory ◽  
Planning Horizon ◽  
Simultaneous Optimization ◽  
Linear Selection ◽  
Non Linear ◽  
Profit Functions ◽  
Selection Indexes

AbstractA method to obtain linear selection indexes that maximize objectives that involve average profit in one or more generations within a planning horizon based on non-linear profit functions, was derived through application of optimal control theory. The method involves simultaneous optimization of indexes for each generation in the planning horizon. Optimum linear indexes were found to be conform indexes derived from selection index theory, with economic values equal to a weighted sum of partial derivatives of the profit function at the trait means which result in each generation of the planning horizon. Numerical procedures to derive optimum indexes are presented. Methods and properties of alternative strategies for selection witli non-linear profit functions are illustrated for selection on egg weight and rate of lay in poultry. In the example, the additional benefit of selection indexes that maximize cumulative net present value of profit over a planning horizon of10 years was small relative to use of traditional selection procedures. Optimal indexes were also derived with a derivative-free non-linear programming optimizer, with identical results. The latter method also allows incorporation of additional constraints.Possible extensions of the optimal control methodology to address other problems related to optimization of selection over multiple generations are discussed.

Optimum linear indices for non-linear profit functions

1993 ◽  
Vol 56 (1) ◽  
pp. 43-50 ◽  
Author(s):  
H. Pasternak ◽  
J. I. Weller
Keyword(s):  
Selection Index ◽  
Selection Intensity ◽  
Production Traits ◽  
Milk Production Traits ◽  
Optimum Selection ◽  
Non Linear ◽  
Linear Index ◽  
Standard Linear ◽  
Profit Functions ◽  
Selection Intensities

AbstractAn iterative method is presented, based on the method of Moav and Hill (1966) to derive the optimum linear selection index for any number of traits with linear or non-linear profit functions. For non-linear profit functions the index weights will be functions of the trait means prior to selection and the selection intensity. Using the equations developed, the optimum selection index for three dairy cattle milk production traits was computed. Convergence was obtained after three to four iterations, and was robust to the starting values used for iteration. The ratio of expected genetic gains were only marginally different for selection intensities of 1 and 4 standard deviation units. Differences were greater for the index coefficients. All alternative indices tested gave lower gains in profit than the optimum index. For linear profit functions this index reduces to the standard linear index, and for two uncorrelated traits this index reduces to the index of Moav and Hill (1966).

Bite performance surfaces of three ecologically divergent Iguanidae lizards: relationships with lower jaw bones

2019 ◽  
Vol 127 (4) ◽  
pp. 810-825
Author(s):  
Monique Nouailhetas Simon ◽  
Renata Brandt ◽  
Tiana Kohlsdorf ◽  
Stevan J Arnold
Keyword(s):  
Biomechanical Model ◽  
Disruptive Selection ◽  
Head Shape ◽  
Linear Combinations ◽  
Mechanical Advantage ◽  
Jaw Bones ◽  
Correlational Selection ◽  
Lower Jaw ◽  
Linear Selection ◽  
Non Linear

Abstract Traits that interact to perform an ecologically relevant function are expected to be under multivariate non-linear selection. Using the lower jaw morphology as a biomechanical model, we test the hypothesis that lower jaw bones of lizards are subjected to stabilizing and correlational selection, associated with mechanical advantage and maximum bite force. We used three closely related tropidurine species that differ in size, head shape and microhabitat: Eurolophosaurus nanuzae, Tropidurus hispidus and Tropidurus semitaeniatus. We predicted a common pattern of correlational selection on bones that are part of in-levers or part of the out-lever of the lower jaw. The predicted pattern was found in E. nanuzae and T. hispidus, but this could not be shown to be statistically significant. For T. semitaeniatus, we found significant disruptive selection on a contrast involving the surangular, and also significant directional selection on linear combinations of traits in all species. The results indicate that the non-linear selection on lower jaw bones does not reflect an optimum to enhance mechanical advantage in all species. Divergent functional demands and specific ecological contexts of species seem relevant in shaping patterns of selection on morphology.

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