Indirect costs counteract the effects of pollinator-mediated phenotypic selection on corolla size in the mediterranean shrub Halimium atriplicifolium

Aims larger corollas receive more pollinator visits but involve higher production and maintenance costs,especially under hot and dry conditions.this can result in indirect costs on reproductive output,which may counteract the effects of pollinator-mediated phenotypic selection on corolla size.In this study,I explored the relationship between corolla size and indirect costs and whether these costs counteract the effects of pollinator-mediated phenotypic selection on this trait in the mediterranean shrub Halimium atriplicifolium.I hypothesized that(i)corolla production entails direct costs in dry mass,N and P,(ii)corollas entail significant indirect costs in terms of fruit and seed production,(iii)indirect costs increase with corolla size,(iv)this species may suffer pollen limitation to a certain degree and(v)indirect costs counteract the effects of pollinator-mediated selection on corolla size.Methods I compared fruit set and seed production of petal-removed flow-ers(r flowers)and unmanipulated control flowers(C flowers)and evaluated the influence of individual mean corolla size on relative fruit and seed gain of r compared to C flowers.I also estimated phenotypic selection on corolla size mediated by indirect costs and the combined effect of costs and pollinators(i.e.total selection).Important Findings Corollas allocated sizeable amount of resources in terms of dry mass relative to the other floral structures.Fruit set and seed per fruit were significantly higher in r flowers,while individual mean corolla size showed a positive relationship with relative fruit gain.Phenotypic selection analysis revealed cost-mediated negative directional selection and absence of positive directional total selection on corolla size through fruit set.this translated into stabilizing total selection.these results suggest that mediterranean environments can impose constraints on corolla size,counteracting advantages of larger corollas from the pollination point of view with increased indirect costs of such flowers.

New loop pairing criterion based on interaction and integrity considerations

Loop pairing is one of the major concerns when designing decentralized control systems for multivariable processes.Most existing pairing tools,such as the relative gain array(RGA) method,have shortcomings both in measuring interaction and in integrity issues.To evaluate the overall interaction among loops,we propose a statistics-based criterion via enumerating all possible combinations of loop statuses.Furthermore,we quantify the traditional concept of integrity to represent the extent of integrity of a decentralized control system.Thus,we propose that a pairing decision should be made by taking both factors into consideration.Two examples are provided to illustrate the effectiveness of the proposed criterion.