Estimates for heritability and consumer-validation of a penetrometer method for phenotyping softness of cooked cassava roots

Although breeders have made significant progress in the genetic improvement of cassava ( Manihot esculenta Crantz) for agronomic traits, lack of information on heritability and limited testing of high-throughput phenotyping methods are major limitations to improving root quality traits, such as softness after cooking, which rank high among Ugandan consumers. The objectives of this study were to determine heritability for softness of cooked cassava roots, and quantify the relationship between penetrometer and consumer testing methods for phenotyping softness of cassava roots. Softness defined as the maximum force (N) needed to penetrate cooked root samples using a penetrometer, was evaluated at four cooking time intervals: 15, 30, 45, and 60 min on 268 cassava genotypes. Estimates of broad-sense heritability (repeatability) ranged from 0.17 to 0.37, with the highest value observed at 45 min of cooking time interval. In the second study involving 135 cassava consumers from Kibaale district in Uganda, penetrometer measurements of cooked roots from six cassava varieties were found to be in strong agreement (r2 = 0.91; P-value = 0.003) with ordinal scores of root softness from consumer testing. These results suggest that: (a) softness of cooked cassava roots is a trait amenable for evaluation and selection; and (b) a penetrometer can readily be used for assessment of cooked root softness. These findings form the basis for operationalising the routine assessment of root softness in cassava breeding trials, an output that will enhance ongoing efforts to breed for desired end-user root quality traits.Les s\ue9lectionneurs ont fait des progr\ue8s consid\ue9rables dans l\u2019am\ue9lioration g\ue9n\ue9tique des caract\ue8res agronomiques du manioc ( Manihot esculenta Crantz). Cependant un manque de m\ue9thodes de ph\ue9notypage haut-d\ue9bit adapt\ue9es aux caract\ue8res de qualit\ue9s tel que la fermet\ue9 de la racine apr\ue8s cuisson, essentiel pour les consommateurs Ougandais. Cette \ue9tude ambitionne a) de determiner l\u2019h\ue9ritabilit\ue9 de la fermete de racine cuite b) de quantifier la relation entre l \ue9valuation de la fermet\ue9 de racine cuite au p\ue9n\ue9trom\ue8tre et un panel consommateurs. Cette \ue9valuation a \ue9t\ue9 realisee a quatre intervals de temps: 15, 30, 45 et 60 minutes sur 268 genotypes de manioc. Pour d\ue9finir l\u2019h\ue9ritabilit\ue9 de la fermet\ue9 de la racine, celle ci a \ue9t\ue9 d\ue9finie par la force maximum (N) n\ue9cessaire pour p\ue9n\ue9trer des \ue9chantillons de racines incluant diff\ue8rent temps de cuisson (15, 30, 45, and 60 min) a l\u2019aide d\u2019un p\ue9n\ue9trom\ue8tre. L\u2019h\ue9ritabilit\ue9 au sens large (ou r\ue9p\ue9tabilit\ue9) observ\ue9e varie de 0.17 a 0.37, la valeur la plus \ue9lev\ue9 \ue9tant observ\ue9e pour un temps de cuisson de 45 minutes. Dans une seconde \ue9tude impliquant 135 consommateurs du district de Kibaale (Ouest de l\u2019Ouganda), les mesures au p\ue9n\ue9trom\ue8tre de racines cuites de six vari\ue9t\ue9s ont confirm\ue9es la forte correlation (r2 = 0.91; P-value = 0.003) avec les valeurs ordinales de fermet\ue9 de racine du panel consommateur. Les r\ue9sultats de cette \ue9tude indiquent que cette m\ue9thodologie de ph\ue9notypage est a) utile pour l\u2019 \ue9valuation de la fermet\ue9 sur des racines cuites en selection et b) d\ue9montre que l\u2019usage du p\ue9n\ue9trom\ue8tre est efficace pour celle ci. Ces r\ue9sultats offrent aux s\ue9lectionneurs une methode d\u2019 \ue9valuation de routine de la qualite de racine pour les essais experimentaux. Ceux ci contribueront aux efforts actuels pour l\u2019am\ue9lioration des caract\ue8res qualit\ue9s chers aux consommateurs

Glauber Dynamics for the mean-field Potts Model

We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\beta_s(q)$ strictly lower than the critical $\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\beta<\beta_s(q)$ the mixing time is asymptotically $C(\beta, q) n \log n$ and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order $n$. At $\beta=\beta_s(q)$ the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order $n^{4/3}$. For $\beta>\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\beta \uparrow \beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\beta_s$. These results form the first complete analysis of mixing around the critical dynamical temperature --- including the critical power law --- for a model with a first order phase transition.Comment: 45 pages, 5 figure