Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization

We describe a simple experimental implementation of the Malkus-Lorenz water wheel. We demonstrate that both chaotic and periodic behavior is found as wheel parameters are changed in agreement with predictions from the Lorenz model. We furthermore show that when the measured angular velocity of our water wheel is used as an input signal to a computer model implementing the Lorenz equations, high quality chaos synchronization of the model and the water wheel is achieved. This indicates that the Lorenz equations provide a good description of the water wheel dynamics.Comment: 12 pages, 7 figures. The following article has been accepted by the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp

The Genetic Architecture of Climatic Adaptation of Tropical Cattle

<div><p>Adaptation of global food systems to climate change is essential to feed the world. Tropical cattle production, a mainstay of profitability for farmers in the developing world, is dominated by heat, lack of water, poor quality feedstuffs, parasites, and tropical diseases. In these systems European cattle suffer significant stock loss, and the cross breeding of taurine x indicine cattle is unpredictable due to the dilution of adaptation to heat and tropical diseases. We explored the genetic architecture of ten traits of tropical cattle production using genome wide association studies of 4,662 animals varying from 0% to 100% indicine. We show that nine of the ten have genetic architectures that include genes of major effect, and in one case, a single location that accounted for more than 71% of the genetic variation. One genetic region in particular had effects on parasite resistance, yearling weight, body condition score, coat colour and penile sheath score. This region, extending 20 Mb on BTA5, appeared to be under genetic selection possibly through maintenance of haplotypes by breeders. We found that the amount of genetic variation and the genetic correlations between traits did not depend upon the degree of indicine content in the animals. Climate change is expected to expand some conditions of the tropics to more temperate environments, which may impact negatively on global livestock health and production. Our results point to several important genes that have large effects on adaptation that could be introduced into more temperate cattle without detrimental effects on productivity.</p></div

Cattle genetic differences: (a) a Tropical Composite (left) and a Brahman bull (right).

<p>(b) Distribution of indicine% across the two samples showing a mode at ∼30% for Tropical Composite (red) and ∼95% for Brahman (blue) cattle. (c) Multi-dimensional scaling plot showing a clustering of the Brahman (blue) and Tropical Composite (red) cattle relative to the reference samples of Angus (black) and Nelore (green). (d) Genetic relationship matrices based on genotype similarity among individuals for Tropical Composite (left) and Brahman (right) samples where the diagonal blocks show paternal half-sib families.</p

Genetic architecture of climatic adaptive traits: (a) Heat map of the number of significant SNP (<i>P</i><0.0001) from few (blue) to many (red) across the 30 chromosomes for the ten traits in Tropical Composite and Brahman.

<p>(b) Manhattan plots of the significance (-log<i>P</i> on the y-axis) of each SNP in genome order (x-axis) for Sheath score (left panels) and Coat Colour (right panels) for Tropical Composite (upper panels) and Brahman (lower panel) cattle. Note the similarity on BTA5 for Sheath score in both samples but different genes for colour, (c) Average frequency of the forward allele for sliding windows of 100 consecutive SNP along BTA5 at 1 SNP pace for Brahman (blue) and Tropical Composite (red) cattle relative to the reference samples of Angus (black) and Nelore (green). The insert shows regions of divergent allele frequencies between taurine and indicine cattle on BTA5 from 20 to 60 Mb. (d) Heat map of LD (<i>r</i>²) on BTA5 in the Tropical Composite sample, with red dots corresponding to <i>r</i>²>0.1, showing LD blocks spanning several Mb. (e) The effect of BTA5 on Sheath score in Tropical Composite and Brahman cattle was not due to indicine% but to a major gene. 50 SNP were selected from 5 regions of BTA5 with divergent alleles in Angus and Nelore cattle. The average additive association (based on –log(<i>P</i>), y-axis) of these 50 SNP across the ten traits was calculated (green bars) and compared with the association of 50 SNP (orange bars) also with divergent alleles in Angus and Nelore cattle but randomly located to regions other than BTA5 or BTAX. A total of 10 random selections were chosen and the average plotted. (f) Genes close (< = 3 Kb) to SNP significantly associated (P<0.0001) with Sheath in both breeds.</p

Selected positional-candidate genes (P<0.01 both breeds) and its different-expression (P<0.05) in muscle before and after undernutrition period^*.

<p>*BRM – Brahman; COMP – Tropical Composite; DE – fold change in gene-expression; Ref trait – trait for which the gene was significantly associated: C – COND, Y – YWT; a – estimated SNP effect; LogP BRM and LogP COMP – -log(p-value) in Brahman and Tropical Composite. If a gene had more than one SNP associated to the trait, the SNP with lower p-value combined in both breeds was selected to represent the gene. REML estimates of genetic variance: COND BRM  = 0.175, COND COMP  = 0.110, YWT BRM 157.30, YWT COMP 348.14.</p><p>Selected positional-candidate genes (P<0.01 both breeds) and its different-expression (P<0.05) in muscle before and after undernutrition period^{<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113284#nt105" target="_blank">*</a>}.</p

Heritabilities (diagonal), genetic (top) and phenotypic (bottom) correlations.

<p>Heritabilities (diagonal), genetic (top) and phenotypic (bottom) correlations.</p

Estimated effect of indicine content (indicine%).

A<p>The observation of the empirical density having a clear mode at ∼30% of indicine% (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113284#pone-0113284-g001" target="_blank">Figure 1b</a>) encouraged the exploration of the effect of indicine content separate for each group.</p><p>Estimated effect of indicine content (indicine%).</p

Adaptation phenotypes in Brahman and Tropical Composite cattle.

<p>Summary statistics (number of records (N), mean and standard deviation (SD)), effect of percentage of indicine (indicine%), heritability estimates (h²) and associated SNP (from a total of 729,068) and false discovery rate (FDR) at P<0.001. FT flight time (sec), TEMP rectal temperature (C), EPG worm eggs per gram of faeces, SHEATH pendulousness of the penile sheath (score), COLOUR coat colour (score), FLY lesions due to biting by buffalo flies (score), TICK tick score, COAT coat score, COND body condition score, YWT yearling weight (kg). Trait definitions and measurement procedure contained in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113284#pone.0113284.s004" target="_blank">Table S1</a>.</p><p>Adaptation phenotypes in Brahman and Tropical Composite cattle.</p

Locations of the SNP explaining the largest genetic variance for each trait within each breed of cattle¹.

1<p>The estimated SNP effect is given for both breeds even though rarely a SNP explained a large proportion of the variance in both breeds. ² SNP location, chromosome:position (bp). ³ Percent of the genetic variance explained by the SNP. ⁴ P-value for the genome-wide association.</p><p>Locations of the SNP explaining the largest genetic variance for each trait within each breed of cattle^{<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113284#nt103" target="_blank">1</a>}.</p