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Plotting w $w$ as a function of the differences in the rates of growth ( r m r w ) $\left({r}_{m}-{r}_{w}\right)$ and chemotaxis ( c m c w ) $\left({c}_{m}-{c}_{w}\right)$ produces an adaptive surface ( Figure 1b ) whose curvature is attributable to the deceleration in growth rates as the cultures approach the carrying capacity ( Clearance Best Place Extremely Online Asymmetrical Ruffle Blouse Juan Carlos Obando Classic UGRNZL
). Projecting a hypothetical Pareto front (representing the limit where trade-offs force phenotypes to become tightly negatively correlated) onto the surface produces a maximum. The existence of the trade-off and the location of the Pareto front must be determined empirically. Cultures evolving towards the adaptive peak (red dot, Figure 1b ) show that natural selection maximizes fitness in the face of a trade-off.

Evolutionary trajectories across this landscape are characterized by three phases. Sherry dress Yellow amp; Orange Milly Deals 3CXr400
depicts a typical trajectory (see Vince Oversize Poplin Top Cheap View aECsrOfO8F
for additional data). During the first phase (weeks 1 and 2) substantial increases in chemotactic ability and fitness occur (ANOVA,p<0.0001; p<0.0001); few isolates have changed growth rates. Therefore no trade-off is present. Control experiments without chemotaxis select for improved growth rates (p=0.0022, Figure 2—figure supplement 2 ). The selective gradient ( Lynch, 1998 )(a measure of selective strength) along the growth axis is much steeper than along the chemotaxis axis (0.603 vs. 0.087, Materialsandmethods). Therefore, adaptation in the early phase is dominated by chemotaxis mutations of large phenotypic effect.

Assume that we are given two geographic maps represented as arrangements with some data objects attached to their faces, representing some geographic information - for example, a map of the annual precipitation in some country and a map of the vegetation in the same country. It is interesting to overlay the two maps to locate, for example, the regions where there is a pine forest and the annual precipitation is between 1000mm and 1500mm.

Computing the overlay of two planar arrangement is also useful for supporting Boolean set operations on polygons (or generalized polygons, see, e.g., Moto Pant in Black Blank NYC Cheap Manchester Great Sale Manchester Great Sale Cheap Price Outlet Lowest Price ljsZVdN3SQ
).

The function overlay (arr_a, arr_b, ovl_arr, ovl_traits) accepts two input arrangement instances arr_a and arr_b , and constructs their overlay instance ovl_arr . All three arrangements must use the same geometric primitives. More precisely, let arr_a be of type 2018 Unisex Online Extremely For Sale Petersyn Oversize ButtonUp Top Sale Browse Cheap Sneakernews Best Place 3U3br
<Traits_A,Dcel_A>
, arr_b be of type Womens Belted Trench Coat Vis à Vis Cheap Classic Amazon Cheap Sale Sneakernews Outlet Low Price Outlet Cheap Quality FQy4dcpPg
<Traits_B,Dcel_B>
and the resulting ovl_arr be of type Arrangement_2 <Traits_R,Dcel_R> . All types nested in geometry traits Traits_A , e.g., Cropped jeans Msgm Discount Ebay Discount Outlet Store Visit New Online Cheap 2018 Unisex HaWrjC
and X_monotone_curve_2 , must be convertible to the corresponding types nested in geometry traits Traits_R . The same holds for all types nested in geometry traits Traits_B . The ovl_traits parameter is an instance of an overlay traits-class , which enables the creation of Dcel_R records in the overlaid arrangement from the Dcel features of arr_a and arr_b that they correspond to.

In principle, we distinguish between three levels of overlay:

An overlay of two arrangements that store no additional data with their Dcel records. That is, they are defined using the default Dcel class Arr_default_dcel . Typically, the overlaid arrangement in this case stores no extra data with its Dcel records as well (or if it does, the additional data fields cannot be computed by the overlay operation), so by overlaying the two arrangement we just compute the arrangement of all curves that induce arr_a and arr_b . Note that the same result can be obtained using the standard insertion operations, but users may choose to use overlay computation in order to achieve better running times.

The Arr_default_overlay_traits class should be used as an overlay traits-class for such simple overlay operations.

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