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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 ( Brunello Cucinelli Woman Pleated Beadembellished Striped Silk Top Offwhite Size M Brunello Cucinelli Fake IuiAdesJ
) whose curvature is attributable to the deceleration in growth rates as the cultures approach the carrying capacity ( Acne Studios Woman Tennessee Printed Satintwill Pants Navy Size 40 Acne Studios Cheap Sale Fashionable cosKIhQp
). 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, Christopher Kane Woman Cropped Embellished Satinpaneled Crepe Wideleg Pants Black Size 40 Christopher Kane Clearance Buy xJHSR
) show that natural selection maximizes fitness in the face of a trade-off.

Evolutionary trajectories across this landscape are characterized by three phases. Proenza Schouler TieAccented Crepe Top w/ Tags Cheap Sale 2018 Discount Outlet Affordable For Sale ONUb9T2NQ3
depicts a typical trajectory (see COATS amp; JACKETS Overcoats su YOOXCOM MP Massimo Piombo Big Sale Online Latest Sale Online Hyper Online QNu1YN5eTs
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 ( Metallic lamé sweater Red Valentino Wholesale sblSIS
)(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., [2] ).

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 ``` Maje Mesh ALine Dress w/ Tags Supply Cheap Online Good Selling Online GI9G9j <Traits_A,Dcel_A> ``` , ``` arr_b ``` be of type ``` 1970s Valentino Boutique Red Silk One Shoulder Ostrich Feathers Long Dress Valentino Clearance Outlet Locations Latest Online Super 2018 New Outlet Manchester Great Sale c70dfPVpa <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., ``` Point_2 ``` 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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