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p = 10p = 30p = 60p = 90
VOL. 83, No. 2148
SPECIAL ARTICLESTHE BAR "GENE" A DUPLICATION
THE nature of the Bar gene has been the subject ofextensive investigation and speculation since February,1913, when Tice' found this reduced-eye mutant as asingle male in the progeny of normal-eyed parents.The eye-reduction behaves as a sex-linked dominant,with a locus at 57.0, and has been one of the most im-portant of all the sex-linked characters of D. melano-gaster. A remarkable peculiarity of the mutant is thatoccasionally the homozygous stock gives rise to a flyindistinguishable in appearance and genetic behaviorfrom wild-type.2 More rarely the stock gives rise toan even more extreme reduction in eye-size, a typewhich was called Ultra-Bar by Zeleny,3 who found it.
Sturtevant and Morgan4 and Sturtevant5 found thatthese two-way changes were the result of a novel typeof "'unequal" crossing-over, by which the two genesoriginally present in the two parental chromosomesboth emerged in the same chromosome (Bar-double)while the other resultant chromosome was without Bar(Bar-reverted). The change from Bar to Bar-doublewas considered to be a single gene duplication, whilethe converse change, from Bar to Bar-reverted, corre-sponds to a one-gene deficiency. Since the Bar-re-verted type proved to be indistinguishable from thenormal unmutated wild-type, the gene present in Barand lost in Bar-reverted must have itself correspondto a new addition or one-gene duplication.6
Sturtevant5 found the unexpected relation that twoBar genes in the same chromosome (BB/B+) gave agreater reduction in the size of the Bar eye than didtwo Bar genes in opposite chromosomes (B/B), anintensification of action which he formulated as a"position effect." Dobzhansky7 interpreted his allelicBaroid mutant as a position effect due to the substi-tution of material at or near the Bar-locus (in thenormal X) by material translocated from the rightlimb of chromosome 2, and the reduction in the Bareye to the interaction between a gene in the X chromo-some and the duplication.A chance to clear up some of the puzzles as to the
origin and behavior of Bar was offered by the salivarychromosomes. Study of the banding in a stock of Bar(forked Bar) showed that an extra, short section ofbands is present in excess of the normal complement,forming a duplication. The insertion point of thisduplication is in the bulbous "turnip" segment, not farfrom the basal end of the X.8
1 S. C. Tice, Biol. Bull., 26: 221-51, 1914.2 H. G. May, Biol. Bull., 33: 361-95, 1917.3 C. Zeleny, Jour. Exp. Zool., 30: 293-324, 1920.4 A. H. Sturtevant and T. H. Morgan, SCIENCE, 57:
746-7, 1923.5 A. H. Sturtevant, Genetics, 10: 117-47, 1925.
The exact point of the insertion is ambiguous, for areason which will appear below. The normal X in thisregion (see revised map in Fig. 1) shows in sub-sec-
B BAR- REVERTEDCD -
16A
,e -*,-.B
C t.,BA L
NORMAL BAR- DOUBLEFIG. 1
tion 16A a heavy band, which in well-stretched chro-mosomes, or with certain fixations, is a clear doublet,usually with the halves united in a capsule, but occa-sionally completely separate. This is followed by avery faint dotted line, which can be seen only in themost favorable conditions. Next follows a fairly weakline which is distinctly "dotted" in texture, with theseparate dots loosely connected across the width of thechromosome. Next follows closely a still fainter, dif-fuse, continuous-textured doublet, with the doublenessgenerally appearing as mere broadening. The last lineof sub-section 16A is again a very faint dotted singlet.Sub-section 16B starts with a sharply discontinuousline of fairly heavy dots or vesicles and is a line veryeasy to recognize. The greatest width of the bulboussegment 16A is at the two fairly weak bands, while avery sharp change in size occurs at the transitionfrom 15F to 16A.In the Bar chromosome the condition may be de-
scribed observationally as the repetition of section16A, with the exception of the final very faint dottedline. But the whole region of this bulb has undergonechanges in the Bar chromosome as follows: the "puff"of the bulbous segment is more pronounced and itssize is increased; the banding is more discontinuous bybeing broken into blocks and vesicles, and the regu-larity of synapsis is disturbed by oblique junctions.Thus, in Bar the heavy doublet following the last faintdotted line of 15F is more segmented than normal andmore rarely shows its doubleness clearly. This ten-dency is more pronounced in the heavy broken line of
6 S. Wright, Amer. Nat., 63: 479-80, 1929.7 Th. Dobzhansky, Genetics, 17: 369-92, 1932.8 C. B. Bridges, Jour. Hered., 26: 60-4, 1935.
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Usually around 16 mutations per generation are performed.This provides a trade off between generation time and variety.With increased computation (or more patience) larger populationscan be created. The screen size also limits the number ofphenotypes that can be displayed an manipulated. The parentphenotype is displayed in the upper left-hand corner of the screenfollowed by its mutated children (figure 3).
At the conclusion of the mutation and generation process, theuser may interactively manipulate and examine the phenotypes inspace and over time. At some stage the user decides whichphenotype is the most suitable and this becomes the new parent.Selecting the existing parent provides more mutations if none ofthe current generation are deemed suitable. At any time thegenotype (rule set) for a particular phenotype may be saved to diskas a ASCII file. This file can be latter used as a parent for furthermutations or generated with a higher degree of accuracy for finaloutput.
The mutation/generation/selection process is repeated until asatisfactory form is achieved or the user runs out of time orpatience.
Figure 3: Parent (top left) and 14 mutations
5. IMPLEMENTATION
The system has been implemented in the C programminglanguage, on Silicon Graphics workstations under the IRIX
operating system. The workstations high speed graphicsperformance permits real time previewing interpreted strings.Since models evolve over time this is previewed as well. A displaysub-system accepts graphics primitives on an object time basis.While the models are defined continuously over time they areusually sampled at regular discrete moments in time for playback.For the case of video animation this is either 25 times per secondfor frame rendered animation or 50 times per second for fieldrendered animations.
The generation of several seconds of animation for 16 or morephenotypes can be quite time consuming and thus for previewpurposes the samples are taken at wider intervals. For complexgeometries, simplified representations of complex surfaces can besubstituted to increase display speed.
Once generated, the models are stored in the workstationsgraphics memory as display lists. This enables to user to examinethe generated models from any position or angle, play thedevelopment either forward or backward. Once the most suitablephenotype is picked the display lists are cleared and a new set ofphenotypes are created. At any time the user can save the L-system rules for a particular resultant phenotype to a humanreadable file. This can be used to regenerate the model at a lattertime or as a genotype for further mutation and evolution work.
Even simple rules can evolve highly complex models whichcan not be displayed in real time by the workstation graphicshardware. An option exists to save geometry to disk for renderingby the Advanced Visualizer system. Advanced Visualizer is ananimation and rendering package from Wavefront Technologies[21]. The software rendering of these models has a number ofadvantages over the simplistic real time display of the workstationhardware. It allows advanced shading and illumination models(such as ray-tracing), texture, bump and transparency mapping andas well as anti-aliasing and spectral sampled colour spacedefinition. This extra quality comes at a price, however, asrendering of even a single frame can take 20-30 minutes or more(including model generation time). Integrating with the animationsystem was a key goal in development and the system takesadvantage of the features of a powerful existing animation andrendering system.
To date the system has been used to produce a variety ofsuccessful works, both still and animated [22, 23, 24]. Figure 4shows some of the results achieved with the system. Theemphases on the system has been one of a sculptural tool formodelling and observing growth, form and behaviour.
Gen. 2
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113
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Fig. 6. Fitness function with component weights of: a = 100, b = 90, c = 40, d = 20, e = 30.
Finally, structures that resemble animals were also obtained with a fitness func- tion favoring bilateral symmetric organisms (Fig. 7).
Fig. 7. Organisms obtained with fitness function favoring bilateral symmetric structures.
4. Discussion
A model has been described that can generate complex 2D branching structures without requiring cumbersome user specifications, design efforts, or knowledge of algorithmic details. We argue that L-Systems constitute an adequate genetic repre- sentation for studies which simulate natural morphological evolution. They allow the necessary, and very convenient, distinction between genotype and phenotype, and provide a well-defined process (morphogenesis) to generate the latter from the former. Moreover, they satisfy most of the important properties identified by Jeffer- son et al. (1991) for genetic encodings in biologically motivated studies. Among them: (a) L-systems provide a simple, uniform model of computation, because deri- vation and turtle interpretation of strings constitute a well defined way to go from genotypes to phenotypes; (b) they are syntactically closed under the designed ge- netic operations; and (c) they are well conditioned under genetic operators. This last requirement is not formally defined. Essentially, it requires that "small" mutational changes should (usually) cause "small" phenotypic changes, and that crossover usually produces offspring whose phenotypes are in some sense a "mixture" of the parents' phenotypes, with occasional jumps and discontinuities.
The model has employed the simplest type of L-systems (DOL-systems). Further studies may be done using complex ones, considering, for example, genotypes with several rules, context sensitive L-systems, and inclusion of 3D morphologies
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