Proceedings of the Third International Conference on Invasive ...

Chapter 2: Spartina Distribution and Spread<strong>Proceedings</strong> <strong>of</strong> <strong>the</strong> <strong>Third</strong> <strong>International</strong> <strong>Conference</strong> on Invasive SpartinaFig. 2 (a) The distribution <strong>of</strong> gamete genotypes as a function <strong>of</strong> parental genotypes. The broad distribution <strong>of</strong> hybrid genotypes reflects <strong>the</strong> higher geneticdiversity <strong>of</strong> <strong>the</strong> hybrids compared with <strong>the</strong> pure lineages. (b) Functional form <strong>of</strong> <strong>the</strong> genotype-dependent (bold line) and genotype-independent (dashed line)trait values (growth rate, seedling survival or pollen production).outlined in Hall et al. 2006. In order to elucidate <strong>the</strong> role <strong>of</strong>genetic recombination in driving this invasion, we makeseveral simplifying assumptions about <strong>the</strong> populationdynamics. Specifically, we assume spatial andenvironmental homogeneity, and focus on <strong>the</strong> spread <strong>of</strong>plants into open mudflat (i.e., we ignore density-dependenteffects such as crowding). In <strong>the</strong> spirit <strong>of</strong> many quantitativegenetics models (e.g., Bulmer 1980), we assume that a largenumber <strong>of</strong> loci interact independently and additively todetermine phenotypic fitness, and ignore <strong>the</strong> effects <strong>of</strong>environment on phenotype.Plants are classified by <strong>the</strong>ir genotype value, x, scaledsuch that pure S. foliosa has genotypes clustered around x=-1, pure S. alterniflora around x=+1, with hybrids spanning<strong>the</strong> intermediate range <strong>of</strong> genotype values. Plants <strong>of</strong>genotype x produce gametes whose genotype is drawn froma Normal distribution with mean x/2. The variance <strong>of</strong> thisdistribution is genotype-specific, under <strong>the</strong> assumption thathybrids can produce genetically more diverse <strong>of</strong>fspring thanei<strong>the</strong>r parental lineage (Fig. 2a). When pollen <strong>of</strong> genotype ysuccessfully combines with an ovule <strong>of</strong> type z, <strong>the</strong> resultingseed has genotype y+z.The population-level model is formulated in terms <strong>of</strong><strong>the</strong> total area occupied by plants <strong>of</strong> genotype x in year t,denoted P t (x). The area occupied by plants in year t+1 isgiven by <strong>the</strong> sum <strong>of</strong> vegetative growth <strong>of</strong> adult plants in yeart and <strong>the</strong> area occupied by new seedlings. Ma<strong>the</strong>maticallythis is expressed byP t+1 (x)=G(x) P t (x)+S(x) N t (x),where G(x) is <strong>the</strong> (genotype-dependent) vegetative growthrate, S(x) is <strong>the</strong> survival <strong>of</strong> seedlings <strong>of</strong> genotype x, and N t (x)is <strong>the</strong> total number <strong>of</strong> seeds produced in year t <strong>of</strong> type x. Thenumber <strong>of</strong> seeds produced <strong>of</strong> type x is <strong>the</strong> product <strong>of</strong> <strong>the</strong>frequency <strong>of</strong> pollen produced by male parents <strong>of</strong> genotype y(proportional to <strong>the</strong> genotype-specific pollen production rateM), <strong>the</strong> number <strong>of</strong> ovules from female parents <strong>of</strong> genotype z,and <strong>the</strong> probability that pollen <strong>of</strong> type y and ovules <strong>of</strong> type zcombine to produce a seed <strong>of</strong> type x, summed over allpossible genotype values <strong>of</strong> <strong>the</strong> male and female parents.The above model is used to test <strong>the</strong> effects <strong>of</strong> elevatedhybrid growth rate, seedling survival and pollen production(G, S and M respectively) on <strong>the</strong> total area occupied bySpartina <strong>of</strong> all genotypes, and <strong>the</strong> frequency <strong>of</strong> hybridgenotypes in <strong>the</strong> population. For comparison, <strong>the</strong> model isalso run under a null scenario whereby all genotypes areequally fit. The functional dependence <strong>of</strong> an elevated traitvalue on a plant’s genotype is depicted in Fig. 2b. Twolevels <strong>of</strong> seedling recruitment are also considered: low (asmight be expected at a site subject to strong tidal action) andhigh (e.g. in a sheltered inlet or marsh restoration site).RESULTSWhen <strong>the</strong> model is run under <strong>the</strong> assumption that allSpartina genotypes are equally fit, <strong>the</strong> population does notundergo super-exponential growth. However, even in <strong>the</strong>absence <strong>of</strong> any fitness advantage to <strong>the</strong> hybrid, <strong>the</strong> frequency<strong>of</strong> pure S. foliosa plants in <strong>the</strong> population suffers a slowdecline, suggesting that given sufficiently long time, <strong>the</strong>hybrid swarm could dominate.If <strong>the</strong> baseline level <strong>of</strong> seedling recruitment is low, anelevated vegetative growth rate <strong>of</strong> hybrids can produce <strong>the</strong>observed faster-than-exponential population growth.Elevated seedling survival <strong>of</strong> hybrids also results in superexponentialgrowth, but at a much less dramatic rate.Conversely, in regions where seedling recruitment is high,elevated hybrid seedling survival produces faster population- 118 -