ESM 2 Simulations with reduced heritability
We tested the robustness of our simulation results with assumptions of reduced heritability.
While high heritability value in a trait implies that most of the phenotypic variation is explained by genetic variation, it is not a measure of the proportion of the phenotype transmitted to the next generation, does not imply that environmental variation is small and is not an estimate of genetic determination (Visscher et al. 2008). Carlson and Seamons (2008) provide a meta-analysis of trait heritability for salmonids. Funk et al. (2005) estimated heritability of size at age 1 as the regression slope of mid-parent value and mean offspring value and found a value of about 0.4.
To model less than perfect heritability we adapted the method of Dunlop et al. (2008) and Enberg et al. (2009) for eco-genetics models, despite relevant differences in the modeling of body growth and the inclusion of both males and females in the models presented by Dunlop et al. (2008) and Enberg et al. (2009).
We introduce stochasticity in the correlation between genotypes and selection pressures to broadly represent different processes, as:
- inheritance of trait;
- phenotypic expression of trait.
We thus have two additional parameters:
- t, which is added to f and represents stochasticity due to mutation-segregation-recombination processes. t is randomly drawn from N(m=0,sd=0.05). The growth parameter of the offspring fo now depends on the growth parameter of the parent (female) fp and the parameter t:
- e, which represents stochasticity due to gene expression. e is derived once for an individual and kept for all life. e is randomly derived from N(1,sd(expr)) once for an individual and kept for all life. e is multiplied by f.
For a an individual of age a, length growth rate f and density of marble trout ≥ age-1 during its first year of life (DU), strength of density-dependence g and expression noise e, length-at-age is:
The expression stochasticity does not influence mortality. We chose the parameter sd(expr) following a pattern-oriented modeling strategy (Grimm et al. 2005). We performed simulations using the individual-based model of population dynamics by varying sd(expr) and looking for values of heritability of growth at age 1 in the range 0.2-0.4. We estimated heritability using the slope of parent-offspring relationship (Fig.1).
Fig.1 Relationship between female length at age 1 and mean length of progeny at age 1.
We simulated the population dynamics of marble trout with sd(expr) = 0.2.
In case of reduced heritability, some of the metrics used lose their meaning. For example, since new f values (i.e., not present in the population at time t) are continually generated (and thus present at time t+1), f almost never has quasi-stable distribution (fqs), as defined in the manuscript. Therefore we chose to stop simulations after 700 years. Bi- and uni-modality were difficult to estimate and to interpret since new f are continually generated and thus we did not use this metric with reduced heritability.
We thus focused on mean(f), max(f), min(f) and (max (f) - min (f)) at the end of simulation time.
Here below, we report an example of replicate for each scenario (Fig. 2).
Fig.2 Selection for intrinsic growth rates in random replicates for scenarios CON, VAR and CAT.
Here, we report mean(f), max(f), min(f) and (max (f) - min (f)) for each scenario (100 replicates each).
The distribution of range of f at the end of simulation time shows that very fast growers (f à 2) can be found, albeit in low numbers, in many replicates of scenario CAT. They are less likely to be present in VAR and CON. The persistence of very slow growers was likely in CON and VAR. In all the three environments, the mean of f was located in the proximity of f = 1, but higher than 1 in scenario CAT.
The main qualitative difference with respect to the results obtained with perfect inheritance is the presence of very fast growers in the vast majority of the CAT replicates. The most likely explanation is the generation of a limited number of individuals with very fast growth due to mutation-segregation-recombination (Fig. 2).
References
Carlson SM, Seamons TR (2008) A review of quantitative genetic components of fitness in salmonids: implications for adaptation to future change. Evol Appl 1:222-238.
Dunlop ES, Heino M, Dieckmann ULF (2009) Eco-genetic modeling of contemporary life-history evolution. Ecol Appl 19:1815-1834.
Enberg K, Jørgensen C, Dunlop ES, Heino M, Dieckmann U (2009) Implications of fisheries-induced evolution for stock rebuilding and recovery. Evol Appl 2:394-414.
Funk WC, Tyburczy J a, Knudsen KL, Lindner KR, Allendorf FW (2005) Genetic basis of variation in morphological and life-history traits of a wild population of pink salmon. J Hered 96:24-31.
Grimm V, Revilla E, Berger U, Jeltsch F, Mooij WM, Railsback SF,Thulke H-H et al. (2005) Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–991.
Visscher PM, Hill WG, Wray NR (2008). Heritability in the genomics era – concepts and misconceptions. Nat Rev Genet 9:255–266.