Abstract
The ability of the animal to cope with environmental changes may be measured by log-transformed variance of deviations from expected weights (LnVar). We calculate LnVar by fitting the expected individual growth curve based on longitudinal weights (LnVarind) of Nile tilapia that were grown in either an aerated or a non-aerated freshwater pond. We estimated genetic parameters for LnVarind in Nile tilapia, the genetic correlation between LnVarind and growth and the genetic correlation for LnVarind between aerated and non-aerated pond. The heritability estimate for LnVarind (0.28) in the non-aerated pond was higher than in aerated pond (0.06). In the aerated pond, genetic correlations of LnVarind were − 0.44 ± 0.23 with daily growth coefficient (DGC) and − 0.45 ± 0.24 with harvest weight (W5). In the non-aerated pond, genetic correlations with DGC and W5 were − 0.68 ± 0.12 and − 0.52 ± 0.17, respectively. These values suggest that selection for fish with high growth rate will reduce LnVarind. However, genetic correlation of LnVarind between aerated and non-aerated pond was 0.50, suggesting that genetic improvement in the aerated environment will reduce LnVarind in the non-aerated environment. Therefore, incorporating records from relatives in non-aerated pond is beneficial for breeding programs targeting this environment.
Keywords: Variance of deviation of individual growth, Resilience, Nile tilapia, Heritability, Genetic improvement
Subject terms: Genetics, Animal breeding
Introduction
All animals, including fish, respond to environment disturbances with changes in behaviour and increased levels of stress hormones, such as cortisol and adrenalin1–3. Stress, either acute or chronic, affects feed intake, digestion, and ultimately growth4–6. However, the magnitude of these responses can vary significantly between individuals. This has led to the idea that individual deviations in growth over time could be used as an indicator for sensitivity to stressful conditions. Resilience is then defined as the ability of the animal to cope with environmental perturbations or to rapidly return to the condition it had before exposure to a disturbance7–10. Resilience is also seen as the ability to have consistent performance throughout time. Animals that show consistent performance are expected to be less affected by environmental perturbations than animals with less consistent production. Therefore, resilience indicators can be based on observed production variations even though the causes of these variations are unknown9,10. Resilience, expressed as the consistency in growth, can be measured from the deviations of actual weight from the expected weight in longitudinal measurements7,11. Several indicators to measure resilience from the deviation of actual weight have been proposed10. Of these, 
is the most promising based on its moderate heritability and ease of calculation from longitudinal records12–14.
Ideally, the reference used to calculate individual deviations would be as close as possible to the trajectory that a fish would have realized in the absence of disturbances. Therefore, it is important to estimate a reference or expected performance that is independent of environmental conditions. A previous study by Mengistu, et al.14 measured fish response to the disturbance using 
, calculated based on individual deviations from the mean weight of the fish cohort (
). However, the changes in the mean weight of the fish cohort are also dependent on environmental conditions across various time points. Consequently, the response of individual fish to the disturbance, calculated based on the mean weight of the fish cohort, is relative to the response of the group or cohort to environmental changes. An alternative approach is to fit an expected growth curve from longitudinal measurement of fish weights. Growth curves can be fitted using weight and age in calendar days or temperature days15. Feeding levels also affect growth rate but animals in commercial production are typically fed to satiation.
In aquaculture and fisheries, nonlinear functions to model the age–weight relation have been intensively used to describe the growth curve of different aquatic species, including the Gompertz function, von Bertalanffy growth function and Schnute function15. The application of nonlinear models for fitting growth curves was also helpful in describing the growth in Nile tilapia16. Most of these growth models are based on the metabolic growth model, assuming that growth depends on weight exponent of 2/3[17, 18]. von Bertalanffy reasoned that the area of surfaces involved in anabolism is proportional to a linear dimension squared and that the weight related to catabolism is proportional to a linear dimension cubed17,18. The weight exponent of fish can be estimated from weight data using nonlinear regression. Mayer, et al.19 and Janssen, et al.20 estimated a weight exponent of ~ 2/3 in Seabream.
In this study, we apply non-linear regression to fit individual growth curves using longitudinal weight measurements of tilapia grown in Malaysia (described in detail in Mengistu, et al.14). Tilapia were grown in an aerated and non-aerated freshwater pond and weight was measured at 5-time points during the grow-out period. The individual growth curves were then used to calculate 
(
). We hypothesize that 
measures growth resilience and therefore should be expressed more in the non-aerated environment due to high fluctuations in dissolved oxygen levels. The objectives of this study were: (1) to estimate genetic parameters of 
in Nile tilapia (Oreochromis niloticus), (2) to estimate the genetic correlation between 
and growth to explore the effects of selection for growth rate on 
and (3) to estimate the genetic correlation for 
between aerated and non-aerated pond.
Results
We estimated the weight exponent (
) to be 1.77 for the fish in this experiment. The non-linear regression coefficient (
) obtained from Eq. 1, that is equivalent to the daily growth coefficient (
) per fish showed heterogeneous variances in expected weight between time points (Supplement 1.). The estimate of the expected weight, obtained using the slope of the linear regression at the 
scale and the deviations from straight-line regression on the 
scale (calculated with Eq. 3; Fig. 1) reduces the heterogeneous variances of the deviations compared to the deviations at the observed scale (calculated with Eq. 4; Fig. 2) and reduces the bias of deviations, particularly at the initial and final time point of measurement, compared to the deviations at the 
scale (calculated with Eq. 5; Fig. 3).
Fig. 1.
Mean and standard deviation of the weight deviation from expected individual weight (gram) with non-linear regression in 
scale at stocking (
), three interval time points (
: 55, 104 and 167 days) and at harvest (
: 217 days) for all fish. The weight of each fish is plotted as a dot with the standard error limits shown by two short horizontal lines and the mean is located at the mid-point between these.
Fig. 2.
Mean and standard deviation of the observed weight deviation from expected individual weight (gram) with non-linear regression in observed 
scale at stocking (
), three interval time points (
: 55, 104 and 167 days) and at harvest (
: 217 days) for all fish. The weight of each fish is plotted as a dot with the standard error limits shown by two short horizontal lines and the mean is located at the mid-point between these.
Fig. 3.
Mean and standard deviation of the standardized weight deviation from expected individual weight (gram) with cubic root transformations at stocking (
), three interval time points (
: 55, 104 and 167 days) and at harvest (
: 217 days) for all fish. The weight of each fish is plotted as a dot with the standard error limits shown by two short horizontal lines and the mean is located at the mid-point between these.
Descriptive statistics
Descriptive statistics for 
, 
, 
and 
are shown in Table 1. There were no significant differences for the mean 
between aerated and non-aerated ponds. Mean 
, 
and 
in the aerated pond were significantly higher compared to non-aerated pond (P < 0.01). The coefficient of variation for 
in the non-aerated pond was higher compared to that for the aerated pond.
Table 1.
Descriptive statistics of harvest weight (
), daily growth coefficient (
) and log transformed variance from individual and cohort approach (
, 
).
| Aerated (N = 884) | Non-aerated (N = 800) | |||||||
|---|---|---|---|---|---|---|---|---|
| mean (sd) | min | max | CV | mean (sd) | min | max | CV | |
 (gram)* |
781.04 (265.58) | 185.7 | 1588.6 | 0.34 | 579.87 (154.60) | 135.5 | 1003.4 | 0.26 |
 (g1/1.77 /day)* |
0.16 (0.04) | 0.05 | 0.26 | 0.25 | 0.13 (0.03) | 0.05 | 0.20 | 0.23 |
 * |
1.33 (1.04) | -3.33 | 3.47 | 0.78 | 1.03 (1.26) | -3.90 | 3.53 | 1.22 |
|
-1.09 (0.98) | -5.68 | 1.35 | 0.90 | -1.23 (1.03) | -5.27 | 2.18 | 0.83 |
N = number of observations (n) in the aerated and non-aerated ponds.
* t-tests indicated that mean values were significantly different between the aerated and non-aerated pond (P < 0.001).
Genetic and phenotypic parameters
Table 2 shows the estimated genetic parameters of 
, 
, 
and 
from the aerated and non-aerated ponds. For 
and 
, the heritabilities were higher in the aerated pond than in the non-aerated pond, although the means were overlapped by the standard error limits of the other value. In the non-aerated pond, genetic variances for 
were more than four times higher than for 
, and heritability estimates two times higher. In the aerated pond the estimates were higher for 
than for 
. Heritability estimates for both 
and 
were higher in the non-aerated pond (0.28 and 0.12 respectively) compared to the aerated pond (0.06 and 0.10 respectively; Table 3).
Table 2.
Genetic variances (σ2A), phenotypic variances (σ2P), heritability (h2) of log transformed variance from cohort and individual approach (
and 
), daily growth coefficient from five weight records 
) and harvest weight (
) and their standard errors (se) in the aerated and non-aerated pond.
| Trait | Aerated | Non-aerated | ||||
|---|---|---|---|---|---|---|
| σ2A | σ2P | h2 ± se | σ2A | σ2P | h2 ± se | |
|
0.060 | 1.057 | 0.06 ± 0.03 | 0.440 | 1.563 | 0.28 ± 0.06 |
|
0.091 | 0.907 | 0.10 ± 0.05 | 0.118 | 0.988 | 0.12 ± 0.05 |
 (g1/1.77 /day) |
0.25 × 10− 03 | 0.88 × 10− 03 | 0.29 ± 0.06 | 0.12 × 10− 03 | 0.48 × 10− 03 | 0.25 ± 0.07 |
 (g) |
8444.79 | 37,274 | 0.23 ± 0.06 | 2791.11 | 15,148 | 0.18 ± 0.06 |
Table 3.
Estimated genetic (above diagonal) and phenotypic (below diagonal) correlations of log transformed variance from individual and cohort approach (
and 
), daily growth coefficient (
) and harvest weight (
) of tilapia in the aerated pond. Standard errors are in the brackets.
|
|
|
|
|
|---|---|---|---|---|
|
X |
0.46 (0.32) |
-0.44 (0.23) |
-0.45 (0.24) |
|
0.32 (0.03) |
X |
0.43 (0.24) |
0.35 (0.26) |
|
-0.29 (0.03) |
0.07 (0.04) |
X |
0.99 (0.00) |
|
-0.23 (0.03) |
0.10 (0.04) |
0.92 (0.01) |
X |
Genetic correlations
The genetic correlations between 
, 
, 
and 
in the aerated pond are shown in Table 3. In the aerated pond, the genetic correlation between 
and 
was moderate (0.46). We found moderate and positive genetic correlations between 
and both 
and 
in the aerated pond (0.43 and 0.35, respectively). In contrast, the genetic correlations between 
and 
, as well as between 
and 
were moderate and negative (-0.44 and − 0.45, respectively).
Table 4 shows the genetic correlations between 
, 
, 
and 
in the non-aerated pond. In the non-aerated pond, the genetic correlation between 
and 
was observed to be low (0.20). We estimated low genetic correlations between 
and both 
and 
in the non-aerated pond, (-0.06 and 0.01, respectively). The genetic correlations between 
and 
and those between 
and 
were moderate and negative (-0.68 and − 0.52, respectively).
Table 4.
Estimated genetic (above diagonal) and phenotypic (below diagonal) correlations of log transformed variance from individual and cohort approach (
and 
), daily growth coefficient (
) and harvest weight (
) of tilapia in the non-aerated pond. Standard errors are in the brackets.
|
|
|
|
|
|---|---|---|---|---|
|
X |
0.20 (0.24) |
-0.68 (0.12) |
-0.52 (0.17) |
|
0.03 (0.04) |
X |
-0.06 (0.26) |
0.01 (0.29) |
|
-0.42 (0.03) |
-0.01 (0.04) |
X |
0.99 (0.00) |
|
-0.33 (0.03) |
0.04 (0.04) |
0.96 (0.00) |
X |
The genetic correlations between the aerated and non-aerated pond for 
and 
were estimated from the bivariate model. The genetic variation for 
in the non-aerated pond was higher than in the aerated pond whereas the genetic variance for 
in the non-aerated pond was comparable to the aerated pond (Table 2; Fig. 4). The genetic correlation between the aerated and non-aerated pond was lower for 
(0.50 ± 0.30) than for 
(0.80 ± 0.17, Mengistu et al., 2022). Taking into account the large standard errors, this result shows that 
is genetically different in both environments with a substantial degree of genotype by environment interaction (GxE).
Fig. 4.
The individual estimated breeding values (EBV) for log transformed variance of deviations from (A) individual approach (
) and (B) cohort approach (
) between the aerated and non-aerated pond. The genetic correlations (
) with standard error are included inside the plot.
Discussion
This study investigated the resilience indicator 
when calculated using the individual growth curve as the expected growth performance (
). We aimed to improve the definition of 
to better capture the response of individual fish to environmental disturbances. In the next part, we discuss the comparison of resilience measured with 
and 
, the implications of including 
in tilapia breeding programs and the potential for further improvements to calculate 
as the indicator for resilience.
Definition of 
We calculated 
based on deviations from expected individual weights fitted from weight observations at five time points. To obtain the expected individual weights, we estimated the weight exponent from nonlinear regression of observed weight on the five fish ages. The nonlinear growth model uses regression parameters to describe the shape of the generated curve15. Our estimated growth exponent (f) of 1.77 is comparable to the growth exponent from studies by Mayer, et al.19 and Janssen, et al.20 who reported weight exponents for gilthead seabream of 1.54 and 1.63, respectively. The change in fish size between time points typically leads to the heteroscedasticity. However, the calculation of variance of the deviation from straight-line regression on the 
scale removes heteroscedasticity. Furthermore, we fitted the weight data at the 
scale to both a linear model (Model 1) and a quadratic model (Model 2) and compared these two models to investigate if the use of a straight-line regression is reasonable. Although the estimated regression coefficients between Models 1 and 2 are significantly different (P < 0.05), the slope of the quadratic term in Model 2 is very small (-0.0002), suggesting that the quadratic term may not add much explanatory power to the model.
Comparison with 
We found that the heritability estimate for 
was more than two times higher than for 
in the non-aerated pond (0.28 and 0.12, respectively). The heritability estimate of 
was also four times higher in the non-aerated pond, compared to the aerated pond (0.28 vs. 0.06), while the study by Mengistu, et al.14 showed no significant difference in the heritability for 
between non-aerated and aerated pond (0.12 ± 0.05 and 0.10 ± 0.05, respectively). These significance differences may indicate that 
more accurately captures the response of fish to environmental disturbances than 
. We measured resilience using 
based on the deviations of the observed weight from the expected weight. These deviations indicated the response of an individual to the environmental change. The expected weight as the baseline to calculate the deviation should be independent from the environmental change. 
was calculated based on the deviation from the mean weight of the fish cohort. Changes in the mean weight of the fish cohort depend on environmental conditions between time points that affect all fish in the cohort in the same manner. If the mean weight of the fish cohort changes due to the environmental effect, the response of individual fish is relative to these “group” changes. Therefore, the calculation of 
using the deviation from the mean weight of the fish cohort actually estimates the residual response, as the fish cohort response is already embedded within the mean weight of the fish cohort and is not shown in the deviation used to calculate 
.The expected individual growth curve to calculate 
is fitted from five individual weight records and therefore, produces a smoother curve compared to the mean cohort weight that exhibits more erratic behaviour between time points. The expected individual growth curve is independent of the change in environmental conditions and able to disentangle the response of fish cohort to the environmental change. Therefore, using the expected individual growth curve to calculate the deviation in calculation of 
can better capture the response of fish to environmental disturbances.
The implication of including 
in the tilapia breeding program
is moderately heritable in non-aerated pond, indicating the presence of additive genetic variance for resilience in the challenging environment. The heritability for 
in our study was higher than that reported for layer chicken (0.10 ± 0.0410) and pigs (0.11 ± 0.0321). Berghof, et al.13 calculated 
based on the deviation from the mean weight of the cohort in chicken. Gorssen, et al.21 used individual body weight records of pigs which were fitted with a Gompertz growth curve. The heritability estimates for 
are higher in non-aerated pond than the aerated pond. Non-aerated pond are typical for smallholder tilapia production systems14. We hypothesize that fish grown in non-aerated pond face significant challenges due to daily recurrent hypoxia, leading to increased expression of genetic variation in 
.
Growth remains the primary trait of interest in aquaculture production and breeding programs22,23. Understanding the genetic correlation between growth and resilience is essential for optimizing breeding programs for both growth and resilience. The expected correlation between growth and 
can be explained by resource allocation theory, where energy allocation to cope with environment disturbance may divert energy away from growth24,25, leading to decreased fish growth. However, in this study, the genetic correlations between 
and both 
and 
were found to be moderately negative in both aerated (-0.44) and non-aerated pond (-0.68) with high standard error. Here, a negative correlation is favourable for simultaneous improvement in 
and growth, while a positive correlation is unfavourable. Therefore, selecting for growth in the challenging environment can be expected to improve 
. Simultaneous selection for two traits often results in a negative correlation due to the action of pleiotropic genes, which affect both traits in the desired direction by selection and are rapidly brought toward fixation26. The Genetically Improved Farmed Tilapia (GIFT) strain tilapia used in this study had already undergone 17–18 generations selection for growth14. The observed favourable correlation between growth rate and 
suggests that long-term selection for growth has led to increase in 
.
We observed a substantial genotype by environment interaction (GxE) for 
, as indicated by the genetic correlation of 0.50 between the aerated and non-aerated pond. In non-aerated pond, a correlated response is defined as the multiplication of the genetic correlation between aerated and non-aerated pond, the ratio of genetic standard deviations between aerated and non-aerated pond, and the selection response in aerated pond. When the genetic correlation is less than one, the correlated response is smaller than the direct response, assuming that the heritabilities in the two environments are similar27. We used data from the experiment by Mengistu et al.28 to estimate the genetic correlation of 
between aerated and non-aerated ponds. This estimate was based on a genomic relationship matrix (GRM) derived from SNPs obtained through genotyping-by-sequencing (GBS). Mengistu et al.28 highlighted several limitations related to convergence problems: (1) limited sample size, (2) missingness and genotyping errors in GBS data, and (3) mass spawning and unbalanced family sizes. Therefore, refinements are needed, including the use of the complete dataset with approximately 1,000 animals per environment for estimating genotype-by-environment (GxE) interactions29,30, reducing missingness and genotyping errors in GBS data, genotyping the parents, and equalizing the number of individuals per family. However, Mengistu et al.28 also demonstrated that by clustering animals into groups based on high molecular co-ancestry, individuals with weak genomic relationships to all others could be identified.
Given the presence of GxE between the aerated and non-aerated pond for 
, it is obvious that the genetic improvement in the aerated selection environment will not be fully realized in the non-aerated production environment. If the breeding goal is to increase resilience in non-aerated production environments and selection must be conducted in an aerated nucleus, it is crucial to integrate information of own individual performance in the aerated environment with relative’s records in the non-aerated environment. This integration of information could enhance selection accuracy and the genetic gain for resilience. A study by Mulder and Bijma31 showed that incorporating performance data from the production environment in an index significantly increases genetic gain in that environment if GxE is present. However, caution should be taken due to the limitations of this study, which include the use of only one aerated and one non-aerated pond, and the possibility of a pond effect independent of aeration. Mengistu et al.28 showed that that aeration positively impacted harvest weight (26% higher in the aerated pond), improved tilapia survival rates, and resulted in a lower feed conversion ratio (FCR) in the aerated pond (1.73) compared to the non-aerated pond (2.31).
, as the indicator for resilience
measures the constancy of fish growth during the grow-out period. The constancy of fish growth can be an indicator for the fish’s response to the perturbations. As the available energy for growth at a specific moment is limited, coping with stress, including restoring homeostasis, may divert energy away from growth4,32,33 and potentially lead to growth fluctuations. Various mechanisms for coping with environment stress, such as reducing feed intake, decreasing food assimilation and increasing energy demand for maintenance processes, modify energy fluxes, all result in decreased energy proportion for growth4,5,33. A study by Folkedal, et al.34 showed that fish prioritize coping with the stressor through reduced feeding activity. Later, when the favourable conditions are restored, and food is available, fish compensate for the growth by temporarily accelerating somatic growth35. Compensatory growth is characterized by an elevated growth rate from enhanced feed intake and efficiency36. This feeding response of fish to environmental stressors, with decreasing feed intake and compensating for growth, may lead to growth fluctuation. We hypothesize that more resilient fish can maintain their feed intake during stress period and may grow more constantly and perhaps better survive environmental perturbations. However, there is limited understanding in this area and further study is needed. Selecting more resilient fish could lead to more constant growth, which plays a vital role in optimizing feeding strategies. In aquaculture practice, farmers predict feeding requirements using information on fish biomass based on the average weight of fish from periodic sampling to avoid under or overfeeding37,38. Accurately predicting growth is essential for estimating fish feeding requirement39. Optimal feeding strategies improve the feed conversion ratio (FCR), which holds considerable economic value40 and reduces environmental impact41. Gorssen, et al.21 recently showed a moderate and positive genetic and phenotypic correlation between 
and individual biological FCR in pigs (0.33). Further study is needed to estimate the genetic and phenotypic correlation between individual biological FCR and the constancy of growth measured with 
in tilapia. The assumption that selecting resilient fish could lead to more efficient growth opens the opportunity to harness the economic benefits from the genetic improvement of 
.
Further improvement to calculate 
as indicator for resilience
The effect of environmental stressors on fish metabolism is evident, but finding evidence for effects on growth is often complex5,33. Whole-animal changes such as growth represent the tertiary response of fish to perturbations, following hormonal changes and physiological adjustment, which are the primary and secondary physiological responses, respectively24. Stressor exposure may affect fish growth via various factors, including feed intake, food absorption and maintenance energy4,5,33. 
, as a resilience indicator, measures the constancy of fish growth in response to perturbations. Understanding the biological mechanisms underlying 
as a resilience indicator is crucial, as well as confirming its relationships with factors that may influence growth, such as feed intake and feed efficiency. Furthermore, improved resilience could lead to enhanced immunity and disease resistance, as these are categorized as a tertiary response to perturbations, similar to growth. Infectious diseases continue to pose a significant challenge affecting aquaculture productions23,42. In chickens, Berghof, et al.13 estimated a low genetic correlation between 
for growth and natural antibodies. However, there is limited understanding, and further research is needed to understand the relationships between 
and resilience indicators.
Less frequent records and longer intervals between measurements may be sufficient for traits like growth, which reacts more slowly to disturbances than traits measuring physiological response. Mengistu, et al.14 and our study found genetic variation in 
for growth with monthly weight measurements. Calculating 
for growth requires longitudinal records of individual fish weight. In the context of commercial breeding practices, acquiring longitudinal data has been challenging as it is expensive and requires manual handling, which itself can induce stress in fish43,44. Manual handling can cause physical disturbance and acute stress, affecting fish behaviour, welfare and growth45,46. Therefore, there is a need for low- or non-invasive tools to enable frequent measurements. Automated phenotyping offers a non-invasive solution, making longitudinal measurements per individual fish more effortless and potentially more accurate37,44. Automated phenotyping technology has been developed and applied in various aquaculture species, including salmon, catfish, tilapia and seabream47–51. The evolving technology of automated phenotyping in fish will significantly facilitate the application of 
as the resilience indicator in breeding programs for aquaculture species.
Conclusion
In conclusion, we improved the calculation of 
to better capture the response of individual fish to environmental disturbances in the fluctuating environment with 
. 
should be measured on 
scale to avoid heteroscedasticity. The exponent “f” should be estimated directly from the data. 
was found to be highly heritable in the more challenging environment and this can be exploited by selective breeding. The negative correlation between 
and growth rate implies that selection for growth may also improve 
. Whether selection for 
improves resilience and FCR remains to be tested. We recommend measuring 
through repeated weight records and based on the individual expected growth trajectories in fish breeding programs to simultaneously improve resilience and growth.
Materials and methods
The experiment was conducted in the Aquaculture Extension Centre, Department of Fisheries, Jitra, Kedah State, Malaysia. The source of the experimental fish is the Genetically Improved Farmed Tilapia (GIFT) Breeding Program that is run by WorldFish in Malaysia. The details of family production and grow-out of tilapia were described by Mengistu, et al.28. Below, we summarize family production, nursery, and grow-out of tilapia for this study.
Family production
We produced our experimental fish using the 16th generation of the GIFT strain as selected parents. We maintained the male and female breeders in separate 9 m2 hapas (3 m × 3 m) with a mesh size of 1 cm in an earthen pond for two weeks. Mating was done in four hapas (each 30 m2) suspended in a 500 m2 earthen pond. Eighteen males and 50 female breeders were stocked in each of the mating cages. In total, 72 males and 200 females were used. We conducted this mating process for 15 days. On the sixteenth day, the parents were removed, and the fry were kept in the same cages for a nursing period of 60 days.
Grow-out period
The fingerlings from each net cage were transferred into one of four aerated tanks after the 60 days nursing period and conditioned for three days before tagging. A random sample of fingerlings was anesthetized using clove oil and individually tagged using PIT (passive integrated transponder) tags. At tagging, a 1 cm2 fin clip sample was collected and PIT tag number and body weight were recorded. Equal numbers of individually tagged fingerlings from each nursery cage were randomly allocated to two earthen ponds. In total, 1570 fish were stocked in each pond with a stocking density of 3 fish/m2. The size of each of the pond was 511 m2 with a water depth of 1 to 1.2 m. To test the effect of oxygen availability on resilience in growth, we created two different environments: One of the ponds was aerated using a paddle wheel and blower to create a normoxic environment. The second pond was without aerators which resulted in natural diurnal dissolved oxygen (DO) fluctuations.
Trait measurements
Longitudinal measurement
We measured the weight of tilapia at five time-points: at stocking (
: day 1), three interval time points (
: 55, 104 and 167 days) and at harvest (
: 217 days). Fish from the non-aerated and the aerated pond were always measured on two consecutive days.
The calculation of 
needs the expected performance from which the observed deviation can be calculated. In this study we calculated 
from the individual expected growth trajectories (
). We compared 
to the calculation of 
as used by14 (hereafter cohort approach: 
). The methods differ in their approach to calculate the expected performance.
Calculation of 
was calculated from the deviations of observed weights from the expected weights of the individual at timepoints 
to 
. To obtain the expected weights we fitted an exponential curve to the observed weights:
 |
1 |
where 
is the weight of fish i at age 
, a is the intercept, 
is the slope of the non-linear regression for fish i, 
is the fish age and 
is the overall weight exponent. The growth curve exponent 
was estimated for the fish in this experiment using the nls function in R52. The non-linear regression coefficient (
) obtained from Eq. (1), is equivalent to the daily growth coefficient (
) per fish. Then, we transformed the five observed weights per fish as 
to linearize the growth curve and we estimated 
per fish as the slope of the linear regression of 
on the age of the fish at the five time points t and calculated the expected weight of individual fish at times t:
 |
2 |
where 
is the expected weight of fish i at age 
, a is the intercept, 
is the daily growth coefficient as the slope of the non-linear regression for fish i, 
is the fish age. Per fish, we then calculated the deviations (
) as:
 |
3 |
Where 
is the deviation of observed weight from expected weight of fish i at time point t, 
is the observed body weight of fish i at time point 
and 
is the expected body weight of fish i at time point 
. Next, for each fish, we calculated variance of the resulting five deviations (Var-dev) and transformed the Var-dev using the natural logarithm to obtain 
.
To investigate the effect of the heteroscedasticity for the deviations between time points, we compared the deviations that were calculated at 
scale in Eq. (3) with the deviations that were calculated at 
scale (observed) and at 
scale (Eqs. 4 and 5, respectively). The growth exponent 3 is commonly used for fitting growth curves of fish with rounded shapes that grow in volume15,53–55. The deviations (
) from 
scale were calculated as:
 |
4 |
Then, the deviations (
) from cubic scale were calculated as:
 |
5 |
Where 
is the observed body weight at 
and 
is the expected body weight at 
.
Calculation of 
The expected performance for 
is defined as the mean weight of fish that belong to the same cohort14. Fish cohort is defined as the fish belonging to the same nursery hapa, sex and grow-out pond. The details calculation for 
were described by Mengistu, et al.14. We refer to 
based on expected weights from the cohort as 
.
Genetic parameter Estimation
Records from 1686 genotyped fish were available for genetic analyses. Genomic relationship matrix was computed based on 11,293 SNPs using the calc_grm program56 with the vanraden2 option, as described in Mengistu, et al.14. Phenotypic and genetic variances of 
, 
, 
and harvest weight (
) were estimated using ASReml version 4.2 57 fitting a bivariate animal model with a genomic relationship matrix. Phenotypic (
) and genetic (
) correlations between the four traits within the aerated pond and within the non-aerated pond were estimated from bivariate linear models. We used the following animal model:
 |
6 |
where: 
is the vector of 
, 
and 
for the univariate models or two of those traits for the bivariate models; 
is overall mean; 
is fixed effect that accounts for nursery hapa effects (i = 1– 4); 
is the fixed effect of sex (j = male, female, unknown); 
is a covariate start-weight of the k-th individual (included only for estimation of harvest weight: 
); 
is random additive genetic effect of the k-th individual; 
is the random residual effect associated with an individual. We calculated the heritability as the ratio between additive genetic variance (
) and phenotypic variance (
), 
.
Genetic and residual correlations between traits in the same environment were obtained from bivariate analysis. The animal effects for bivariate model were distributed as N(0,G⊗C) with the additive genetic variance covariance matrix (C) is 
, and G is the genomic relationship matrix, 
and 
is the additive genetic variance of trait 1 and trait 2. 
is the additive genetic covariance between trait 1 and trait 2. The residuals were distributed as N(0, I⊗R) with residual variance-covariance matrix (R) is 
, where I is an identity matrix, 
(
) is the residual variance of trait 1 (trait 2), and 
is the residual covariance between trait 1 and trait 2. Genetic and phenotypic correlations among traits were calculated as the covariance divided by the product of the standard deviations of the two traits.
We estimated the genetic correlation between the same traits measured on different (related) individuals in the aerated and non-aerated ponds with the bivariate model 1. The additive genetic variance-covariance matrix is the same as the bivariate model 1 where 
is the additive genetic variance for the traits in the aerated pond, 
is the additive genetic variance for the traits in the non-aerated pond and 
is the additive genetic correlation between aerated and non-aerated ponds.
The covariances of residuals between environments was set to zero, as a fish performed in only one environment. The residual variance-covariance matrix is 
where 
is the residual variance for the trait in the aerated pond and 
is the residual variance for the trait in the non-aerated pond.
Acknowledgements
This study was made possible through support provided by Indonesia Endowment Fund for Education, Ministry of Finance Indonesia (LPDP - RI) grant number 20195221414387, by the International Fund for Agricultural Development (IFAD) and by the CGIAR Research Program on Fish Agri-Food Systems (FISH) and by the CGIAR Research Initiative on Resilient Aquatic Food Systems for Healthy People and Planet by the CGIAR Sustainable Animal and Aquatic Foods (SAAF) Science Program. Both these programs are supported by contributors to the CGIAR Trust Fund. We acknowledge WorldFish GIFT breeding team, and the Aquaculture Extension Centre, Department of Fisheries Malaysia, Jitra, Kedah state for their technical support throughout the project.
Author contributions
MHFA: Writing—Original draft preparation, Data curation, Methodology, Formal analysis, Funding acquisitionSBM: Writing— Review & Editing, Designing the experiment, Data collectionJAHB: Writing— Review & Editing, Funding acquisition, ResourcesHK: Writing—Review & Editing, Methodology, Conceptualization, Supervision, Funding acquisitionJWMB: Writing—Review & Editing, Conceptualization, Methodology, Analysis, Supervision, Funding acquisition.
Data availability
The data that has been used is confidential and can be obtained by requesting WorldFish or Animal Breeding and Genomics, Wageningen University & Research (John W.M. Bastiaansen; email: john.bastiaansen@wur.nl).
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.SchreckC. Accumulation and long-term effects of stress in fish. CABI147-15810.1079/9780851993591.0147 (2000).
- 2.Bœuf, G. & Payan, P. How should salinity influence fish growth? Comp. Biochem. Physiol. C: Toxicol. Pharmacol.130, 411–423. 10.1016/S1532-0456(01)00268-X (2001). https://doi.org:. [DOI] [PubMed] [Google Scholar]
- 3.3 Kültz, D. Physiological mechanisms used by fish to Cope with salinity stress. J. Exp. Biol.218, 1907–1914. 10.1242/jeb.118695 (2015). [DOI] [PubMed] [Google Scholar]
- 4.Wendelaar Bonga, S. E. The stress response in fish. Physiol. Rev.77, 591–625. 10.1152/physrev.1997.77.3.591 (1997). [DOI] [PubMed] [Google Scholar]
- 5.Van Weerd, J. H. & Komen, J. The effects of chronic stress on growth in fish: a critical appraisal. Comp. Biochem. Physiol. A: Mol. Integr. Physiol.120, 107–112. 10.1016/S1095-6433(98)10017-X (1998). [Google Scholar]
- 6.Silva, P. I. M. et al. Individual differences in cortisol levels and behaviour of Senegalese sole (Solea senegalensis) juveniles: evidence for coping styles. Appl. Anim. Behav. Sci.124, 75–81. 10.1016/j.applanim.2010.01.008 (2010). [Google Scholar]
- 7.Colditz, I. G. & Hine, B. C. Resilience in farm animals: biology, management, breeding and implications for animal welfare. Anim. Prod. Sci.56, 1961–1983. 10.1071/AN15297 (2016). [Google Scholar]
- 8.Mulder, H. A. & Rashidi, H. Selection on resilience improves disease resistance and tolerance to infections1. J. Anim. Sci.95, 3346–3358. 10.2527/jas.2017.1479 (2017). [DOI] [PubMed] [Google Scholar]
- 9.Scheffer, M. et al. Quantifying resilience of humans and other animals. Proceedings of the National Academy of Sciences 115, 11883–11890 (2018). 10.1073/pnas.1810630115 [DOI] [PMC free article] [PubMed]
- 10.Berghof, T., Poppe, M. & Mulder, H. A. Opportunities to improve resilience in animal breeding programs. Front. Genet.910.3389/fgene.2018.00692 (2019). [DOI] [PMC free article] [PubMed]
- 11.Friggens, N. C., Blanc, F., Berry, D. P., Puillet, L. & Review Deciphering animal robustness. A synthesis to facilitate its use in livestock breeding and management. Animal11, 2237–2251. 10.1017/s175173111700088x (2017). [DOI] [PubMed] [Google Scholar]
- 12.Elgersma, G. G., de Jong, G., van der Linde, R. & Mulder, H. A. Fluctuations in milk yield are heritable and can be used as a resilience indicator to breed healthy cows. J. Dairy. Sci.101, 1240–1250. 10.3168/jds.2017-13270 (2018). [DOI] [PubMed] [Google Scholar]
- 13.Berghof, T., Bovenhuis, H. & Mulder, H. A. Body weight deviations as Indicator for resilience in layer chickens. Front. Genet.1010.3389/fgene.2019.01216 (2019). [DOI] [PMC free article] [PubMed]
- 14.Mengistu, S. B. et al. Fluctuations in growth are heritable and a potential indicator of resilience in nile tilapia (Oreochromis niloticus). Aquaculture560, 738481. 10.1016/j.aquaculture.2022.738481 (2022). [Google Scholar]
- 15.Lugert, V., Thaller, G., Tetens, J., Schulz, C. & Krieter, J. A review on fish growth calculation: multiple functions in fish production and their specific application. Reviews Aquaculture. 8, 30–42. 10.1111/raq.12071 (2016). [Google Scholar]
- 16.Oliveira Zardin, A. M. et al. Growth curves by Gompertz nonlinear regression model for male and female nile tilapias from different genetic groups. Aquaculture511, 734243. 10.1016/j.aquaculture.2019.734243 (2019). [Google Scholar]
- 17.von Bertalanffy, L. A quantitative theory of organic growth (Inquiries on growth laws. II). Hum. Biol.10, 181–213 (1938). [Google Scholar]
- 18.Taylor, C. C. Growth equations with metabolic parameters. ICES J. Mar. Sci.27, 270–286. 10.1093/icesjms/27.3.270 (1962). [Google Scholar]
- 19.Mayer, P., Estruch, V. D. & Jover, M. A two-stage growth model for Gilthead sea Bream (Sparus aurata) based on the thermal growth coefficient. Aquaculture358–359, 6–13. 10.1016/j.aquaculture.2012.06.016 (2012). [Google Scholar]
- 20.Janssen, K., Berentsen, P., Besson, M. & Komen, H. Derivation of economic values for production traits in aquaculture species. Genet. Selection Evol.49, 5. 10.1186/s12711-016-0278-x (2017). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 21.Gorssen, W. et al. A promising resilience parameter for breeding: the use of weight and feed trajectories in growing pigs. J. Anim. Sci. Biotechnol.14, 101. 10.1186/s40104-023-00901-9 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 22.Chavanne, H. et al. A comprehensive survey on selective breeding programs and seed market in the European aquaculture fish industry. Aquacult. Int.24, 1287–1307. 10.1007/s10499-016-9985-0 (2016). [Google Scholar]
- 23.Houston, R. D., Kriaridou, C. & Robledo, D. Animal board invited review: Widespread adoption of genetic technologies is key to sustainable expansion of global aquaculture. animal 16, 100642 (2022). 10.1016/j.animal.2022.100642 [DOI] [PMC free article] [PubMed]
- 24.Barton, B. A. Stress in fishes: A diversity of responses with particular reference to changes in Circulating Corticosteroids1. Integr. Comp. Biol.42, 517–525. 10.1093/icb/42.3.517 (2002). [DOI] [PubMed] [Google Scholar]
- 25.Guderley, H. & Pörtner, H. O. Metabolic power budgeting and adaptive strategies in zoology: examples from scallops and fishthe present review is one of a series of occasional review articles that have been invited by the editors and will feature the broad range of disciplines and expertise represented in our editorial advisory board. Can. J. Zool.88, 753–763. 10.1139/z10-039 (2010). [Google Scholar]
- 26.Falconer, D. S. Introduction to Quantitative GeneticsPearson Education,. (1996).
- 27.Falconer, D. S. Selection in different environments: effects on environmental sensitivity (reaction norm) and on mean performance. Genet. Res.56, 57–70. 10.1017/S0016672300028883 (1990). [Google Scholar]
- 28.Mengistu, S. B. et al. Genotype by environment interaction between aerated and non-aerated ponds and the impact of aeration on genetic parameters in nile tilapia (Oreochromis niloticus). Aquaculture529, 735704. 10.1016/j.aquaculture.2020.735704 (2020). [Google Scholar]
- 29.Sae-Lim, P., Komen, H. & Kause, A. Bias and precision of estimates of genotype-by-environment interaction: A simulation study. Aquaculture310, 66–73. 10.1016/j.aquaculture.2010.10.020 (2010). https://doi.org:. [Google Scholar]
- 30.Lozano-Jaramillo, M., Komen, H., Wientjes, Y. C. J., Mulder, H. A. & Bastiaansen, J. W. M. Optimizing design to estimate genetic correlations between environments with common environmental effects. J. Anim. Sci.9810.1093/jas/skaa034 (2020). [DOI] [PMC free article] [PubMed]
- 31.Mulder, H. A. & Bijma, P. Effects of genotype X environment interaction on genetic gain in breeding programs. J. Anim. Sci.83, 49–61. 10.2527/2005.83149x (2005). [DOI] [PubMed] [Google Scholar]
- 32.Wieser, W., Krumschnabel, G. & Ojwang-Okwor, J. P. The energetics of starvation and growth after refeeding in juveniles of three cyprinid species. Environ. Biol. Fish.33, 63–71. 10.1007/BF00002554 (1992). [Google Scholar]
- 33.33 Sadoul, B. & Vijayan, M. M. in In Fish Physiology. Vol. 35, 167–205 (eds Schreck, C. B., Tort, L., Farrell, A. P. & Brauner, C. J.) (Academic, 2016).
- 34.Folkedal, O. et al. Food anticipatory behaviour as an indicator of stress response and recovery in Atlantic salmon post-smolt after exposure to acute temperature fluctuation. Physiol. Behav.105, 350–356. 10.1016/j.physbeh.2011.08.008 (2012). [DOI] [PubMed] [Google Scholar]
- 35.Ali, M., Nicieza, A. & Wootton, R. J. Compensatory growth in fishes: a response to growth depression. Fish Fish.4, 147–190. 10.1046/j.1467-2979.2003.00120.x (2003). https://doi.org:. [Google Scholar]
- 36.Won, E. & Borski, R. Endocrine regulation of compensatory growth in fish. Front. Endocrinol.410.3389/fendo.2013.00074 (2013). [DOI] [PMC free article] [PubMed]
- 37.Li, D., Hao, Y. & Duan, Y. Nonintrusive methods for biomass Estimation in aquaculture with emphasis on fish: a review. Reviews Aquaculture. 12, 1390–1411. 10.1111/raq.12388 (2020). [Google Scholar]
- 38.Rodríguez-Sánchez, V., Rodríguez-Ruiz, A., Pérez-Arjona, I. & Encina-Encina, L. Horizontal target strength-size conversion equations for sea bass and gilt-head Bream. Aquaculture490, 178–184. 10.1016/j.aquaculture.2018.02.034 (2018). [Google Scholar]
- 39.Bureau, D., Hua, K. & Azevedo, P. 547–567 (2008).
- 40.Omasaki, S. K., Janssen, K., Besson, M. & Komen, H. Economic values of growth rate, feed intake, feed conversion ratio, mortality and uniformity for nile tilapia. Aquaculture481, 124–132. 10.1016/j.aquaculture.2017.04.013 (2017). [Google Scholar]
- 41.Besson, M. et al. Environmental impacts of genetic improvement of growth rate and feed conversion ratio in fish farming under rearing density and nitrogen output limitations. J. Clean. Prod.116, 100–109. 10.1016/j.jclepro.2015.12.084 (2016). [Google Scholar]
- 42.Naylor, R. L. et al. A 20-year retrospective review of global aquaculture. Nature591, 551–563. 10.1038/s41586-021-03308-6 (2021). [DOI] [PubMed] [Google Scholar]
- 43.Iversen, M., Finstad, B., McKinley, R. S. & Eliassen, R. A. The efficacy of metomidate, clove oil, Aqui-S™ and Benzoak® as anaesthetics in Atlantic salmon (Salmo Salar L.) Smolts, and their potential stress-reducing capacity. Aquaculture221, 549–566. 10.1016/s0044-8486(03)00111-x (2003). [Google Scholar]
- 44.Fu, G. & Yuna, Y. Phenotyping and phenomics in aquaculture breeding. Aquaculture Fisheries. 7, 140–146. 10.1016/j.aaf.2021.07.001 (2022). [Google Scholar]
- 45.Pickering, A. D., Pottinger, T. G. & Christie, P. Recovery of the brown trout, Salmo trutta L., from acute handling stress: a time-course study. J. Fish Biol.20, 229–244. 10.1111/j.1095-8649.1982.tb03923.x (1982). [Google Scholar]
- 46.Ashley, P. J. Fish welfare: current issues in aquaculture. Appl. Anim. Behav. Sci.104, 199–235. 10.1016/j.applanim.2006.09.001 (2007). [Google Scholar]
- 47.Sanchez, G., Ceballos Arroyo, A. & Robles-Serrano, S. Automatic measurement of fish weight and size by processing underwater hatchery images. Eng. Lett.26, 461–472 (2018). [Google Scholar]
- 48.Fernandes, A. F. A. et al. Deep learning image segmentation for extraction of fish body measurements and prediction of body weight and carcass traits in nile tilapia. Comput. Electron. Agric.170, 105274. 10.1016/j.compag.2020.105274 (2020). [Google Scholar]
- 49.Gümüş, E., Yılayaz, A., Kanyılmaz, M., Gümüş, B. & Balaban, M. Evaluation of body weight and color of cultured European catfish (Silurus glanis) and African catfish (Clarias gariepinus) using image analysis. Aquacult. Eng.93, 102147. 10.1016/j.aquaeng.2021.102147 (2021). [Google Scholar]
- 50.Tuckey, N. P. L. et al. Automated image analysis as a tool to measure individualised growth and population structure in Chinook salmon (Oncorhynchus tshawytscha). Aquaculture Fish. Fisheries. 2, 402–413. 10.1002/aff2.66 (2022). [Google Scholar]
- 51.Xue, Y., Bastiaansen, J. W. M., Khan, H. A. & Komen, H. An analytical framework to predict slaughter traits from images in fish. Aquaculture566, 739175. 10.1016/j.aquaculture.2022.739175 (2023). [Google Scholar]
- 52.RStudio. Integrated Development for R (RStudio, Inc, 2022).
- 53.Iwama, G. K. & Tautz, A. F. A simple growth model for salmonids in hatcheries. Can. J. Fish. Aquat. Sci.38, 649–656. 10.1139/f81-087 (1981). [Google Scholar]
- 54.Bureau, D., Azevedo, P., Tapia-Salazar, M. & Cuzon, G. Pattern and cost of growth and nutrient deposition in fish and shrimp: Potential implications and applications. Avances en Nutrición Acuícola V. Memorias del V Simposium Internacional de Nutrición Acuícola (2000).
- 55.Jobling, M. The thermal growth coefficient (TGC) model of fish growth: a cautionary note. Aquac. Res.34, 581–584. 10.1046/j.1365-2109.2003.00859.x (2003). [Google Scholar]
- 56.Calus, M. & Vandenplas, J. Calc_grm—a program to compute pedigree, genomic, and combined relationship matrices. ABGC Wageningen UR Livest. Res. (2016).
- 57.Gilmour, A. R., Gogel, B. J., Cullis, B. R. & Welham, S. J. T. R. ASReml User Guide Release 4.1 Functional Specification (VSN International Ltd, 2015).
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The data that has been used is confidential and can be obtained by requesting WorldFish or Animal Breeding and Genomics, Wageningen University & Research (John W.M. Bastiaansen; email: john.bastiaansen@wur.nl).