Challenges of transferring models of fish abundance between coral reefs

Introduction

Understanding patterns of species’ abundance and their causes remains a central challenge to assist ecological management (Stuart-Smith et al., 2013; Atwood et al., 2015), particularly in marine ecosystems (e.g., Worm et al., 2006). Obtaining reliable abundance estimates for marine fishes can be challenging (Pauly, Hilborn & Branch, 2013) as abundances can vary rapidly and substantially through time and space (Caley et al., 1996; Rana et al., 2014). Marine surveys can also be prohibitively expensive rendering many marine systems severely under-surveyed, or when they are possible, estimates are often constrained by the efficiency of surveys (Reynolds, Thompson & Russell, 2011). This situation is exemplified on coral reefs where underwater visual censuses (UVCs) are commonly used to estimate fish abundances. The application of UVCs is constrained in space and time by the cost of field expeditions and by bottom time and depth limits for divers. These censuses do, however, have the advantage of estimating abundances directly (Halford & Thompson, 1996), including exploited (e.g., lutjanids and lethrinids) and non-exploited species (e.g., pomacentrids). They have been successfully used for estimating fish distributions and population trends in coastal ecosystems (Willis, Millar & Babcock, 2003; Stuart-Smith et al., 2013; among many others), and UVC-estimated fish abundances have served as input for predictive models aiming to estimate abundances at the scale of entire reef ecosystems using broad-scale predictors (e.g., Mellin et al., 2010).

Predictive models can assist identifying affinities of species or individuals for particular environmental conditions and thereby predict their patterns of spatial distribution. By being able to provide such information, predictive models can also help fill knowledge gaps essential for coral reef management (Fisher et al., 2011b). However, the robustness (degree of model fit) of predictive models of fish abundances can vary substantially. While relatively robust predictions of abundance have been obtained for single species (up to ∼70% deviance explained) (e.g., Young & Carr, 2015), considerably less variation has been explained for total fish abundances (∼35%) (e.g., Mellin et al., 2010) or even less for some functional groups (e.g., 16% for piscivores; Pittman, Costa & Battista, 2009).

Because abundance is an important and commonly used ecological metric, having readily available spatial predictions of fish abundances in situations where direct estimates are currently unavailable could be highly beneficial. For example, such information could be used to support stock assessments or guide the establishment of management strategies (Bejarano, Mumby & Sotheran, 2011). In the absence of predictive models, or data with which to build them for a particular location, successful transfer of a pre-existing model built for a data-rich location could be of considerable utility. This procedure of using an existing model to derive predictions for a new location is defined as model transfer, with model transferability being the model’s ability to transfer to new locations (Sequeira et al., 2018). Indeed, a recent study (Sequeira et al., 2016) demonstrated the transferability of predictive models of fish species richness between distant coral reefs. However, species richness and fish abundance are two distinct ecological metrics, with inherent differences in spatio-temporal variability caused by different processes. While species richness can be informative for conservation management in the design of marine protected areas, abundance models can provide relevant information for the management of fisheries in stock assessments and setting spatially explicit catch thresholds (Bejarano, Mumby & Sotheran, 2011). Here, we explore the transferability of models for the more variable metric fish abundance considering the same two widely separated reefs recently investigated by Sequeira et al. (2016): the Great Barrier Reef (GBR), a relatively well-studied reef system located off the northeast coast of Australia, and Ningaloo Reef (NR), a fundamentally different and less-studied reef, located off the northwest coast of Australia. In this study, we examine the effects of annual variability in fish counts by accounting for the number of years when fish were surveyed. We investigate a number of scenarios with subsets of data collected in different years and also covering a range of 1 or 4 years at a time. The latter multi-year scenarios allow averaging of inherently variable fish abundance estimates. We also investigate potential effects associated with fishing effort by considering ten representative fish families separately including the exploited fish families Lethrinidae and Lutjanidae. The number of species within each fish family also varies (e.g., Pomacentridae comprises several hundred species, while Zanclidae only one species). Therefore, examining these ten fish families separately allows testing for effects associated with different degrees of abundance variability within and among fish families. We then provide an overview of the difficulties of modelling fish abundances and highlight some of the issues that will need to be overcome before such models can be successfully transferred.

Materials & Methods

Results

Models for GBR (N_total and N_fam)

The N_total models for the GBR resulted in R² ranging from 9.0–18.6% across all scenarios, with significant correlations between predictions and observations (p ≤ 0.002) (Table 2). Model rankings were similar across all scenarios (Table 2, A–G) with the highest wAICc obtained for model 7 (nutrients) but sometimes shared with models 3 (depth), 4 (sand) or 5 (gravel). Most important predictors commonly included NO ₃. $R_{\mathrm{m}}^2$ was ∼20% for the best model in all scenarios while $R_c^2$ was close to 100% (>98.5% for all N_total models in all scenarios). Cross-validation errors varied between 12.8–22.5% with predicted ranges generally overestimating minimum observed fish abundances in the GBR but maximum values close to the observed for most scenarios (Table 2). The predicted patterns of N_total for the GBR were also similar for all scenarios with generally greater abundances predicted in two main areas of the southern sections of the GBR (Fig. 1— N_total and Fig. S3).

Table 2:

Modelling results for the Great Barrier Reef (GBR) scenarios predicting total fish abundance (N_total) to the GBR and to Ningaloo Reef (NR).

Observed N: observed fish abundance; Top model: the best performing model/s ranked by the weight of the Akaike Information Criteria corrected for small sample sizes (wAICc); $R_m^{\mathbf{2}}$: marginal R²; $R_c^{\mathbf{2}}$: conditional R² with R²: variance explained; High effect: predictors with the highest effect size; Pred N: range of predicted fish abundance and the respective standard error (Pred se N); CVerror: cross-validation error and its percentage (CVerror(%)); Val_R²: results of the direct validation of the observed abundances versus the predicted values for the same locations and the respective p-value. All scenarios resulted in some wAICc support for the null model. Italics indicate non-significant correlations between the observed values at NR and transferred predictions from the GBR based on a p-value <0.05. A total of 133 sites were considered in the GBR.

Scenario	A	B	C	D	E	F	G
Observed N	59–2,127	108–2,826	54–1,413	110–654	55–827	17–472	29–2,945
Top models	7	7	7	7	7	7	7
	5			3	3	4	4
wAICc	0.342	0.803	0.805	0.493	0.488	0.362	0.355
	0.252			0.260	0.261	0.325	0.331
$R_m^{\mathbf{2}}$	17.3	19.0	18.9	21.5	21.3	21.0	21.2
	12.4			13.4	13.3	23.2	23.4
$R_c^{\mathbf{2}}$	99.0	99.4	98.8	99.3	98.7	98.7	99.4
	99.0			99.4	98.8	98.8	99.4
Highest effect	Depth/NO3	NO3/Si	NO3	NO3	NO3	Crbnt	Crbnt
			Si
Prediction to the GBR
Pred Nt	561–1,415	444–2,904	222–1,447	493–3,113	248–538	173–958	345–1,914
Pred se Nt	0.05–0.2	0.06–0.4	0.06–0.4	0.07–0.34	0.07–0.34	0.07–0.27	0.07–0.27
CVerror	100.4 ± 31.9	99.2 ± 28.7	53.1 ± 14.2	157.4 ± 55.1	80.6 ± 26.2	51.7 ± 11.8	119.5 ± 21.0
CVerror(%)	12.8 ± 3.4	13.0 ± 5.3	14.0 ± 6.0	15.8 ± 2.6	19.5 ± 4.2	16.1 ± 6.2	22.5 ± 8.9
Val_R2	13.0	9.0	9.0	13.6	13.6	18.5	18.6
p-value	<0.001	0.002	0.002	<0.001	<0.001	<0.001	<0.001
Transferred prediction to NR
Pred Nt	0–729	0–589	0–294	0–650	0–327	0–365	0–734
Pred se Nt	0–0.2	0–0.27	0–0.3	0–0.23	0–0.2	0–0.2	0–0.2
Val_R2	<0.1	0.2	0.2	<0.1	<0.1	<0.1	<0.1
p-value	0.937	0.799	0.796	0.892	0.894	0.586	0.578

DOI: 10.7717/peerj.4566/table-2

Table 3:

Results from the Great Barrier Reef (GBR) scenarios predicting fish abundance by fish family to the GBR.

Results are summarised for all scenarios for each family unless otherwise specified by splitting results by rows and using letters A–G to identify scenarios. Observed N: observed fish abundance; Best model: the best performing model/s ranked by the weight of the Akaike Information Criteria corrected for small sample sizes (wAICc); $R_m^2$: marginal R²; $R_c^2$: conditional R² with R²: variance explained; Highest effect: predictors with the highest effect size; Pred N: range of predicted fish abundance; CVerror: cross-validation error; Val_R²: results of the direct validation of the observed abundances versus the predicted values for the same locations and the respective p-value indicated with asterisks: <0.001 (***), <0.01 (**) and <0.05 (*). Scenario F for Lethrinidae resulted in highest wAICc support for the null model and it is not shown. Italicised text: results where direct validation with values observed in the GBR was non-significant. For details on predictors with highest effect refer to Table 1.

Family	Observed N	Best model	wAICc	$R_m^2$	Rc2	Highest effect	Pred N	CVerror	Val_R2
Acanthuridae	0–432	2	0.739–0.861	73.7–80.0	96.4–98.7	Barrier	1–135	4.9 ± 1.9– 25.9 ± 7.5	–50.6***
Chaetodontidae	0–163	ADE: 7	0.521–0.684	31.5–36.5	77.6–90.4	SST2/PO4	12–84	4.5 ± 0.9– 9.8 ± 2.6	25.1–29.5***
		BC: 10	0.772–0.855	20.4–22.3	76.5–87.8	SST2	14–51	3.2 ± 0.6– 5.8 ± 1.6	22.1***
		FG: 8	0.608–0.689	20.1–24.5	71.2–86.5	S	9–35	3.9 ± 1.5– 7.3 ± 1.8	34.7–36.1***
Labridae	0–44	ABCDE: 4	0.799–1.000	15.5–39.0	41.1–69.3	PO4/Gravel	3–21	1.8 ± 0.3– 4.2 ± 1.2	11.5–23.5**
		FG: 8	0.912–0.957	19.5–30.7	42.0–65.2	S	5–22	2.1 ± 0.5– 3.9 ± 0.9	9.4–9.7*
Lethrinidae	0–27	ABC: 10	0.614–0.885	9.1–22.5	21.3–52.1	PO4/SST	2–6	0.8 ± 0.2– 1.3 ± 0.4	9.9–18.7***/**
		DEG: 10	0.305–0.681	9.5–13.0	34.3–61.6	PO4/SST/ Barrier	2–4	0.9 ± 0.3– 2.2 ± 0.9	<6
Lutjanidae	0–101	ABCDFG: 2	0.465–0.869	40.1–47.8	71.4–86.9	Coast	2–29	2.6 ± 0.9– 5.2 ± 2.4	31.1–65.6***
		E: 7	0.556	31.0	64.7	Coast	2–23	2.9 ± 1.0	70.7***
Pomacentridae	18–3,561	ABCDE: 3	0.423–0.712	7.6–15.3	98.8–99.5	Depth/NO3	171–912	42.3 ± 9.6– 148.5 ± 59.8	8.3–17***/**
		FG: 5	0.699–0.702	21.0–21.3	98.8–99.4	Sand	137–725	45.5 ± 8.7– 112.7 ± 42.3	28.7***
Scaridae	0–472	ABCDE: 2	0.709–0.816	50.9–54.3	90.5–96.7	CRBNT/ Barrier	9–118	9.1 ± 5.1– 24.3 ± 10.1	9.5–14.5***/*
		FG: 4	0.734–0.785	33.0–36.7	89.1–95.1	CRBNT	17–93	12.1 ± 3.2– 22.1 ± 3.8	<0.2
Serranidae	0–46	ABCDEF: 10	0.326–0.957	9.1–37.5	30.0–69.9	SST/PO4	2–12	0.9 ± 0.2– 2.3 ± 0.7	13.2–36.2***/*
		G: 10	0.365	11.3	61.9	SST2	3–5	1.7 ± 0.5	<4
Siganidae	0–129	A: 2	0.775	35.9	83.4	Barrier	6–28	3.2 ± 1.2	14.1***
		BCDEG: 10	0.464–0.984	22.1–50.0	69.6–86.7	SST2/Barrier2	1–21	1.9 ± 0.4– 5.0 ± 3.1	<3
		F: 10	1.000	47.5	75.1	SST2	1–10	2.9 ± 1.4	16.1***
Zanclidae	0–13	2	0.494–0.902	27.6–41.3	29.7–61.2	PO4/ Light/Si	1–8	0.7 ± 0.1– 1.3 ± 0.4	33.7–61.5***

DOI: 10.7717/peerj.4566/table-3

Modelling results were generally improved when the data were analysed by fish family. However, for most families, the wAICc rank obtained for all GBR scenarios varied and no evident pattern for best scenarios was obtained across all families (Table 3). Acanthuridae and Zanclidae were the only fish families for which all GBR scenarios led to the same wAICc results with model 2 (distance to domain boundaries) being the highest ranked for both families (Table 3). Across all fish families, $R_m^2$ was highest for all Acanthuridae scenarios (73.7–80.0%) while cross-validation errors were lowest for Zanclidae (<1.3 ± 0.4%) (Table 3). $R_c^2$ was generally high for all fish families and across all scenarios highlighting high variability within each reef section of the GBR, as was already evident in the Ntotal models. Predictions from most GBR scenarios for all families were positively and significantly correlated with values observed on the GBR and resulted in higher R² (e.g., 44.1 ≤R² ≤ 50.6%; p < 0.001 for Acanthuridae, and 31.1 ≤ R² ≤ 70.7%; p < 0.001 for Lutjanidae). Exceptions included some scenarios for Lethrinidae (D, E and G), Scaridae (F and G), Serranidae (G) and Siganidae (B, C, D, E and G). Cross-validation errors were generally low (<10%) but ∼25% for Acanthuridae and Scaridae, and >100% for Pomacentridae (Table 3). Predictions for each GBR scenario are presented in Fig. 1.

Models for NR (N_total and N_fam)

When modelling N_total for NR, model 7 (nutrients) also got the highest wAICc support, explaining 16.4% of the deviance (Table 4), and the predictor with greatest effect was also NO ₃. Predicted N_total was highest around Point Cloates (central area of NR) (Figs. 2A and 2B—All) however, the cross-validation error was high (49.3 ± 21.2%) and model-averaged predictions were unrelated to observed values in NR (R² = 9.3% and p = 0.108) (Table 4). The test with the additional model including a quadratic term for the predictor rugosity ranked the highest (wAICc = 0.882) and explained 20.6% of deviance, followed by model 7 (wAICc = 0.108, DE% = 16.4) (Table S1). Rugosity also had a large effect jointly with NO₃, however, the cross validation error was still ∼50%.

For the N_fam models for NR, highest wAICc support also varied among models and fish families. It was highest for model 7 (nutrients) for Acanthuridae and Chaetodontidae, model 3 (physical predictors) for Lutjanidae, and model 10 (temperature) for Siganidae. However, for other families, wAICc support was below 0.5 for all models. Generally, most of the deviance was explained by the full model (model 1) (e.g., >23% for Acanthuridae and Chaetodontidae) except for Lutjanidae where model 3 explained most of the deviance (26.5%; Table 4). The most common predictors with biggest effect sizes were NO ₃ and O ₂, notably for Acanthuridae, Chaetodontidae, Pomacentridae and Scaridae (Table 4). Predicted ranges of fish abundances to NR were always narrower than the observed range, and resulted in high cross-validation errors (>>50%) but were lowest for Labridae (∼52.2%) (Table 4, Fig. S4) possibly associated with the limited amount of data available for NR to detect large-scale patterns, i.e., those not associated with fine-scale changes in the habitat. Direct validation of predicted abundances against observed values in NR resulted in positive significant correlations only for Chaetodontidae (R² = 37.1%, p < 0.001). For this family, higher predicted abundances were concentrated in the central area of NR (Figs. 2A and 2B). The test with the additional model including a quadratic term for rugosity in NR was ranked highest for five fish families: Chaetodontidae, Labridae, Lethrinidae, Pomacentridae and Scaridae. Rugosity generally had a large effect size in these tests (Table S1), however, similarly to the model of N_total cross-validation errors were of the same order of magnitude as those obtained without rugosity in the model set (Table S1).

Table 4:

Results for the models predicting total fish abundance (N_total) and abundance by fish family (N_fam) for Ningaloo Reef (NR).

Observed N: observed fish abundance; Top model: the best performing model/s ranked by the weight of the Akaike Information Criteria corrected for small sample sizes (wAICc); R²: variance explained; High effect: predictors with the highest effect size; Pred N: range of predicted fish abundance and the respective standard error (Pred se N); CV_error: cross-validation error and its percentage (CV_error(%)); Val_R²: results of the direct validation of the observed abundances versus the predicted values for the same locations and the respective p-value. Models for the fish families Serranidae and Zanclidae resulted in high wAICc support for the null model and therefore results are not shown. Underlined wAICc values indicate highest ranked models in the model set received wAICc >0.5. Italicised text: values for which non-significant correlations (i.e., p-value >0.05) for the direct validation of observed versus predicted abundance were obtained. A total of 81 sites were used in NR.

Family:	Ntotal	Acanthuridae	Chaetodontidae	Labridae	Lethrinidae	Lutjanidae	Pomacentridae	Scaridae	Siganidae
Observed N	129–1,855	0–579	0–146	31–358	0–41	0–35	11–623	0–450	0–215
Top model	7	7	7	5	1	3	7	8	10
			9	2	2		1	7	2
wAICc	0.916	0.957	0.690	0.222	0.339	0.993	0.284	0.429	0.607
			0.200	0.199	0.220		0.222	0.247	0.238
R2	16.4	20.5	20.2	7.3	19.9	26.5	7.0	10.2	16.3
			16.0	14.1	14.0		16.0	9.1	18.7
High effect	NO3	NO3	Chla/NO3	Sand/Mud/Crbnt	Coast	Depth	NO3/Barrier	NO3/ O2	SST2
Prediction to NR
Pred N	282–187	7–89	6–7	104–25	2–8	1–	265–499	40–164	3–37
Pred se N	42.0–17.3	3.9–2.5	1.8–17.1	8.8–109.4	0.7–5.3	0.4–.7	35.6–1.2	10.5–8.4	1.4–27.5
CVerror	304.5 ± 83.4	77.6 ± 31.0	27.4 ± 6.9	54.7 ± 15.9	3.9 ± 1.6	2.4 ± 1.1	221.9 ± 67.7	74.9 ± 21.2	14.3 ± 7.4
CVerror(%)	49.3 ± 21.2	393.3 ± 337.3	487.8 ± 374.2	52.2 ± 19.3	178.8 ± 64.2	132.7 ± 39.4	100.02 ± 110.1	905.3 ± 930.0	613.3 ± 213.1
Direct validation: observedversuspredicted abundance
Val_R2	9.3	3.3	37.1	3.6	12.9	6.6	8.7	5.3	12.9
P-value	0.108	0.358	<0.001	0.331	0.061	0.187	0.129	0.236	0.060

DOI: 10.7717/peerj.4566/table-4

Table 5:

Comparison of reference and transferred modelling results.

Comparison of results between the reference NR model and the transferred models from the Great Barrier Reef (GBR) predicting fish abundance by fish family (N_fam) to Ningaloo Reef (NR). The observed fish counts in NR are included in the first row to assist comparison, and the prediction results obtained by the NR model in the second row (italic values indicate non-significant validation of the reference NR predictions). Results not shown for Serranidae and Zanclidae due to the higher wAICc support obtained for the null model in the NR reference models. Results for GBR scenarios are only shown where we obtained significant direct validation with values observed in the GBR and low wAICc support (≤0.1) for the null model. Bold font indicates best values in each section for each fish family. Underlined values for Chaetodontidae indicate the only fish family for which the NR models resulted in significant correlations between predicted abundance and observed values.

Scenario		Acanthuridae	Chaetodontidae	Labridae	Lethrinidae	Lutjanidae	Pomacentridae	Scaridae	Siganidae
Observed Nfam		0–579	0–146	31–358	0–41	0–41	11–1,623	0–450	0–215
NR Pred Nfam sd		5–171	6–66	104–225	2–8	1–4	265–99	40–164	3–37
		1.2–4.2	1.8–17.1	8.8–109.4	0.7–53.3	1.1–1.7	35.6–91.2	10.5–48.4	1.4–27.5
Range of predictions	A	0–100	0–3,913	0–22	0–266	6–15	0–595	0–100	0–34
	B	0–136	0–1,125	0–22	0–122	4–15	0–629	0–115
	C	0–67	0–423	0–12	0–25	3.0–8.5	0–315	0–57
	D	0–104	0–1,199	0–24		12–58	0–605	0–96
	E	0–51	0–624	0–13		9–34	0–303	0–48
	F	0–67	0–16	0–8	0–5	3–8	0–383		0 –4
	G	0–132	0–28	0–15		3–12	0–767
Abs difference/(percentage)	A	106.2 ± 54.1 (96.5 ± 4.4%)	237.9 ± 505.6 (763.7 ± 1,819.3%)	120.3 ± 29.2 (88.6 ± 6.7%)	18.4 ± 35.7 (590.5 ± 1,307.9%)	8.1 ± 1.8 (464.8 ± 162.5%)	187.7 ±132.1 (46.7±32.4%)	80.4±38.8 (69.3 ± 22.3%)	11.9 ± 8.0 (147.3 ± 140.0%)
	B	105.6 ± 54.1 (95.9 ± 4.7%)	109.2 ± 182.0 (356.9 ± 653.3%)	120.2 ± 29.1 (88.6 ± 7.2%)	10.9 ± 18.3 (336.2 ± 672.2%)	5.8 ± 2.3 (328.2 ± 149.9%)	177.5 ± 128.5 (43.4 ± 30.0%)	86.2 ± 36.8 (75.0 ± 19.5%)
	C	106.8 ± 54.2 (97.4 ± 3.1%)	44.8 ± 62.3 (141.3 ± 232.7%)	127.3 ± 29.1 (93.9 ± 3.8%)	4.1 ± 3.7 (105.4 ± 136.7%)	3.2 ± 1.3 (185.6 ± 89.2%)	210.1 ± 118.0 (49.9 ± 26.5%)	98.4 ± 31.5 (87.0 ± 10.1%)
	D	106.9 ± 54.1 (97.6 ± 3.1%)	103.6 ± 184.4 (333.9 ± 664.6%)	119.7 ± 28.4 (88.2 ± 7.5%)		15.9 ± 4.2 (919.9 ± 397.4%)	200.4 ± 132.3 (49.8 ± 32.4%)	85.2 ± 37.1 (74.1 ± 19.6%)
	E	107.2 ± 54.2 (97.8 ± 2.7%)	60.1 ± 93.8 (189.3 ± 344.6%)	126.8 ± 29.0 (93.6 ± 4.1%)		9.9 ± 2.4 (571.2 ± 239.9%)	211.8 ± 127.3 (50.3 ± 29.3%)	97.7 ± 31.6 (86.4 ± 10.2%)
	F	105.3 ± 54.2 (95.4 ± 5.2%)	25.3 ± 12.8 (68.9 ± 24.0%)	130.2 ± 29.9 (96.0 ± 2.7%)	2.6 ± 1.8 (52.6 ± 26.3%)	2.4 ± 1.1 (139.6 ± 75.8%)	230.0 ± 124.4 (55.2 ± 27.7%)		11.1 ± 7.5 (89.0 ± 18.3%)
	G	103.4±54.2 (93.2 ± 7.6%)	18.6 ± 14.1 (55.3 ± 55.4%)	126.4 ± 30.3 (96.1 ± 4.7%)		3.7 ± 1.8 (208.6 ± 113.6%)	200.4 ± 136.9 (47.1 ± 30.8%)
% grid–cell ≤ 15%	A	0.0	13.0	0.0	5.2	0.0	15.6	0.0	10.4
	B	0.0	7.8	0.0	10.4	0.0	15.6	0.0
	C	0.0	6.5	0.0	9.1	1.3	2.6	0.0
	D	0.0	18.2	0.0		0.0	11.7	0.0
	E	0.0	5.2	0.0		0.0	2.6	0.0
	F	0.0	2.6	0.0	9.1	3.9	7.8		1.3
	G	0.0	13.0	0.0	–	2.6	11.74
% high-versus-low	A	0.0	96.1	0.0	98.7	0.0	11.7	1.3	42.9
	B	5.2	0.0	0.0	1.3	1.3	0.0	89.6
	C	1.3	0.0	0.0	1.3	2.6	0.0	0.0
	D	88.3	0.0	14.3		53.2	28.6	5.2
	E	0.0	0.0	57.1		28.6	41.6	0.0
	F	1.3	0.0	0.0	1.3	0.0	0.0		16.9
	G	3.9	3.9	28.6		14.3	18.2–

DOI: 10.7717/peerj.4566/table-5

Discussion

Readily available models that reliably predict fish abundances would have the potential to assist management and conservation of marine ecosystems (Knowlton et al., 2010; Bejarano, Mumby & Sotheran, 2011; Plaisance et al., 2011). Following recent success in transferring predictive models of fish species richness between coral reefs (Sequeira et al., 2016), we assessed here the transferability of predictive models of reef fish abundances between the same two coral reef systems and using the same set of environmental predictors. Due to the relevance of fish abundance models for stock assessments (Bejarano, Mumby & Sotheran, 2011), we specifically developed models of total abundance and of abundance by fish family to compare transferability results when the response variable does and does not include exploited species. Model transferability from the GBR to NR varied among the response variables tested (i.e., for N_total and N_fam) with no obviously superior model emerging for the GBR scenarios tested.

Predicting fish abundance for each system individually was challenging but generally improved when considering fish families separately. For example, our N_fam models for most GBR scenarios resulted in greater and significant R² for all families, including the exploited Lutjanidae for which predictions resulted in the highest R² (70%). This result highlights that good predictive models of abundance by fish family including exploited species is achievable, and that predictions will be useful to understand patterns in abundance. This improvement when considering fish families separately was also verified for NR, where models of Chaetodontidae abundance were of moderate goodness-of-fit. Chaetodontidae are of little commercial interest, and are usually sedentary (site-attached) occurring as single individuals or in pairs. These factors may reduce survey bias in estimating their abundances, contributing to the better performance of the NR models despite the low number of sampling locations considered. However, with limited availability of fish abundance data at the scale of the entire NR, most models resulted in weak, non-significant correlations with observed abundances in that system (Table 2).

Due to the general lack of significant modelling results at NR, we could only directly assess and compare the transferred and reference models’ results for Chaetodontidae. For this fish family, we found small absolute differences between the transferred and reference predictions and also a high similarity in the predicted patterns of low and high abundance (i.e., %low-versus-high predictions). With Chaetodontidae including highly sedentary and territorial species, our results suggest that local-scale processes of relevance to these species might be well captured by the variables in our models, whereas the possible reasons behind the lack of transferability for other fish families deserves further investigation. While the focus here was to understand what is required to transfer models successfully, application of these findings are also likely to be valuable for families including commercial species. Overall, our results indicate that similarities between predictions from transferred and reference models of fish abundance may be achievable. Transferring a model of abundance could, therefore, be useful where data are insufficient to build a new reference model for that location. However, at this point, we were unable to identify a consistent approach to transferring these models that would give confidence in other similar applications.

Our inability here to construct consistently transferable models of abundance should not be taken as failure, but rather as an opportunity to begin learning about how transferable models can be built, and ultimately, their utility improved. For example, the importance of nitrate (NO₃) as a predictor suggests that productivity might be an important habitat characteristic that contributes to determine abundance in these reef systems (Barneche et al., 2016). Therefore, if available, related predictors could be included to try and improve the models and their transferability. Indeed, the results of our models highlight that a major challenge in understanding and improving model transferability lies first in obtaining consistently robust predictions of fish abundances for the reference and target locations. Therefore, a useful way forward might be to first construct better, and more ecologically meaningful, predictive models of abundance than attempting the construction of more transferable ones.

To assist model improvement, where available, inclusion of variables that better represent the biology of reef systems or their benthic communities and habitats (Pittman, Costa & Battista, 2009; Yates et al., 2016) should be considered. As shown here for the NR models with the inclusion of rugosity (which in coral reefs is a largely biogenic variable), local, fine-scale topographic predictors might considerably improve model fit. If such predictors, more directly associated with patterns of fish abundances, were available for the GBR as well, it is plausible that better model transferability would have been obtained. Our contention here is supported by previous studies showing that models using different abundance-related response variables have different data needs, such as levels of replication (sensu Jones et al., 2015). In turn, these needs will depend, for example, on the variability of fish abundances, as these can be strongly influenced by many factors, such as recruitment, predation or fishing, i.e., demographic stochasticity (Sale & Douglas, 1984), or ecosystem biodiversity and human impacts (Ridgway, Dunn & Wilkin, 2002), with better models expected for fish species with more stable abundances (Jones et al., 2015).

The fish abundance data used here resulted from the application of different survey designs targeting different habitats in each reef system. It included the exposed side of the reef slope with greater coral cover on the GBR (Sweatman et al., 2008), while at NR, most samples were taken on reef flat areas with less three dimensional structure. Because greater structural complexity (i.e., high coral cover) can promote greater abundances of reef fishes (e.g., Gratwicke & Speight, 2005), this difference in the habitats sampled on the GBR and NR may have hindered the transferability of the GBR models to NR. Results for Zanclidae are a good example. Being a monospecific family with low population densities, predictions for this species were consistent across all GBR scenarios considered, while with the NR reference model wAICc support was greatest for the null model. This result is in agreement with this species’ occurrence on reef flats, which includes much lower densities than in other habitats. Therefore, targeting equivalent habitats at the two locations may also assist model transferability, but direct tests will be required to better understand the magnitude of such an effect.

Another possible reason for the lack of model transferability observed here might be the spatial heterogeneity of the habitats in both reef ecosystems, as both geographical and geomorphological drivers affect the distribution of reef fish species (Pinca et al., 2012). Moreover, some species groups vary among habitats within the GBR. For example, the cross-shelf patterns of herbivores can be markedly different between inner-, mid- and outer-shelf reefs (Wismer, Hoey & Bellwood, 2009). When testing model transferability in space, observations for the same set of predictors also need to be available for both study systems. Here we used environmental and spatial predictors available around Australia to maximize the number of predictors that could be included and tested in our model set. Even still, this information was only available at a coarse resolution, and the results we report here may contrast with those that would have been obtained from finer resolution predictors such as roughness (e.g., estimated by acoustic methods) and fishing pressure that can affect fish abundances by removing individuals and destabilizing population dynamics (Hsieh et al., 2006; Anderson et al., 2008; Bejarano, Mumby & Sotheran, 2011; Rana et al., 2014).

To test the transferability of predictive models of fish abundances between two widely separated coral reefs, we constructed models that used a similar same set of predictors and scenarios previously shown to produce transferable models for fish species richness (Sequeira et al., 2016). The poor transferability of our abundance models compared to those developed for species richness highlights potential dissimilarities between the drivers of richness and abundance or in the way different ecological processes are captured by the predictors used and translated into this response variable. In particular, spatial predictors contributed to the transferability of the species richness models applied to the same two distant reefs (Sequeira et al., 2016) but were much less important when predicting fish abundances, with the exception of models for Acanthuridae and Zanclidae on the GBR. Interestingly, Acanthuridae were also previously shown to be an exception in beta-diversity stability relationships across fish families, potentially because of the way they respond to temporal variation in macro-algal availability (Mellin et al., 2014). Such differences in model transferability suggest that species richness patterns are more stable and better explained at large spatial scales (Caley & Schluter, 1997) than fish abundances, and models may therefore be more transferable for species richness. Conversely, fish abundances in marine systems are notable for their variability (Sale & Douglas, 1984; Caley et al., 1996) that might diminish model transferability. Generally, the predictors we used explained more variance in fish species richness than in fish abundance (Mellin et al., 2010; Sutcliffe et al., 2014) but because changes in abundance may be a more immediate indicator of changes in climate or responses to management intervention, it is also important to find ways to overcome challenges associated with building transferable predictive models of abundances.

Potentially, improvements to both fish abundance models and their transferability could be achieved by using different combinations of predictors (e.g., mixing physical and biological variables in the same model), by using biomass estimates, or by grouping species in different ways, such as, trophic role or ecological function. Here we grouped species by family and then tested for predictability and transferability. However, because species within families might differ considerably in behaviour, territoriality, food requirements, and thus, their resilience to change, other classification schemes such as, by functional group or size spectra, might result in better transferability. Furthermore, due to high abundance variability, relating yearly abundances to lagged effects of disturbance and/or fishing instead of averaging across years might also assist in improving transferability.

Conclusions

Having tools available that can rapidly and efficiently increase our understanding of marine ecosystems and their capacity to respond to accelerating impacts of anthropogenic disturbances is crucial. Such capacities are particularly important for the most understudied regions, which also host the greatest amount of biodiversity (Fisher et al., 2011b) and understudied taxa (Fisher et al., 2011a). However, the challenges associated with developing such tools can only be overcome through establishing a set of predictors that are more relevant at a local scale across ecosystems leading to a better understanding of the causes of abundance patterns. Ultimately, as such information increases so should our knowledge of how to build transferable predictive models of abundances of fishes and other taxa.

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