Ecology

Natural soundscapes have always called to me. As an eco- and electro-acoustics researcher, with a background in sound engineering and electronic music composition, I have always tried to strike a balance between art and science in my work.
In 1998, when I first heard about the extinction crisis — more than 35,500 species of flora and fauna are endangered — the idea for the Fragments of Extinction project came to me very quickly. My vision was to build a collection of 24-hour-long ‘acoustic fragments’, recorded at the highest definition possible, capturing the sonic heritage of ancient, biodiverse, untouched tropical rainforests — before climate change damages them irreversibly.
In these forests, some species vocalize from the canopy, some from the ground and others from big tree trunks that act like sound diffusers. To capture a 3D acoustic portrait of the forest, we simultaneously record on 38 audio channels and microphones.
In this photograph, I am standing in the Sonosfera, a geodesic theatre in Pesaro, Italy, in which audiences can experience rainforest soundscapes captured in the Amazon, Africa and Borneo. Forty-five high-definition loudspeakers are positioned in an isolated, acoustically perfect space, realistically reproducing the ecosystems’ natural sounds.
For the first 15 minutes of the performance, the Sonosfera is completely dark. Sound helps listeners to ‘build’ the forest space around them — the position of every insect and amphibian; the birds and mammals moving through the canopy. My team then projects the spectrograms shown here to explain the sounds, and present data showing that these ecosystems are disappearing.
We have captured the deep infrasound calls of elephants and have recorded insects that sound exactly like violins or trumpets. Our ecosystem recordings are very different. But I don’t have a favourite — they’re a collection. More

Genome sequencing and assembly
We performed a de novo genome sequencing and assembly of CBB using a hybrid approach by combining 454-FLX and Illumina reads from female and male individuals. A total of 3.02 Gb of high-quality 454-FLX sequences and 26 Gb of Illumina sequences were obtained in this study (Table S1), which represent approximate 19 × and 160 × genome coverage respectively based on a previously estimated CBB genome size of 163Mb21. The genome hybrid assembly approach we used involved an initial pre-assembly of the 454FLX data with Newbler and the Illumina data with ABySS22, followed by merging of these two pre-assemblies into a single genome consensus with Metassembler23. Our final hybrid H. hampei CENICAFE_Hham1.1 (Hham1.1) genome assembly had a size of 162.57 Mb, comprising 8198 genome scaffolds (Table 1). This assembly represents an improvement in sequence contiguity, containing a 36.3-Kb contig-N50; 340.2-Kb scaffold-N50 and 4.9 Mb for the largest genome scaffold, compared with a previously published CBB genome assembly21, which resulted in contig and scaffold N50 of 10.5-Kb and 44.7-Kb respectively and largest genome scaffold of 440-Kb. The Hham1.1 genome assembly completeness was assessed using Benchmarking Universal Single-Copy Orthologs (BUSCO)24. BUSCO recovered 98.22% of the 1066 Arthropoda core gene set, from which 96.25% were complete genes and 2% were fragmented genes (Fig. S1). BUSCO results indicate that almost the entire genome of H. hampei was sequenced and de novo assembled in this study.
Table 1 Hypothenemus hampei genome assembly (CENICAFE_Hham1.1) statistics.
Full size table

Transcriptome assembly
Illumina RNA-seq data obtained from whole-body female and male adults were de novo assembled using rnaSPades25 and sequence redundancy reduced by CD-HIT26. The resulting transcript assembly was composed of 64,244 contigs (available at NCBI TSA accession: GIPB00000000.1). The average transcript length was 1103-bp, transcript N50 of 2145-bp and largest transcript of 26,019-bp. The transcript assembly completeness with BUSCO recovered 99.6% (98.97% completed and 0.65% fragmented genes) of the 1066 Arthropoda core gene set. (Fig. S1). Using TransDecoder27, we extracted 35,558 protein-encoding transcripts with full Open Reading Frames (ORFs), from which 33,378 (95%) were annotated against InterPro and NCBI NR proteins. As expected, top BLAST hits were against the Coleoptera species, including D. ponderosae (61%) Sitophilus orizae (22%), Anoplophora glabripennis (3%) and Tribolium castaneum (5.7%); whereas the remaining hits were against other insect species (14%).
Gene prediction and functional assignations
We identified 18,765 gene models encoding 20,801 proteins on the Hham1.1 genome assembly using BRAKER2 gene predictor and all available RNA-seq evidence for H. hampei at NCBI. The number of gene models found here for our Hham1.1 assembly is slightly smaller than the previous gene prediction (19,222) performed on the first published H. hampei genome draft21. Completeness of the Hham1.1 gene set using BUSCO recovered 97.2% (94.1% completed and 3.1% fragmented genes) of the Arthropoda core gene set (Fig. S1). BLASTP found 18,364 (88.3%) Hham1.1 predicted proteins similar (e-value  More

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Study site
Small passerines were caught using a 13 m mist net placed between trees and shrubs on the edge of the village of Tarbet, Argyll & Bute (56.21 N 4.71 W), adjacent to a large forestry plantation. Siskins can forage up to at least 5 km from their nest during the breeding season5,18, and the area within 5 km was therefore considered likely to include breeding siskins that would move through the catching site. Plantation forestry species, age, and area were determined from maps from the Forestry Commission compartment data base. There were 1152 ha of plantation forestry within 5 km of the catching site, comprising 79% Sitka spruce, 7% Norway spruce Picea abies, 13% larch and  More

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National yield stability
We used the FAOSTAT database (http://www.fao.org/faostat, visited in September 2019) to obtain data on annual crop production (in tons) and area harvested (in hectares) from 1961 to 2010 for 138 crops in 91 populous nations. Following Renard and Tilman16, we accounted for differences among nations in data quality and excluded five nations, namely North Korea, Guinea, Kenya, Mozambique and Zambia, for which at least 20% of the data on area harvested or production were extrapolated by the FAO (see details in16). We calculated for each nation and each year the total annual caloric yield (millions of kcal ha-1). To do so, we first calculated the kcal production of each crop by multiplying the production of each crop by its commodity-specific kilocalorie conversion factor from the USDA Nutrient Database32. In doing so, we were able to compare the production of different crops. Then, we summed these kcal harvests across all crops and divided this value by the sum of harvested area for all crops. We calculated national yield stability (S) as the ratio of mean total annual caloric yield (µT) over its time-detrended standard deviation (σT) for fifty consecutive years (1961–2010). We accounted for a temporal trend of increasing total annual crop yield by implementing a loess regression between annual crop yield and years. σT corresponds to the standard deviation of the residuals of this regression. Finally, we compared this stability index (largely used in the biodiversity-ecological functioning research, e.g.14,16,17,18) with the resilience index used by Zampieri et al.22. Both indices were strongly correlated (r = 0.992), strengthening our findings.
Individual crop yield stability and yield asynchrony
For each country, we quantified the average stability of yields of individual crops as the mean of the inverse of the coefficient of variation of yield of each crop:

$$ {{left( {mathop sum limits_{i = 1}^{N} frac{{mu_{i} }}{{sigma_{i} }}} right)} mathord{left/ {vphantom {{left( {mathop sum limits_{i = 1}^{N} frac{{mu_{i} }}{{sigma_{i} }}} right)} N}} right. kern-nulldelimiterspace} N} $$
(1)

where (mu_{i}) is the temporal mean of crop’s annual kcal yield and (sigma_{i}) its time-detrended standard deviation. Time-detrended crop yield was computed through a loess regression between individual, annual crop yield and years.
We computed the asynchrony between crop yield fluctuations following the index developed by Loreau and De Mazancourt11:

$$ Phi = 1 – frac{{sigma^{2}_{T} }}{{left( {mathop sum nolimits_{i = 1}^{N} sigma_{i} } right)^{2} }} $$
(2)

where Φ is the asynchrony of crop species based on annual caloric yield (millions of kcal ha−1) with (sigma_{T}^{2}) the temporal variance of the time-detrended national yield and (sigma_{i}) the time-detrended standard deviation of each crop’s annual kcal yield. The value of asynchrony varies between zero (perfect synchrony) and one (perfect asynchronous temporal fluctuations).
To test whether yield fluctuations of the most abundant crops have a greater impact on the stability of national food production, we weighted the annual yield of each crop by the proportion of total harvested area occupied by that crop. Average stability of yields of individual crops and yield asynchrony were computed on both the non-weighted and abundance-weighted yields.
Crop diversity
For each country and year, we used both the total number of crop commodities (i.e. crop richness) and the Shannon information index (H′) to quantify crop diversity. H′ weights each crop in a nation by the proportion of total cropland it occupies (pi):

$$ H^{prime } = – mathop sum limits_{i = 1}^{N} left( {p_{i} lnleft[ {p_{i} } right]} right) $$
(3)

with N being the total number of crops grown in a country each year.
The exponential form of the Shannon diversity index gives the effective crop diversity that is the number of crops representing an equal share of harvested area24. In other words, the exponential of the Shannon diversity index weighs all species by their frequency, without favouring either common or rare species24. We averaged the annual effective diversity of crop across the fifty years studied to test the effect of crop diversity on national yield stability.
Agricultural inputs
We extracted the annual national application of nitrogen and the annual cropland area equipped for irrigation from the FAOSTAT database. Because Ireland, New Zealand and Netherlands use much of their fertilizers on pastures rather than croplands, we excluded these nations from our analysis. Similarly, we excluded Egypt because it has 100% of cropland equipped for irrigation. We calculated the annual rates of nitrogen application and irrigation per hectare by dividing their use by the total annual cropland area.
Climate variability
We used global gridded climatic data from the Climate Research Unit of the University of East Anglia33 to compute the year-to-year variability of growing season precipitation and temperature for each country, both strongly affecting the stability of national food production16. From these data, we derived annual precipitation and temperature for each grid cell in a country by taking the sum of monthly precipitation and the mean of monthly temperature values weighted by the proportion of cropland in each grid cell34. We then computed the year-to-year coefficient of variation of cropland-based temperature and precipitation for each country.
Statistical analysis
We used structural equation models (SEMs) to evaluate how irrigation, intensity of use of nitrogen fertilizers and crop diversity affected national yield stability through changes in the average stability of yields of individual crops and asynchrony of yields. SEMs represent a powerful way to disentangle complex mechanisms controlling crop diversity-stability relationships, as previously done in natural ecosystems (e.g.14,15,35,36). We set up two different structural equation models, one based on non-weighted indices of stability of individual crops and asynchrony, the other based on the same indices weighted by the proportion of total harvested area accounted for by each crop. We firstly considered the effects of agricultural inputs and crop diversity on the stability of national food production via the path of average yield stability. The second path quantified the indirect effects of agricultural inputs and crop diversity on national stability via their impacts on crop yield asynchrony. We also accounted for the direct effects of agricultural inputs and crop diversity on national yield stability. Finally, we controlled for the effects of climate variability on total, national yield stability, individual crop yield stability and yield asynchrony. SEMs were run with the lavaan R library37. We used the standardized estimates to compare the relative importance of the different paths. The model fit was evaluated using the Fisher C’score and its associated p values. Because the structural equation model assumes linear relationships between predictors and the dependent variable, we also plotted the relationships between total national yield stability and both asynchrony and average stability of individual crop yield to control for linearity (Fig. 2). Similarly, we investigated the relationships between crop diversity and asynchrony (Fig. 3), as well as between irrigation rate and the average stability of individual crop yield (Fig. 4). More

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MDA-MB-231 generally out-compete MCF-7 cells under all pH, glucose and glutamine levels, and starting frequencies
Fluorescently labeled MCF-7 (GFP) and MDA-MB-231 (RFP) cells allowed us to non-destructively measure population dynamics within each micro-spheroid. We used this spheroid system to: (1) observe the outcome of competition (mixed culture), (2) compare population growth models (mono-cultures), (3) measure intrinsic growth rates (DI), (4) measure carrying capacities (DD), and (5) determine competition coefficients (FD). In experiments 1 and 2, spheroids started with a plating density of 20,000 and 10,000 cells, respectively, with initial conditions of 0%, 20%, 40%, 60%, 80% and 100% MDA-MB-231 cells relative to MCF-7 cells. In experiment 1, additional treatments included neutral (7.4) versus low (6.5) pH and varying levels of glucose (0, 1, 2, 4.5 g/L) (Fig. 1b). Experiment 2 had treatments of pH (7.4, 6.5), glucose (0, 4.5 g/L), and glutamine positive and starved media (Fig. 1c). The ranges of these values encompass both physiologic and extreme tumor conditions. For example, pH ~ 6.5 and very low levels of glucose have been measured near the necrotic core of the tumor. Conversely, high glucose and physiologic pH are present at the tumor edge and near vasculature, and also reflect standard culture conditions for our cell lines. In experiment 1, microspheres were grown for 670 h with fluorescence measured every 24–72 h. In experiment 2, microspheres were grown for 550 h with fluorescence measured every 6–12 h. Growth medium was replaced every 4 days without disturbing the integrity of the microsphere.
Counter to our hypothesis, MDA-MB-231 outcompete MCF-7 cells in physiologic (2 g/L glucose, 7.4 pH) conditions (Fig. 2). However, in more acidic conditions (2 g/L glucose, 6.4 pH) the MCF-7 cells appear to persist, suggesting coexistence (Fig. 3, Supplementary Fig. 1). Furthermore MCF-7 cells persist in either pH condition with high 4 g/L glucose (Fig. 4). This raises two questions: (1) Is the success of MDA-MB-231 in most conditions a consequence of higher initial growth rates, increased carrying capacity, or consistently favorable competition coefficients? and, (2) what characteristics of MCF-7 cells allow them to competitively persist at high glucose conditions?
Figure 2

Photographs of spheroids illustrative of the progression and outcome of competition in normal pH. This series shows the progression of spheroids grown physiological conditions (2 g/L glucose, 7.4 pH). Note that, in this case, the MDA-MB-231 cells appear to take over the spheroids by day 20.

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Figure 3

Photographs of spheroids illustrative of the progression and outcome of competition in acidic pH. This series shows the progression of spheroids grown in acidic conditions (6.5 pH) with 2 g/L glucose. Note that, in this case, the MCF-7 cells appear to persist to the end of the experiment.

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Figure 4

Three time points spanning from the middle to the end for all culture conditions.

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Analysis of growth rate
The growth rate of MCF-7 and MDA-MB-231 cells was quantified by measuring the instantaneous exponential growth rate (in units of per day) for each monoculture during the first 72 h. In general, MCF-7 cells had equal or higher growth rates under all growth conditions when compared to MDA-MB-231 cells. MCF-7 cell growth rate with lower (10,000 initial cells) plating density was reduced when grown in low pH 6.5 (Fig. 5b,c) environments compared to physiologic pH 7.4 (Fig. 5e,f). The higher (20,000 initial cells) plating density resulted in reduced growth rates in normal pH compared to low 6.5 pH (Fig. 5a,d). Not surprisingly, in the harshest environment of low pH 6.5, no glucose, and no glutamine, MCF-7 cells had the lowest, even negative, growth rate (Fig. 5c). Interestingly, the absence of glutamine (Fig. 5c,f) reduced the difference in growth rates between the two cell types, regardless of pH or glucose concentration, consistent with glutamine’s role as a substrate for respiration, which is more pronounced in MCF-7 cells.
Figure 5

Growth rates (per day) of both MCF-7 and MDA-MB-231 cells as measured by the instantaneous exponential growth rate for each monoculture in the first 72 h under all experimental conditions. ANOVA analysis is provided in Supplementary Tables 1–3.

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While the growth rates of MDA-MB-231 cells during these early time points were generally unaffected by changes in environmental conditions, the initial plating density had a significant effect. The higher (20,000 initial cells) plating density (Fig. 5a,d) resulted in slower, even negative, growth rates when compared to the lower (10,000 initial cells) plating density. This suggests that these plating densities may be approaching MDA-MB-231’s carrying capacities.
Analysis of carrying capacity
Due to small differences in the RFU intensity between the GFP and RFP used for the MCF-7 and MDA-MB-231 cells respectively, a direct comparison of carrying capacity using these RFU measurements cannot be made. In this way we split the results in to two figures (Figs. 6 and 7). We see RFU’s higher than 60 in the MCF-7 data while the maximum RFU for MDA-MB-231 data is never greater than 20 (please note the varying y-axis limits in the corresponding figures). Even with this difference in RFU intensity, it is not unreasonable to assume, due to the large difference, the MCF-7 cells do indeed have a higher carrying capacity across all experimental conditions.
Figure 6

Carrying capacities of MCF-7 cells under all experimental conditions, as measured by the mean fluorescence of the final ten time points. ANOVA analysis is provided in Supplementary Tables 4, 5.

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Figure 7

Carrying capacities of MDA-MB-231 cells under all experimental conditions, as measured by the mean fluorescence of the final ten time points. ANOVA analysis is provided in Supplementary Tables 4, 5.

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For MCF-7 cells, an increase in glucose resulted in an increase in carrying capacity across experimental conditions, as would be expected (Fig. 6a–f). Surprisingly, the MCF-7 cells experience a decrease in carrying capacity under normal pH conditions when compared to acidic pH 6.5 conditions suggesting an advantage in acidic conditions.
For the MDA-MB-231 cells, after a high seeding density of 20,000 cells, an increase in glucose resulted in an increase in carrying capacity, just like the MCF-7 cells (Fig. 7a,d). For the low seeding density of 10,000 cells, the opposite occurred (Fig. 7b,c,e, and f), though not as dramatically. Furthermore, the MDA-MB-231 cells experience an increase in carrying capacity in normal pH when compared to acidic pH 6.5 conditions suggesting an advantage in normal pH conditions.
Analysis of initial seeding frequencies
For the analysis of frequency dependent interactions of the two cells lines we analyzed the instantaneous growth rates (in units of per day) during the first 72 h in the mixed spheroids (Figs. 8 and 9). The figures are split between low glucose conditions of 0 g/L (Fig. 8) and high glucose conditions of 4.5 g/L (Fig. 9). Interestingly, under both glucose environments, MDA-MB-231 cells have their maximum growth rates when there are high initial frequencies of MCF-7 cells in the spheroid. This suggests some benefit to the MDA-MB-231 cells from the presence of MCF-7 cells, or less inhibition of growth rates from MCF-7 cells. Furthermore, we see that the MCF-7 cells generally show a maximum growth rate when the seeding frequencies are 40%/60% or 60%/40% (Figs. 8 and 9b,c,e, and f), again suggesting possible benefits to having both cell types in the spheroid.
Figure 8

Based on the first 72 hours, estimates of growth rates (per day) for mixed population tumor spheroids under glucose starved conditions of 0 g/L. ANOVA analysis is provided in Supplementary Tables 1–3.

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Figure 9

Based on the first 72 hours, estimates of growth rates (per day) for mixed population tumor spheroids under glucose rich conditions of 4.5 g/L. ANOVA analysis is provided in Supplementary Tables 1–3.

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In low glucose and at the high seeding density of 20,000 cells, the MCF-7 cells experience a significant decrease in growth rate, even negative growth rates, as the seeding frequency of MDA-MB-231 cells increase. This points to the MDA-MB-231 cells potentially approaching the carrying capacity provided within these nutrient starved conditions, essentially fully depleting all the resources for other cell types. When the glucose is increased, these MCF-7 growth rates increase, suggesting there are now sufficient nutrients for both cell types (Figs. 8 and 9a,d). Upon seeding it appears that both cell types generally have higher initial growth rates when the starting frequencies of MDA-MB-231 are low.
The logistic model best describes individual cell growth
Frequency-dependent effects (here measured as competition coefficients) can only be quantified by modeling the growth of multiple interacting types or species. In order to obtain an accurate estimate of these, the mode of growth must first be determined. In this way, we use the monoculture spheroids of either MCF-7 or MDA-MB-231 alone as a data set to first understand the growth dynamics without the added complexity of the mixed cultured spheroids. Although several growth models have been proposed for spheroids, tumors, and organoids, no specific consensus has been reached34,35. Because of this, we agnostically compared four population growth models: exponential, logistic, Gompertz, and Monod-like (Table 1).
Table 1 The four models considered for estimating the mode of growth of the cancer cells based on data from monoculture spheroids seeded at a low density of 10,000 cells.
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The exponential growth model is commonly used in bacterial studies and assumes unlimited resources. Logistic population growth is the simplest constrained growth model and assumes that per capita population growth rate declines linearly with population size or density36. Although it gives a similar shape, Gompertz growth is exponentially constrained by increasing population. Several authors and works have suggested that the Gompertz equation provides a better fit to the growth of tumors in vivo37. The Monod-like equation imagines resource matching where per capita growth rates are proportional to the amount of resources supplied per individual. It provides a good fit to the population growth curves of bacteria and other single cell organisms grown in chemostats38. Here, we consider all four models when estimating the DI parameter of intrinsic growth rate (r) and the latter three models for estimating the DD parameter of carrying capacity (K).
Using constrained parameter optimization, all four models were fit to the mono-culture spheroid growth of MCF-7 or MDA-MB-231 cells under the eight environmental conditions (Supplementary Fig. 1). Due to the lower number of time points in the experiments with a high seeding density of 20,000 cells, these experiments were not used. Quality of fit for each model was evaluated using adjusted R2, Root Mean Square Error (RMSE), and Akaike Information Criterion (AIC) (Table 2, Supplementary Table 6).
Table 2 Average adjusted R2, RMSE, and AIC when fitting the four growth models to monoculture spheroids.
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Two-way ANOVAs (one for each cell type with pH and nutrient levels as independent variables) showed that adjusted R2’s were similar for the three density-dependent models and significantly lower for the exponential model (Supplementary Table 6). Conversely, the RMSE indicated the best fit for exponential growth (lowest value), lowest quality fit for the Monod-like equation, and similar, intermediate values for the logistic and Gompertz growth models. AIC analysis suggests logistic fits to be the best fit in the majority of scenarios.
While any of these four models could be used to model this system, this analysis suggests either an exponential or logistic model provides the best fit to the data. The principal difference between these two models is that logistic growth includes density-dependence and the growth curve approaches a carrying capacity, whereas exponential growth ultimately leads to extinction (if negative growth rates) or infinitely large population sizes (if positive growth rates). In this way, we evaluated whether the spheroids showed evidence of approaching or reaching a carrying capacity. To do this, we examined the slope of the final ten time points for both the red and green fluorescent values (RFU’s) for all experimental conditions (Supplementary Table 7). As most mono-culture spheroids showed declining slopes, or slopes near to zero, we favor the logistic model for this study.
Parameter estimation for Lotka–Volterra competition model
With the logistic equation showing the best fit for the mono-culture experimental data, we expanded to the Lotka–Volterra competition equations to model the mixed population tumor spheroids. The Lotka–Volterra equations represent a two species extension of logistic growth with the addition of competition coefficients.

$$begin{aligned} frac{{dN_{1} }}{dt} & = N_{1} r_{1} left( {1 – frac{{N_{1} + alpha N_{2} }}{{K_{1} }}} right) \ frac{{dN_{2} }}{dt} & = N_{2} r_{2} left( {1 – frac{{N_{2} + beta N_{1} }}{{K_{2} }}} right) \ end{aligned}$$

where Ni are population sizes, ri are intrinsic growth rates and Ki are carrying capacities. We let species 1 and 2 be MCF-7 and MDA-MB-231, respectively. The competition coefficients (α and β) scale the effects of inter-cell-type competition where α is the effect of MDA-MB-231 on the growth rate of MCF-7 in units of MCF-7, and vice-versa for β. If α (or β) is close to zero, then there is no inter-cell-type suppression; if α (or β) is close to 1 then intra-cell-type competition and inter-cell-type competition are comparable; if α (or β) is > 1 then inter-cell-type competition is severe, and if α (or β) is  (K_{MDA})/β and (K_{MCF})/α  > (K_{MDA}). Similarly, MDA-MB-231 cells are expected to outcompete MCF-7 cells if (K_{MDA})/β  > (K_{MCF}) and (K_{MDA})  > (K_{MCF})/α. Either MCF-7 or MDA-MB-231 will out-compete the other depending upon initial conditions (alternate stable states) when (K_{MCF})  > (K_{MDA})/β and (K_{MDA})  > (K_{MCF})/α. The stable coexistence of MCF-7 and MDA-MB-231 cells is expected when (K_{MDA})/β  > (K_{MCF}) and (K_{MCF})/α  > (K_{MDA}).
To estimate the values for (K_{MCF}), (K_{MDA} ,{ }) α, and β, we fit the co-culture data with low seeding density to the two-species Lotka–Volterra equation creating different fits for each combination of experimental conditions. It is important to note here that the Lotka–Volterra competition equations are not spatially explicit. From Figs. 2, 3 and 4, it can be seen that the cells are segregated within the tumor spheroid. In our application, the Lotka–Volterra competition equations simply provide a first-order linear approximation of between cell-type competition, not a mechanistic model of the consumer-resource dynamics or the spatial dynamics that likely occur in the spheroids.
Using nonlinear constrained optimization, we varied the values for instantaneous growth rates, carrying capacities, and competition coefficients α and β to minimize the RMSE between the Lotka–Volterra model and the experimental data (Fig. 10). In addition to estimating the competition coefficients, this uses the mixed culture data to re-estimate the growth rates and carrying capacities previously estimated from the monoculture spheroids as growth rate and carrying capacity depend on initial seeding density (Figs. 8 and 9).
Figure 10

(a) Estimates for growth rates, carrying capacities, and competition coefficients using nonlinear constrained optimization fitting to the Lotka–Volterra competition growth curves using the low (10,000 cell) seeding density experiments. The average of the four replicates for each experimental condition are shown along with the optimized fit to the Lotka–Volterra model. (b) Optimized parameters for growth rates (per day), carrying capacities, and competition coefficients are shown for each experimental condition. The predicted outcome of competition is given in the last column.

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As in the monoculture parameter estimation, MCF-7 had higher intrinsic growth rates and carrying capacities than MDA-MB-231 under all culture conditions. For all culture conditions, α  > 1 (as high as 12.6) and β ≈ 0 (the magnitude of six of the eight β’s was less than 0.1). Under two conditions (normal Ph and glutamine), the β’s are less than zero allowing for the possibility that MCF-7 cells are actually facilitating the per capita growth rates of the MDA-MB-231. Thus, across all treatments MDA-MB-231 cells had large competitive effects on MCF-7 growth, while the MCF-7 cells had virtually no inhibitory effects on the growth of MDA-MB-231 cells. It appears that this frequency dependent (FD) effect provides a competitive advantage for the MDA-MB-231 cells that allows them to remain in the tumor spheroids despite MCF-7’s higher intrinsic growth rates (DI) and carrying capacities (DD).
The greatest frequency dependent effect of MDA-MB-231 on MCF-7 (highest α) occurred under conditions of 4.5 g/L glucose, 6.5pH, and no glutamine. The greatest effect of MCF-7 cells on MDA-MB-231 (highest β) occurred in the absence of glucose and glutamine at neutral pH. This fits our original predictions; however, the effect of β is not strong enough to rescue MCF-7 cells from competitive exclusion. In accordance with the hypothesis that glucose permits MDA-MB-231 cells to be highly competitive, α’s (the effect of MDA-MB-231 on MCF-7) were generally lower under glucose-starved conditions. Further, both cell types appear to experience decreased growth efficiency and competition when glucose/glutamine starved, and under acidic conditions. This is consistent with more general ecological studies showing that competition between species is generally less under harsh physical conditions39,40.
Using the optimized parameters values calculated by the constrained optimization analysis of the Lotka–Volterra equations can predict the outcome of competition. This analysis suggests that under physiologic pH, regardless of glucose or glutamine concentration, MDA-MB-231 cells will outcompete the MCF-7 cells. Furthermore, under acidic pH, regardless of glucose or glutamine concentration, MDA-MB-231 cells and MCF-7 cells will actually coexist. This is observed experimentally in Figs. 2 and 3 where acidic pH results in coexistence of the two cell types and normal pH results in no MCF-7 cells remaining at the end of the experiment. While a robust result, this does not accord with our original expectations.
In vivo exploration of cell competition
MDA-MB-231 and MCF-7 cells were grown in the mammary fat pads of 8–10 week old nu/nu female mice. Three tumor models were evaluated: only MCF-7, only MDA-MB-231, and 1:1 mix of both cell types with three replicates for each (total of nine mice). Tumor volumes were measured weekly. At 5 weeks, the tumors were harvested and evaluated for ER expression which marks MCF-7 (ER positive) cells providing estimates of the ratio of MDA-MB-231 to MCF-7 cells.
H&E staining indicates that MCF-7 tumors had the greatest viability and lowest necrosis while MDA-MB-231 tumors displayed decreased viability and increased necrosis (Fig. 11a). The small differences in necrotic and viable tissue between the MDA-MB-231 and mixed tumors are indicative of the expansive effect that MDA-MB-231 phenotype has on tumor progression (Fig. 11c).
Figure 11

Results of in vivo mono- and co-culture tumors. (a) Histology slides of MCF-7, MDA-MB-231, and 1:1 co-cultured tumors. Slides were stained with H&E and ER immune stain. (b) Changes in the standardized tumor volume with time (3 mice per treatment). (c) Tumor viability for all three tumor types. Notice a decrease in viability and increase in necrosis in the MDA-MB-231 and mixed tumors. (d) Measures of CAIX, Glut1, and ER biomarker staining for each tumor type. (e) The presence of small clumps of ER staining in mixed tumors reflect the clumping of MCF-7 cells in the progression of the mixed tumor spheroids (these are enlarged photos of the indicated portions of the co-cultured tumors shown in a), suggesting the coexistence of these two phenotypes in certain tumor microenvironments. All error bars show standard error of the mean.

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Changes in tumor size over 5 weeks indicated that MCF-7 cell tumors grew more slowly than MDA-MB-231 tumors and mixed tumors (Fig. 11b; ANCOVA of natural logarithm of standardized size with day as a covariate, F1,49 = 248.0 p  More