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The fines content of the pellets, agglutinated with wheat starch and kraft lignin (both at 4%), was 125 higher and 75% lower than in the control, respectively (Table 1). The fines generation of the pellets in all treatments was lower than 1% (0.03 to 0.27%) and, therefore, they met the marketing standard EN 14961-232.
Table 1 Fine content (%), hardness (%), bulk density (g m−3), apparent density (g m−3) by gravimetric method and apparent density (g m−3) by X-ray densitometry of Pinus wood pellets produced with different percentages of the additives (A) corn and wheat and kraft lignin and in the control.
Full size table

The lower values of the fines content of the pellets produced with kraft lignin are possibly due to the densification process of the pellet matrix with higher contents of this additive, generating pellets with better bonding characteristics between the particles and, consequently, less fines. In addition, lignin has a cementing action between the cells9 during the pressing process, and high temperature causes this compound to reach the glass transition stage, ensuring a strong bond between the particles8,33. Pellets with lower fines production during handling and transport should be preferred commercially34. The fines content increases with the moisture level of the material, causing cracks to exhaust gases, mainly water vapor, and, consequently, reducing their mechanical resistance during handling35. On the other hand, the low moisture content makes biomass compaction difficult, due to the water’s characteristic of helping the heat transfer and promoting lignin plasticization as a natural biomass binder36. The moisture content between 8 and 12% in the dry basis is ideal for reducing fines generation to within the European standard EN 14961-232.
The hardness of the pellets was similar with the different percentages of corn starch, but it was higher with wheat starch (Table 1). The hardness increased by 22% when the percentage of kraft lignin reached 5%, in relation to the control. The hardness of the pellets with 3 and 5% of corn starch and 4% of kraft lignin was similar to the control.
The similar hardness of the pellets with the different percentages of wheat starch confirms studies that binders can reduce the mechanical properties of pellets at a higher moisture content, because water takes the place of hydrogen bonds, affecting cohesion between the particles37. Higher hardness affects pellet length, because the higher the hardness, the greater the breaking strength after contact with the pelletizing press knife15. In addition, pellets with lower hardness have points for water ingress, increasing the moisture content and consequently the breaking point and causing higher fine generation38. The higher hardness of pellets produced with 5% kraft lignin is possibly due to the decrease of their hygroscopic equilibrium moisture, due to the hydrophobic character of this compound. The kraft lignin residue is a compound of C–C and C–O–C phenylpropane units with low water relationship39. In addition, the constant pressing temperature of 120 °C plasticizes kraft lignin as an adhesive, increasing particle contact and reducing expansion due to lower hygroscopicity, consequently increasing hardness40. Kraft lignin, as an additive, facilitates the use of this residue and confers better properties to pellets by increasing their mechanical strength13,14,15.
The bulk density of pellets with 1% corn or wheat starches and 3% kraft lignin was higher than other mixtures (Table 1). The bulk density of kraft lignin pellets was higher than those with corn or wheat starch. The bulk density of pellets with 1% corn starch and 5% kraft lignin was lower than those with 3% lignin, which were denser than those with only wood (control).
The higher bulk density values for 3% kraft lignin pellets may be associated with a higher amount of lignin in the mixture (wood + additive), which plasticizes more efficiently, generating a smooth and uniform texture in the pellets and improving their density. The pelletizing matrix temperature influences the durability and bulk density of pellets36, as lignin is a natural wood binder and requires temperatures above the glass transition (75–100 °C) to produce bonding between the particles. Temperatures above 90 °C improve pellet characteristics, and require lower compaction pressure at increasing compaction matrix temperatures4,41. The lower density values of wheat starch pellets may be due to the high moisture content of the steam generated during the high temperatures in the compaction process (120 °C), causing micro-cracks in the pellet structure and reducing its density35. Starch acts as a lubricating agent in the pelletizing process, facilitating the flow of raw material through the pelletizing matrix36. The bulk density of the pellets was greater than the minimum required by the European Marketing Standard EN 14961-232, equal to or greater than 0.60 g cm−3 in all treatments. This highlights the potential use of additives in pelletizing, which should be at most 2% relative to the dry mass of primary raw material.
The apparent density of pellets varied in a fashion similar to that of bulk density (Table 1), with no effect from the type and amount of additive added to the particles mass, comparing the three different additives and considering the same proportion used, except for pellets produced with 3% wheat starch, with lower apparent density. The apparent density of pellets produced with 1 and 2% corn starch and 1, 3, 4 and 5% kraft lignin was higher, and the other treatments were similar to the control (Table 1). Lignin and corn starch promoted better connection between particles, favoring biomass compaction and increasing pellet density.
The variation in the apparent density of the pellets, similar to that of bulk density between 1.15 g m−3 (3% wheat) and 1.23 g m−3 (3% lignin), is possibly due to the wheat starch gelatinization process starting at lower temperatures (± 70 °C) than that of corn starch (± 85 °C)42. This leads to the starch adhering to the pellet feeder system wall, reducing the proportion of additive that reaches the pelletizing matrix and consequently diminishing the unit density of the pellet. The higher apparent density of pellets produced with 1 and 2% corn starch and 1, 3, 4 and 5% kraft lignin is due to the lower rate of return of the pelletizing process and the higher molecular weight of the additives, influencing the pellet density7,36. Bulk density and apparent density determine pellet storage and transport conditions, and are directly related to energy density in those with 1 and 2% corn starch and 1, 3, 4 and 5% lignin, with higher density and a higher amount of energy per volume unit43.
The apparent density of the pellets produced with additives and evaluated by X-ray densitometry ranged from 1.00 to 1.31 g m−3 in their longitudinal axis (Table 1), with the lowest value for pellets produced with 1% wheat starch, and the highest value with 1% corn starch.
The lower apparent density values of wheat starch pellets can be associated with the presence of cracks (empty spaces), directly related to the susceptibility to rupture2. Low density peaks indicate small cracks that are attributed to a moisture content of the mixture or particle sizes inadequate for pelletizing4, affecting the physical properties of biomass densification44. The average apparent density of pellets is within the range established by the German standard DIN 51731, from 1.00 to 1.40 g m−345.
Pellet density varied in longitudinal density profiles, with one uniform and one irregular pattern (Fig. 1). The apparent density variation of pellets produced without additives along the longitudinal axis (coefficient of variation of 5.29%) was higher. On the other hand, the apparent density variation of the profile (coefficient of variation of 4.19%) with additives was lower, showing greater cohesion between the particles and the additives. X-ray densitometry showed pellet density variations for all additives and in the control.
Figure 1

Longitudinal variation of pellet density with different proportions of the additives kraft lignin and corn and wheat starch.

Full size image

Uniform or irregular density patterns according to longitudinal pellet density profiles are due to variations in pellet internal density, which can be attributed to factors such as additive molecular weight, particle size, and temperature and pressure during pelletization46,47,48. Cracks are common in compacted material during pelletizing4,6, and can be attributed to inadequate pellet moisture content or particle sizes. The density of biomass varies with the moisture content44 and with the temperature strengthening the adhesion between the particles. Density profiles can explain the performance of pellets, whose cracks and high density variability affect their durability and final quality, since reductions in density are associated with cracks and, consequently, pellet breakage or rupture points, which can generate fines5. The apparent density of the pellets by gravimetric and X-ray densitometry, similar between treatments with additives, confirm that this technique, commonly used to evaluate the apparent density of materials and easier to apply than other methodologies, can be used to evaluate the quality of the pellets. Variations in the apparent density and longitudinal density profile obtained with the gravimetric and X-ray densitometry demonstrate that factors such as moisture, binder type, pressure and particle size interfere with the pelletizing process, causing variations in the material’s internal structure46,47. In addition, this technique accesses different parts of the pellet and therefore identifies point variations in the product density as reported for the 2% wheat starch pellet.
In conclusion, the additives reduced the fines content and increased the hardness and density of the pellets. Therefore, they have the potential to produce pellets with greater resistance to the transport, storage and handling processes. Apparent density along the longitudinal axis of the pellets without starch was higher. The apparent density of pellets containing starch increased the cohesion between the particles and reduced the density variation as shown by their densitometric profiles. More

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Myopic reallocation improves collective wealth
Beginning from some initial extraction state, agents within a networked population of multiple common-pool resources play an iterated game in which they observe current resource conditions at each round, and incrementally shift their extraction efforts from lower-quality sources toward higher-quality sources in order to maximize their payoffs in the following round (Eq. 3). Agents’ extraction efforts are thus redirected away from over-exploited sources toward less-exploited sources so that the system approaches a steady state in which all sources equally share the burden of over-extraction. In the process, some sources increase in quality, while others are further degraded; nonetheless, the overall result of these reallocations is a net increase in collective wealth.
To show this, we consider an arbitrary initial extraction state, in which the population’s collective extraction effort is (Q=Nlangle overrightarrow{q}rangle). In this state, the initial collective payoff extracted by the population is ({F}_{0}={sum }_{sin mathbf{S}}overrightarrow{q}(s)cdot b(s)) (where we ignore cost terms, since these remain constant under reallocation), and so the population’s collective wealth per unit extraction effort is

$$frac{{F}_{0}}{Q}=frac{sum_{sin mathbf{S}}overrightarrow{q}(s)cdot left[alpha -beta (s)overleftarrow{q}(s)right]}{sum_{sin mathbf{S}}overrightarrow{q}(s)}=alpha -frac{langle beta {overrightarrow{q}}^{2}rangle }{langle overrightarrow{q}rangle }.$$
(4)

Under reallocation dynamics (Eq. 3), this total extraction (Q) is conserved, and the system will approach a steady state in which all sources share a common quality value

$${b}_{f}=alpha -frac{langle overrightarrow{q}rangle }{langle {beta }^{-1}rangle }.$$
(5)

The population’s collective wealth approaches the steady-state value

$${F}_{f}={sum }_{sin mathbf{S}}left[overrightarrow{q}(s)cdot {b}_{f}right]=Q{b}_{f}.$$
(6)

Collective wealth is increased (or at least conserved) if ({F}_{0}le {F}_{f}), or equivalently, if (frac{{F}_{0}}{Q}le {b}_{f}). Using Eqs. 4 and 5, this condition reduces to

$$langle overrightarrow{q}{rangle }^{2}le langle beta {overleftarrow{q}}^{2}rangle langle {beta }^{-1}rangle .$$
(7)

The validity of this inequality is guaranteed by the Cauchy–Schwarz inequality29, (langle XY{rangle }^{2}le langle {X}^{2}rangle langle {Y}^{2}rangle) for random variables (X) and (Y), with the identifications (X=sqrt{beta (s)}overrightarrow{q}(s)) and (Y=sqrt{beta (s{)}^{-1}}). Furthermore, equality occurs if and only if the quantity (beta left(sright)overrightarrow{q}left(sright)) shares the same value for all sources, that is, when initial conditions are already steady states where all sources share a common quality value. Reallocation dynamics thus increase collective wealth for any initial condition where sources vary from one another in quality (see Section S2.1 of the Supplementary Information). This includes Nash equilibrium initial conditions, upon which we will now focus our attention.
CPR degree heterogeneity leads to greater improvements in efficiency under myopic reallocation
In the unique Nash equilibrium state of a given network26, each agent sets its extraction at each source to the point beyond which further extraction would increase its costs more than it would increase its payoffs, given that all other agents are doing the same. In this state, no agent can increase its payoffs by unilaterally adjusting its extraction levels while other agents hold their extraction levels constant. However, when all agents simultaneously adapt their extraction levels according to the reallocation update rule (Eq. 3), under which each increase in extraction at one source is matched by an equal decrease at another source, then higher payoffs can be achieved. To quantify the extent to which reallocation alone can help alleviate the “tragedy of the commons” represented by Nash equilibrium, we now apply reallocation dynamics to Nash equilibrium initial conditions on a variety of network types, and compare the population’s collective wealth values before and after reallocation.
When network-structured populations of rational individuals extract benefits from multiple linearly-degrading CPRs, the burdens of over-exploitation tend to fall upon sources in a degree-dependent manner. Myopic reallocation tends to shift these burdens among sources of different degrees, and to distribute the resulting increases in collective wealth among individuals of different degree classes. In order to understand how these reallocations shift extraction pressure and agent payoffs among nodes of different degrees, we use a heterogeneous mean-field approach to derive estimates for these shifts. Under this perspective, the conditions defining Nash equilibrium ((frac{partial f(a)}{partial q(a,s)}=0)) lead us to estimate the expected values for extraction pressure on degree-(n) sources, (langle overrightarrow{q}{rangle }_{n}), by solving a linear system defined by

$$langle overrightarrow{q}{rangle }_{n}=frac{1}{{beta }_{n}}left[frac{n}{n+1}right]left[alpha -sum_{m=1}^{{m}_{mathrm{max}}}{P}_{mathbf{A}}left(mright)frac{m}{langle mrangle }cdot left(frac{gamma m}{[gamma mlangle {beta }^{-1}{rangle }_{m}+1]}left[alpha langle {beta }^{-1}{rangle }_{m}-sum_{{n}^{^{prime}}=1}^{{n}_{mathrm{max}}}{P}_{mathbf{S}}({n}^{^{prime}})frac{{n}^{^{prime}}}{langle nrangle }cdot langle overrightarrow{q}{rangle }_{{n}^{^{prime}}}right]right)right],$$
(8)

with one such condition for each unique source degree (nin {1,dots , {n}_{mathrm{max}}}) represented in the network, where brackets subscripted by agent degree (m) indicate expected values (langle x{rangle }_{m}={sum }_{n=1}^{{n}_{mathrm{max}}}{P}_{mathbf{S}}left(nright)frac{n}{langle nrangle }cdot {x}_{n}) and we have assumed no degree-degree correlations (see the Supplementary Information Section S3 for details). Solving this system numerically (here we use Python 3.7.3 with SciPy 1.2.130) for each of the 9 network types under consideration by inserting the corresponding ensemble degree distributions ({P}_{mathbf{A}}left(mright)) and ({P}_{mathbf{S}}left(nright)) (Fig. 1), we use the resulting values of (langle overrightarrow{q}{rangle }_{n}) to compute the expected total extraction by a degree-m agent (langle overleftarrow{q}{rangle }_{m}) at equilbrium as

$$langle overleftarrow{q}{rangle }_{m}=left(frac{m}{mgamma langle {beta }^{-1}{rangle }_{m}+1}right)left[alpha langle {beta }^{-1}{rangle }_{m}-left(sum_{n=1}^{{n}_{mathrm{max}}}{P}_{mathbf{S}}left(nright)frac{n}{langle nrangle }cdot langle overrightarrow{q}{rangle }_{n}right)right],$$
(9)

from which (langle q{rangle }_{m,n}), the expected equilibrium extraction by a degree-(m) agent from a degree-(n) source, can be computed using the Nash equilbrium condition:

$$langle q{rangle }_{m,n}=frac{alpha }{{beta }_{n}}-langle overrightarrow{q}{rangle }_{n}-frac{upgamma }{{beta }_{n}}langle overleftarrow{q}{rangle }_{m}.$$
(10)

These values are then used to compute the corresponding estimated collective wealth (i.e. the sum of all agent payoffs, (F=sum_{ain mathbf{A}}f(a))) and wealth equality (as quantified by Gini index (G)) attained at Nash equilibrium, as well as the subsequent shifts that are brought by myopic reallocation dynamics toward steady states. These values are shown in Fig. 2 for a range of values of the cost parameter (gamma), which quantifies the influence of diminishing marginal utility. The expected changes in extraction pressure for sources of different degrees, as well as the changes in agent fitness expected for agents of each degree class, are illustrated for each network type for cost-free extraction ((gamma =0)) in Fig. 3, and similarly for a representative case of costly extraction ((gamma =0.2)) in Fig. 4. The estimates presented here correspond to a uniform capacity scenario where all CPRs degrade in proportion to the total amount of extraction exerted upon their users. However, we find that qualitatively similar results also hold for a degree-proportional capacity scenario in which sources degrade in proportion to the total extraction per user that they receive (see Section S4 in the Supplementary Information).
Figure 2

Estimates of (a) Ratio of total collective wealth of equilibrium (“Eq”) states relative to efficient (“Ef”) states, ({F}_{mathrm{Eq}}/{F}_{mathrm{Ef}}); (b) increase in efficiency from equilibrium to steady states (“SS”), (({F}_{mathrm{SS}}-{F}_{mathrm{Eq}})/{F}_{mathrm{Ef}}); (c) Gini index of equilibrium states ({G}_{mathrm{Eq}}); and (d) decrease in Gini index from equilibrium to steady states, (({G}_{mathrm{Eq}}-{G}_{mathrm{SS}})), all as functions of cost parameter (gamma). Results shown correspond to a uniform capacity scenario with (alpha =beta =1).

Full size image

Figure 3

Estimated shifts in extraction patterns due to reallocation dynamics from Nash equilibrium (“Eq”) to steady states (“SS”) under cost-free extraction: (a) Change in total extraction pressure (Delta langle overrightarrow{q}{rangle }_{n}=langle overrightarrow{q}{rangle }_{n,mathrm{SS}}-langle overrightarrow{q}{rangle }_{n,mathrm{Eq}}), as a function of source degree (n); and (b) change in expected agent fitness, (Delta langle f{rangle }_{m}=langle f{rangle }_{m,mathrm{SS}}-langle f{rangle }_{m,mathrm{Eq}}) as a function of agent degree (m). Results shown correspond to a uniform capacity scenario with (alpha =beta =1) and (gamma =0). Note that results for all network types sharing a common source degree distribution type (“D”, “N”, or “PL”) are overlapping.

Full size image

Figure 4

Estimated shifts in extraction patterns due to reallocation dynamics from Nash equilibrium (“Eq”) to steady states (“SS”) under costly extraction: (a) Change in total extraction pressure (Delta langle overrightarrow{q}{rangle }_{n}=langle overrightarrow{q}{rangle }_{n,mathrm{SS}}-langle overrightarrow{q}{rangle }_{n,mathrm{Eq}}), as a function of source degree (n); and (b) change in expected agent fitness, (Delta langle f{rangle }_{m}=langle f{rangle }_{m,mathrm{SS}}-langle f{rangle }_{m,mathrm{Eq}}) as a function of agent degree (m). Results shown correspond to a uniform capacity scenario with (alpha =beta =1) and (gamma =0.2).

Full size image

In Nash equilibrium states of the uniform capacity scenario, sources with fewer users (i.e. lower degree) experience lower extraction pressure. Since all networks under comparison here share an equal number of edges, networks having greater heterogeneity among source degrees—and thus a greater abundance of low-degree sources—suffer less over-exploitation overall, and so tend to operate more efficiently at equilibrium (Fig. 2). As agents then shift their extraction away from over-burdened, lower-quality sources toward higher-quality sources, these systems approach steady states where their multiple CPR sources all share a uniform quality value. In this way, steady states of reallocation dynamics qualitatively resemble Pareto efficient extraction states, which are characterized by uniform quality among all CPR sources (though, unlike these steady states, optimal efficiency also requires uniform extraction levels among all agents regardless of degree; see Section S3.2 in the Supplementary Information). The resulting shifts in efficiency (Fig. 2b), source extraction pressure (Figs. 3a and 4a), and agent payoffs (Figs. 3b and 4b) are more pronounced for networks having greater heterogeneity among CPR source degrees due to the greater initial discrepancies among source quality values that these networks support at Nash equilibrium. When simulations of reallocation dynamics from equilbrium are performed on individual networks (see Section S6 in the Supplementary Information), then the shifts in extraction pressure and agent payoffs observed are often more exaggerated than those estimated here. Since the heterogeneous mean-field perspective treats all sources of a common degree as a single class, it does not distinguish higher-order differences among nodes that share the same degree. As a result, the model predicts no shifts under reallocation dynamics for networks in which all sources share a common degree, i.e. delta-function (“D”) source degree distributions, for example. However, on actual networks of this type, reallocation dynamics nonetheless do increase collective wealth by equalizing differences in quality among sources.
When extraction is costly ((gamma >0)), agent degree heterogeneity also plays a secondary role to source degree heterogeneity in determining equilibrium efficiency and the effects of reallocation dynamics (Figs. 2 and 4). Diminishing marginal utility motivates agents to moderate their overall extraction levels; all sources affiliated with any given agent will be affected by its tendency to reduce extraction, and the extent of this reduction will depend in turn on each source’s degree, the degrees of its other users, and so on. Higher agent degree heterogeneity is thus predicted to slightly increase equilibrium efficiency due to the presence of higher-degree agents that reduce their extraction per source by larger amounts than do lower-degree agents. While the overall gains in collective wealth expected to be achieved by way of reallocations are thus slightly reduced by the presence of these higher-degree agents, greater agent degree heterogeneity is also associated with faster times of convergence toward steady states, since high-degree agents are able to simultaneously shift efforts directly between a large number of sources, and so to more rapidly equalize source quality values (see Section S5.1 in the Supplementary Information).
Myopic reallocation from Nash equilibrium reduces wealth inequality
Since reallocation dynamics increase collective wealth, many—if not all—agents will attain improved payoffs under reallocation dynamics from suboptimal states like Nash equilibrium. We now turn our attention to how these increases in collective wealth are distributed throughout a population with respect to agent degree. Under the heterogeneous mean-field approach, we estimate that the shift in expected payoffs due to reallocations from Nash equilibrium are given by

$$Delta langle f{rangle }_{m}=mleft[left(frac{1}{langle nrangle }left[langle frac{n{b}_{n}}{{beta }_{n}}rangle {b}_{f}-langle frac{n{b}_{n}^{2}}{{beta }_{n}}rangle right]right)-upgamma langle overleftarrow{q}{rangle }_{m}left(frac{1}{langle nrangle }left[langle frac{n}{{beta }_{n}}rangle -langle frac{n{b}_{n}^{2}}{{beta }_{n}}rangle right]right)right],$$
(11)

where ({b}_{n}=alpha -{beta }_{n}langle overrightarrow{q}{rangle }_{n}) (see Section S3.1.3 in the Supplementary Information). When extraction is cost-free ((gamma =0)), the increased payoffs brought about by reallocation dynamics are expected to affect each edge in a uniform way, on average, and thus tend to be shared among agents of all degree classes in proportion to their degree (m). This is reflected in the linear increase of expected agent payoff with respect to degree (Fig. 3b), and also in the lack of change in the expected Gini index predicted for all network types under cost-free ((gamma =0)) extraction (Fig. 2d). However, when extraction is costly ((gamma >0)) and diminishing marginal utility acts to disincentivize increased extraction for higher-degree agents, the overall efficiency (Fig. 2a) and equality (Fig. 2c) of equilibrium states are increased from those observed under cost-free extraction. In these cases, reallocation dynamics also tend to increase the equality of the population’s wealth distribution, as reflected in the decreasing—and eventually negative—shifts in payoffs expected for agents of increasingly high degree (Fig. 4b), and also in the expected reductions in Gini index (Fig. 2d), caused by reallocation dynamics. This occurs because diminishing marginal utility motivates high-degree agents to exert less overall extraction effort per source at Nash equilibrium than do lower-degree agents. In the steady states subsequently reached under reallocation dynamics, all sources share a uniform quality value; each agent’s total extracted benefits then becomes strictly proportional to the overall magnitude of its extraction effort. Higher-degree agents end up receiving a smaller payoff per source than do their lower-degree counterparts in steady states. As Eq. (11) suggests, agents with higher initial extraction levels (langle overleftarrow{q}{rangle }_{m}) will experience a lower (and possibly even negative) shift in payoff per source (Delta langle f{rangle }_{m}/m) as a result of reallocations. This levelling-out of degree-based payoff inequities has its most pronounced effects at intermediate levels of the cost parameter (here, for values of (gamma approx .35), as shown in Fig. 2d). In simulations performed on specific networks, we find that reallocation dynamics lead not only to increased collective wealth, but also to increased equality, even on networks with homogeneous, “delta-function” (“D”) source degree distributions, although the heterogeneous mean-field approach predicts no such shift. Networks of other types similarly tend to undergo greater increases in equality than those predicted here due to higher-order types of heterogeneity not captured by the model (see Section S6 in the Supplementary Information). More

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Algicide preparation
Four batches of algicide were used for experiments, labeled Batch 3, Batch 4–5–6, Batch 7, and Batch 8, following methods used by Grasso27. For each batch, a single colony of Shewanella sp. IRI-160 was transferred from a modified LM medium plate to liquid LM medium for overnight growth, then inoculated into f/2 with 0.05% casamino acids and incubated for 10 days at room temperature with bubbling. Bacteria and other compounds greater than 60 kDa in size were filtered out using a HemoFlow HF80S 60 kDa dialysis cartridge (Fresenius Medical Care, Waltham, MA), creating a batch of sterile filtered exudate referred to as IRI-160AA. Samples of the algicide were diluted with ultrapure water, then total nitrogen (TN) was measured with a TOC-V total organic carbon analyzer equipped with a Total Nitrogen Measuring Unit (Shimadzu Corp., Kyoto, Japan). The algicide has approximately 5.02 mg/L TN. The 24-h EC50 for K. veneficum differed among batches but was always close to 1% (actual EC50s ranged from 0.93% in Batch 4–5–6 to 1.5% in Batch 3), thus a 1% concentration of the algicide was included in all invertebrate assays27. Animals were also exposed to a media control to ensure mortality was due to the algicide.
Statistical analyses
For all statistics, data were analyzed using Shapiro–Wilk normality tests and Brown-Forsythe equal variance tests. If they failed either, data were transformed and reanalyzed. If transformed data passed both tests, then analysis proceeded. If neither log or square-root transformed data passed both normality and equal variance tests, then a non-parametric test was run if possible. Specific details on statistical analyses are provided in each section below.
Copepod mortality
Mortality experiments followed established methods for determining acute toxicity in aquatic animals30,31,33,49. For A. tonsa adults, we collected animals in Fall of 2018 after sunset near the mouth of the Broadkill River (Delaware, USA) using a plankton net. Cod ends were diluted and maintained in field collected seawater with ambient food at room temperature (~ 20 °C) until use in experiments. Adults were filtered out of the bulk collection with a 500-μm mesh, then sorted for adult females. We transferred one adult female (n = 24 for 40%, 48 for 30%, and 72 for all other concentrations) into each well of a 12-well plate containing 5 mL of test solution; test solutions included a seawater control (0%); algicide mixtures prepared from Batch 3 of the IRI-160AA in 20 psu, 0.2 μm-filtered sea water collected from Indian River Inlet, DE, USA (FSW) (1%, 5%, 10%, 13.5%, 18%, 24%, 30%, and 40% v/v); and a 24% media solution as a media control. The plates were incubated at 25 °C in low-light (~ 2.37 × 1013 photons cm-2 s−1) on a 14:10 h day:night cycle for 48 h. Every 6 h for the first 24 h, and again at 48 h, we counted the number alive and dead.
For A. tonsa nauplii, adult females and males were placed in two 1 L beakers at room temperature with a 150-μm mesh placed several centimeters off the bottom (to prevent egg cannibalism), a slow bubbler (~ 2 small bubbles s−1), and ambient seawater diluted with 20 psu FSW until the water was mostly clear. Adults were allowed to mate in the beaker for approximately 24 h, after which we removed the mesh, thus removing the adults and leaving behind any nauplii and eggs. After another 24 h, the contents of the beakers were poured through a 20-μm mesh, and we extracted the nauplii and placed them into experimental treatments (0% seawater control, algicide at 1%, 5%, 10%, 13.5%, 18%, 24%, and 30% v/v concentrations, plus a 24% media control; n = 48 animals for all concentrations) following the procedure outlined above for the adult female copepods. This experiment was conducted three times; the first two mortality experiments used Batch 3 of the IRI-160AA, and the third mortality experiment used Batch 8.
From the data collected, we generated a Probit model50 and obtained a 24-h LC50. Another approach looks at mortality over several time points in order to generate a time series of survival (e.g., Robineau et al.51, Keller et al.52). This also allows the generation of an LC50 at several time points (e.g., 6, 12, 18, and 24 h), which can better inform how a certain animal may survive over time. We used SigmaPlot to generate graphs of survival over time, and R statistical software53 and the R package ecotoxicology54 for generating and graphing the Probit model and running a χ2 test to evaluate the model.
Crab mortality
We conducted mortality experiments for the blue crab (Callinectes sapidus) in larval (Z1-stage zoeae) and postlarval (megalopae) stages in a similar manner to mortality experiments with Acartia tonsa. We collected ovigerous female blue crabs during the Summer of 2018 by dip net and drop net at sunset from the Delaware Bay (similar to methods used by Kernehan55) in Cape Henlopen State Park and maintained them in a recirculating water tray containing filtered ambient seawater (~ 30 psu) at room temperature. We staged egg masses every few days55, and females predicted to hatch within ~ 3 days were moved to 7-gallon buckets in a 25 °C incubator containing ~ 30 psu sea water and a bubbler. Zoea larvae (Z1-stage) hatched from these females were kept in large finger bowls with 30 psu sea water at room temperature and were fed lab-reared rotifers (Brachionus rotundiformis, Reed Mariculture). These animals became subjects for mortality and sub-lethal experiments within approximately a day of hatching. Four experiments were conducted; three mortality experiments used Batch 4–5–6 of the IRI-160AA, while the fourth experiment (24 individuals for each concentration) used Batch 7.
Megalopae were collected by plankton net set on rising tides at night during the Summer and Fall of 2018. They were maintained in large finger bowls at room temperature and fed with Artemia nauplii and went into experiments within a few days of collection. Only megalopae in intermolt based on morphology56 were used in experiments. Megalopae experiments used Batch 3 of the IRI-160AA.
Both zoeae and megalopae were exposed to 1%, 5%, 10%, 13.5%, 18%, and 24% algicide concentrations, plus a 0% seawater control and a 24% media control (n = 84 animals for the 0% concentration and 60 for all other concentrations for zoeae, and n = 24 animals for megalopae for all concentrations). Animals were incubated at 25 °C under low-light (~ 2.37 × 1013 photons cm-2 s-1) on a 14:10 light:dark cycle for the duration of experiments. We checked on zoeae and megalopae every 6 h for 24 h; megalopae were checked at an additional 48-h time point.
Oyster mortality
Oyster larvae (eyed pediveligers of Crassostrea virginica) were provided by University of Maryland’s Horn Point Laboratory. Animals were maintained on a damp coffee filter in a sealed plastic container on ice during transport, then released into room-temperature fingerbowls containing 20 psu water and fed a locally-isolated alga (Storeatula major) at room temperature. Experiments occurred in similar fashion to those conducted on Acartia tonsa and Callinectes sapidus. Larvae were assayed in 12-well plates (n = 36 animals for all concentrations). Animals were exposed to 1%, 5%, 10%, 13.5%, 18%, and 24% algicide concentrations, plus a 0% seawater control, and 24% media control. Animals were incubated at 25 °C under a 14:10 light:dark cycle for the duration of experiments. Survival was evaluated every 6 h for 24 h and again at 48 h. Larvae were additionally examined at the start of the experiment and at the 24- and 48-h time points for an activity assay. These experiments used Batch 3 of the IRI-160AA.
Wild-type adult C. virginica were collected from the Delaware Bay near the University of Delaware Lewes Campus, while Haskins-disease-resistant strain individuals were collected from aquaculture cages maintained by the Delaware Center for the Inland Bays. On the first day, individuals were cleaned with a wire brush, and divided into two buckets containing approximately 10 L of 20 psu seawater and were fed Isochrysis galbana (~ 100,000 cells L−1). On the second day the water was changed and they were again fed. On the third day, water was changed and animals were not fed. On the fourth day, individuals were removed from the buckets, dried with a paper towel, labeled with permanent marker, and placed in pairs into forty-one 1 L plastic containers containing 1 L of various algicide solutions: 0%, 1%, 5%, 10%, 13.5%, 18%, and 24% (n = 28 for 0%, 22 for 1% and 18%, and 20 for all other concentrations). Individuals were checked every 6 h for 24 h and assessed if they were alive or dead. Closed individuals were assumed to be alive. If open individuals were observed, we gently tapped on the container to see if the individual shut its shell; animals that responded to this stimulus were marked as alive. Only animals that did not respond to repeated stimuli were scored as dead. Proportion surviving was compared across algicide concentration and strain. These experiments all used Batch 8 of the IRI-160AA.
Copepod sub-lethality
Respiration
We conducted respiration experiments on A. tonsa adult females and young nauplii in a 24-well microplate respirometer (Loligo Systems). First, we sorted animals into fingerbowls containing 100 mL of their respective algicide concentrations. After 24 h of algicide exposure, we removed animals via pipette and put one animal into each well of the respirometer plate (200 μL wells for adult females and 80 μL for nauplii) filled with 0.2 μm filtered FSW, then sealed the plate with Parafilm and a weight. Each experiment also had 4 to 6 wells with only FSW to calculate background oxygen consumption. The experiment occurred in darkness within a 25 °C incubator at night and lasted several hours (n = 26–39 animals for adult females, 11–18 for nauplii). Oxygen concentrations in each well were recorded every minute. At the end of the experiment, respiration rates were calculated in R statistical software using the respR package57 over a period of time when the animals were still in independent respiration, and a one-way ANOVA on ranks in SigmaPlot (Systat Software, San Jose, CA) compared treatments. Experiments with adult females used Batch 3 of IRI-160AA, while nauplii experiments used Batch 8.
Activity
Experiments determining effects on swimming activity utilized Locomotor Activity Monitors (LAMs; TriKinetics). Three beams of infrared light cross a 3 mL test tube containing an animal and register when the animal crosses the beams. We sorted batches of adult female A. tonsa into fingerbowls containing different algicide treatments. Animals were incubated at 25 °C in low-light conditions (~ 2.37 × 1013 photons cm−2 s−1) for 24 h on a 11:13-h light:dark cycle. Animals were pipetted into plastic test tubes (one animal per tube) containing ~ 3 mL of FSW, which then went into the LAMs (n = 21–36 animals). The experiment lasted 24 h with beam breaks summed at one-minute intervals, allowing the data to be analyzed wholly for the 24-h period as well as across different light phases to account for light:dark mediated activity rhythms. Experiments started in the afternoon and ran overnight, creating an initial light phase (L1), a dark phase (D), and a second light phase (L2). Comparing treatments across the entire time period was done using a one-way ANOVA on ranks, while analyzing the data based on the different light phases was performed via a one-way repeated-measures ANOVA. Additionally, at the end of the LAM activity experiments we collected the individuals and noted mortality. This data was analyzed via a one-way ANOVA on ranks. Copepod activity experiments used Batch 3 of the IRI-160AA. Nauplii were too small to generate a reliable signal in the LAMs and were not used in these experiments.
Crab sub-lethality
Respiration
Respiration experiments followed methods described for A. tonsa above and involved zoeae and megalopae. A one-way ANOVA on ranks was calculated using the data for each life stage. The first four zoeae experiments used Batch 4–5-6 of IRI-160AA, while the last two experiments used Batch 7. Megalopae experiments all used Batch 3.
Activity
Activity level experiments followed methods described for A. tonsa above and involved zoeae and megalopae. The 24-h data were analyzed using a one-way ANOVA on square root transformed data for zoeae, and a one-way ANOVA on ranks for megalopae. The data broken down by light phase were analyzed via one-way repeated measures ANOVA on log-transformed data for both zoeae and megalopae. These experiments all used Batch 3 of IRI-160AA.
At the end of experiments we collected the individuals and noted mortality. This data was analyzed via a one-way ANOVA for zoeae and a one-way ANOVA on ranks for the megalopae.
Metamorphosis
We sorted megalopae into finger bowls containing 100 mL of filtered estuary water with different concentrations of the IRI-160AA algicide (0%, 1%, and 17% v/v). After 24-h of exposure, we sorted animals into 12-well plates containing FSW (n = 60 individuals for each treatment). Water was changed daily, and animals were fed freshly hatched Artemia daily. Every 12 h, we counted how many megalopae had molted into first crabs until most had metamorphosed (5.5 days) and used a Kaplan–Meier Survival Analysis with a Gehan-Breslow test to determine if there was a difference in time to metamorphosis (TTM) across treatments. These experiments used Batch 3 of the IRI-160AA.
Abdomen Pumping and Grooming
Crabs with egg masses were collected from the Delaware Bay near Lewes, DE and separated into numbered baskets and maintained in a flow-through sea water table. They were fed thawed squid (Loligo opalescens) every day, and eggs were photographed every two to three days under a dissecting scope until they reached ~ 6 days until hatching (i.e., late-stage sensu Tankersley et al.)36. Homogenized egg water (seawater plus homogenized eggs, designated SW + HE, ~ 20 eggs mL−1) was utilized to induce pumping and grooming behavior and made according to Tankersley et al.36.
Ovigerous females were exposed to several sub-lethal concentrations of algicide combined with the homogenized egg solution and monitored for pumping and grooming behavior. Test solutions were diluted to 1.5 L with filtered 30 psu seawater, and 3.75 mL aliquot of a pre-prepared homogenized egg solution was added to achieve a final concentration of ~ 20 eggs/mL. These experiments used Batch 4–5–6, Batch 7, and Batch 3 of the IRI-160AA.
Between three and six crabs were tested at a time, and all crabs were staged the day of the experiment to verify that their eggs were no more than six days from hatching. All experiments were performed under dim red light to reduce disturbance. Each crab was tested in every treatment. A crab was placed into a translucent container (20.1 × 16.5 × 11.4 cm) with a given treatment condition and acclimated for 2.5 min. Then, for the following 2.5 min, the number of times the crab pumped its abdomen was recorded. Immediately following the end of the first crab’s measurement period, another crab was placed into the same treatment to begin its acclimation period. Each crab was returned to a flowing water table between treatments and remained there for at least twenty minutes before beginning the acclimation period of its next treatment. The treatment series began and ended with 30 psu seawater (SW), and proceeded through an increasing gradient of 0, 7, 11, and 17% IRI-160AA in SW + HE.
Each measurement period of the pumping experiments was filmed. The videos were reviewed later, and the time the crabs spent grooming their egg masses was recorded.
A χ2 test was performed for the 24 crabs tested to assess if the proportion of crabs performing the behaviors differed among treatments. A one-way repeated-measures ANOVA (Friedman Repeated Measures Analysis of Variance on Ranks) was used to assess trends in the number of pumps and the time spent grooming. Only crabs that performed the behavior were included in each analysis.
Oyster sub-lethality
Respiration
Respiration on oyster pediveligers following methods described for A. tonsa nauplii above. Two individuals were placed in each 80 µl well, with rates calculated per individual. Data were analyzed via a one-way ANOVA on Ranks. These experiments all used Batch 3 of IRI-160AA.
Activity
Activity experiments on pediveliger larvae were conducted in LAMs and followed similar methods to Acartia tonsa and Callinectes sapidus. The 24-h data was tested via a one-way ANOVA on ranks, while the data broken down by light phase was analyzed via a one-way repeated measures ANOVA. These experiments used Batch 3 of IRI-160AA.
An additional analysis of pediveliger activity occurred during the mortality experiment by ranking how active each animal appeared to be on a scale of 1 (High Activity, HA, animal was actively swimming), 2 (Medium Activity, MA, animal had its velum extended and cilia active, sometimes scooting across the bottom), 3 (Low Activity, LA, animal was enclosed in its shell but viscera moved when the shell was touched), and 4 (Dead/No Activity, D, animal was completely unresponsive even to repeated stimulation). Ranking occurred at the start of the experiment (where all animals scored as HA), at the 24-h mark, and at the 48-h mark. This assessment was analyzed via a χ2 test for both the 24-h and 48-h data sets. At the end of the LAM experiments, animals were analyzed in the same manner.
Activity experiments on the wild-type adult C. virginica occurred during the mortality experiments. At each 6-h time point, animals in the containers (0%, 1%, 5%, 10%, 13.5%, 18%, and 24% v/v IRI-160AA treatments) were scored as either Open (O) or Closed (C), and analyzed via a two-way repeated measures ANOVA on the proportion of animals that opened at each time point in each concentration.
Feeding
Feeding experiments occurred only on adult C. virginica. Animals and containers from the mortality experiments were rinsed to remove algicide residue, then filled with 1 L of 20 psu seawater and Isochrysis galbana at ~ 100,000 cells L−1, and one animal from each container was returned to it. Five milliliters from each container were removed immediately and in vivo chlorophyll a florescence was measured using a fluorometer (Turner Systems). Air stones were added to the containers to keep the algae in suspension, and lids were added to prevent liquid from bubbling out. After 6 h, another fluorescence reading was taken. Animals were given another 6 h to feed, and a final fluorescence reading was taken at the 12-h time point. Clearance rates (CR) were calculated according to Thessen et al.58 from time zero to six hours (initial rate, 0–6), and from six to twelve hours (end rate, 6–12), and compared across time ranges and treatments and strains using a three-way ANOVA. More