The coefficient of variation of phytoplankton ((CV_P)) varies with the changes in environmental factors, namely, light, temperature and salinity and many more. The focus of our discussion will be on the variation of (CV_P) of phytoplankton.
Case 1: (CV_P < 1)
Measured (CV_P) values are 0.32, 0.37, 0.78 at the depth of 10 m, 50 m, 50 m of Region 3, Region 4 and Region 2 respectively. From Fig. 1c, we observe that for Region 3, concentrated mean of phytoplankton has escalated over a larger domain along the horizontal axis, while spread of phytoplankton is comparatively very low and constant for all times, whereas for Region 2 and Region 4 (Fig. 1,b,e), spread of phytoplankton is comparatively high, but, quantity of concentrated biomass is higher at Region 4 than Region 2, which is also supported by higher phytoplankton productivity at Region 4 than Region 2.
Nature of spread of phytoplankton is obtained from the dynamics of normalized variance x of phytoplankton, which depends on (beta). At a fixed depth, x increases with increasing (beta) (Fig. 5b). For all regions where (CV_P<1), domain of (varepsilon) belongs to (0.035, 0.1), (beta) is very sensitive to half-saturation constant K and total biomass A of the system. If A decreases, then corresponding K will decrease, in this case, range of domain of (beta) reduces. Again, for fixed biomass, if K increases, then range of (beta) decreases.
We already know, (varepsilon) value remains higher for Region 2 and Region 4, whereas for Region 3, it is very low. Hence for fixed A, K, domain of (beta) will be larger for Region 2, Region 4 compared to that of Region 3. So, (beta) value will be very low for Region 3 and therefore overall spread (x) of dominating phytoplankton community remains very low at this zone during observatory period. But, on the other hand highest phytoplankton productivity among all other regions causes phytoplankton biomass to dominate most of the total biomass of the system and hence (p_0) remains close to 1 (Fig. 7a). This nature of spread and mean of phytoplankton has also been observed in field observation (Fig. 1c). From Fig. 1c, we observe that mean of phytoplankton spreads up to 30 units, mostly concentrated between 2 and 20 units. This density of phytoplankton mean is highest among all other regions, whereas spread of phytoplankton is very low. Therefore, since (beta) is the lowest depending on lowest value of (varepsilon) caused by highest productivity at Region 3 in May 2011, (p_0) remains close to 1 (Fig. 7a) and x is very low (Fig. 7b), hence, this fact causes (CV_P) to be the lowest ((CV_p=0.32)) at this zone (Fig. 7c). Similar dynamics is also observed for Region 2 in May 2011 and Region 4 in Sep 2007 with phytoplankton biomass ((p_0)) is substantially less due to low productivity compared to the mouth of Arakawa river in May, 2011 (Region 3).
In case of Region 2 and Region 4, (varepsilon) values are high (slightly higher in Region 4), hence, domain of (beta) will be slightly higher for Region 4 compared to Region 2. Now, if (beta) increases, spread x will also increase. But, from Fig. 1e, we observe that spread of phytoplankton is concentrated between 1 and 1.7 units, which implies (beta) to be low for this region. Now, domain of (beta) decreases depending on two facts, (i) either total biomass A of the system was low (ii) for fixed total biomass (A=2), half-saturation constant K was high at this zone in Sep 2007. If K would be high, then phytoplankton density would also be very high. But from Fig. 1e, we can observe that phytoplankton biomass has only spread up to 3 units along x-axis, it is mostly concentrated between 0.5 and 2 units. So, the second fact is not valid for this zone. Instead, if we consider that total biomass was low at this zone, then phytoplankton biomass will also be low, which explains the nature of mean in Fig. 1e. Therefore, for low total biomass, range of (beta) will be very low, which indicates the spread of phytoplankton is also very low. Now, in Sep, productivity remains very high at this zone, therefore, though total biomass is low but most of the system biomass will be dominated by phytoplankton biomass and hence (p_0) will be close to 1 (Fig. 8a), whereas for very low (beta) value, spread of phytoplankton will be very low compared to this value of (p_0) (Fig. 8b), which generates (CV_P=0.35) (Fig. 1e).
In Region 2, mean and spread of phytoplankton can reach up to 2.5 and 2 units respectively (Fig. 1b) and measured (CV_P=0.78), which is the highest. Though productivity remains high in Region 2 in May 2011 but compared to Region 3, it is very low. As a result, distribution of mean ((p_0)) is low in Region 2, where this distribution is high in Region 3 (Fig. S4a), as a result, (varepsilon) values remain high for Region 2 than Region 3 (for numerical results, chosen (varepsilon =0.037) for Region 3 while (varepsilon =0.075) for Region 2). Therefore domain of (beta) increases for Region 2 than Region 3 (since high (varepsilon) values generate high (beta)). On the other hand, (varepsilon) values remain slightly low for Region 2 than Region 4, due to slightly higher productivity at Region 4 in Sep 2007. Hence, phytoplankton biomass ((p_0)) remains low for Region 2 compared to Region 4 (Fig. S4a), which has also been observed in field observation (Fig. 1b), where concentrated phytoplankton biomass is very low (dense around 0.5 units) for Region 2 than Region 4. So, for higher range of (varepsilon), domain of (beta) should remain higher for Region 4 than Region 2. But, since Region 4 belongs to a zone where total biomass (A) is low, range of (beta) remains more or less the same for both regions, which indicates spread of phytoplankton remains nearly the same for both regions (Fig. S4b). But, (p_0) remains low for Region 2 than Region 4 (Fig. S4a), which causes (CV_P) to be higher for Region 2 than Region 4 (Fig. S4c). Again, though (p_0) remains comparatively low for Region 2 than Region 4, still due to higher productivity, most of the total biomass (A) is dominated by phytoplankton biomass. As a result, (p_0) remains close to 1 (Fig. 7a), whereas due to overall low range (0.035, 0.1) of (varepsilon) caused by high productivity, range of (beta) remains low compared to the range of (beta) corresponding to those zones where (CV_P>1). Therefore, spread x remains comparatively low (Fig. 7b), whereas (p_0) is close to 1 (Fig. 7a), which causes (CV_P) to be less than 1 (Fig. 7c) at this zone.
From above discussion we observe that when (varepsilon) belongs to (0.035, 0.1) and due to this range of (varepsilon), domain of (beta) reduces for a location, then (CV_P) remains less than 1 at that zone. These domains of (varepsilon , beta) are determined from nature of phytoplankton productivity at a location during the period of observation and nature of the spread of dominating class. It has been observed that in case of Region 3, during early summer season (May), the existing phytoplankton communities are Skeletonema Costatum, Navicula species and Pyraminonas Grossii36, for Region 4, the existing phytoplankton communities in Sep are diatom Skeletonema Costatum, Dinoflagellates, Raphidophytes and others35, whereas for Region 2, the existing classes in May are diatom Skeletonema Costatum, Raphidophytes and others35. But, for all three regions during corresponding time periods, most of the phytoplankton biomass is dominated by the diatom class, Skeletonema Costatum35,36. Spread of this phytoplankton class has a peculiar nature, which is influenced by its measure of stickiness (alpha), where (alpha in (0,,0.98))43. Now, during the period of observation, since the dominating class Skeletonema Costatum coexists with some other phytoplankton classes at all three regions, therefore range of its measure of stickiness (alpha) should belong to (0.02, 0.25) for these regions and depending on (alpha), scatteredness of Skeletonema Costatum has varied for these zones, that is, when (alpha) is high, scatteredness of Skeletonema Costatum reduces and when (alpha) is low, this scatteredness increases. In field observation, we have seen that, at Region 3, scatteredness of Skeletonema Costatum is very low in May 2011, whereas for Region 4 and Region 2, it is slightly higher in Sep 2007 and May 2011. For all three zones, (alpha) belongs to ((0.02,,0.25)) but its value has varied differently for each zone. If we consider (alpha) to be high for Region 3 in May 2011, then Skeletonema Costatum will be more sticky for that zone during that time period which will hinder the scatteredness. If we assume (alpha) to be slightly high for Region 2, Region 4 for corresponding time periods, then Skeletonema Costatum will be less sticky than Region 3 and scatteredness will be slightly higher for these zones by that time.
In the model, spread due to scatteredness is controlled by low (beta) value. Therefore, ecologically it might be considered that during early summer at Region 3, (alpha) value was close to 0.25, which has caused Skeletonema Costatum to remain more sticky at that zone, as a result, spread was very low which represents low (beta) value. Similar ecological assumptions can be drawn in case of Region 2, Region 4, but the only difference is probably, for these two zones in summer and early spring season respectively, (alpha) was slightly low than Region 3. As a result, the dominating class Skeletonema Costatum was less sticky than Region 3 and spread due to scatteredness was slightly higher than Region 3 (Fig. S4b). Hence, differences in the nature of total biomass of a system, nature of productivity and finally nature of stickiness of dominating phytoplankton species cause high irregularity in phytoplankton distribution and produce low (CV_P) values for Region 2, Region 3 (Fig. 7c, Fig. S4c) and Region 4 (Fig. 8c, Fig. S4c).
Case 2: (CV_P > 1)
In case of Region 4, at the depth of 50 m, (CV_P) remains 1.61 and 1.36 in Dec 2006 and Feb 2008 respectively. In Dec 2006, Feb 2008, due to very low productivity, range of (varepsilon) remains (0.35, 1.0) at Region 4, which generates larger domain of (beta) (considering total biomass and half saturation constant remain the same at Region 4 during both time periods Dec 2006 and Feb 2008). Since total biomass A is conserved, large value of (beta) indicates larger value of B, which ecologically implies spread of all fluctuating components of nutrient and phytoplankton remains higher. Therefore, in Dec 2006 and Feb 2008, spread of phytoplankton remains higher, whereas due to very low productivity, most of the total biomass A is dominated by nutrient biomass (n_0) and phytoplankton biomass (p_0) remains very low, that is, (p_0<<1) (Fig. S1a), which is also observed in field observation, phytoplankton biomass is concentrated between 0.3 and 1.5 units in Dec 2006 (Fig. 1d) and in Feb 2008, it is concentrated between 0.8 and 2 units (Fig. 1f), whereas for both cases, spread of phytoplankton is concentrated between 0.5 and nearly 3 units (Fig. 1d,f), which is higher than (p_0). Therefore, our numerical result validates the field observation at this zone.
Due to low primary productivity and higher spread of phytoplankton caused by high (beta) value causes (CV_P) to be greater than 1 at this zone in Dec 2006 and Feb 2008. But, due to slightly higher productivity, values of (varepsilon) remain slightly low in Feb than Dec, which causes (beta) to be slightly high in Dec than Feb, as a result, (p_0) is slightly higher in Feb than Dec (Fig. 8a) and observed spread of phytoplankton is slightly high in Dec than Feb (because of higher (beta) value in Dec) (Fig. 8b), which causes (CV_P) to be slightly higher in Dec than Feb, (CV_{P,({text {in}},{text{Dec}})}=1.61>CV_{P,({text {in}},{text{Feb}})}=1.36) (Fig. 8c). As discussed before, (beta) represents the spread of dominating phytoplankton species, which is indirectly related to the nature of stickiness of dominating phytoplankton community. Since (beta) remains high at Region 4, higher spread of dominating class S. Costatum (less sticky) in Dec and Feb is observed from high resolution data, therefore, in Dec and Feb, measure of stickiness of S. Costatum was low at Region 4, which causes higher spread of this class at Region 4, which corresponds to higher (beta) value.
At the experimental depth 200 m of Region 1, phytoplankton biomass remains very low due to very low productivity. Therefore, most of the total biomass of this zone is nutrient biomass ((n_0)) and (p_0<<1), (Fig. 7a), which is also observed in field observation (Fig. 1a). Phytoplankton biomass spreads up to 4.5 units, which happens due to low productivity. Now, because of very low productivity, (varepsilon) belong to the range (0.35, 1) and (varepsilon) values remain close to 1 due to higher depth. High values of (varepsilon) generate larger domain of (beta) for this zone, as a result of which spread should also be higher at Region 1 (Fig. 5b), which is actually observed in field observation (Fig. 1a), where S.D is scattered and it has spread up to 9.7 units along vertical axis. Since spread (x) remains very high and (p_0) remains very low, this fact causes (CV_P) to be greater than 1 at this zone (Fig. 7c).
Since spread of phytoplankton is very high and S.D. of phytoplankton is highly scattered at this zone, this corresponds to the fact that domain of (beta) will be larger for this zone than any other zone. Range of (beta) increases if (i) both A, K decrease or (ii) for fixed (A=2,upmu ,{mathrm{g}},{mathrm{N}},{mathrm{l}}^{-1}), K decreases. Since, most of total biomass at the depth of 200 m of Region 1 is dominated by nutrient, phytoplankton is biomass very low. Therefore, it is ecologically meaningful for only K to be low for fixed (A (=,2,upmu ,{mathrm{g}},{mathrm{N}},{mathrm{l}}^{-1})) at this zone. If we consider half-saturation constant K to be low for this zone, then domain of (beta) increases, which explains higher spread of phytoplankton at this zone.
Ecologically, higher spread of phytoplankton at this zone can be related to less sticky nature of dominating phytoplankton community. Probably during the period of measurement in May 2011, value of measure (alpha) of stickiness of the dominating phytoplankton class was the lowest among all other regions, as a result, dominating class was scattered and has spread most than any other zones. Now, due to seasonal impact (summer season), productivity at this zone was also higher than Region 4 in winter season (Dec 2006, Feb 2008) (Fig. S3a), as a result, (varepsilon) values remain higher for Region 4 in Dec than Region 1 in May, but due to low value of K, (beta) values remain higher for Region 1 in May than any other region, this higher (beta) value indicates higher spread of phytoplankton for Region 1 than Region 4 (Fig. S3b). Now, higher (p_0) has caused (CV_P) of Region 1 to be less than that of Region 4 in Dec, (CV_{P,({text {in}},{text{ Dec}},{text{ at}},{text{ Region}},4)}=1.61>CV_{P,({text {in}},{text{ May}},{text{ at}},{text{ Region}},1)}=1.5) (Fig. S3c), since productivity at Region 4 is the lowest in Dec. But, in case of Region 4 in Feb, productivity is slightly high, so (varepsilon) values are less than that of Region 1 and hence, corresponding domain of (beta) is also small, which indicates less spreading of phytoplankton community at Region 4 in Feb (Fig. S3b). Thus, since (p_0) is comparatively high in Feb than Dec at Region 4 and spread is low, hence, (CV_P,{text {in}},{text{ Feb}},{text{ at}},{text{ Region}},4 =1.36<CV_P,{text {in}},{text{ May}},{text{ at}},{text{ Region}},1=1.5) (Fig. S3c). This variation in (CV_P) at Region 1 and Region 4 during summer and winter season respectively, is caused by change in the nature of phytoplankton productivity due to seasonal impact and differences in the nature of stickiness of dominating phytoplankton communities at two different zones.
Source: Ecology - nature.com
